True or False???????

Which of the following statements about velocity-time graphs are TRUE? List all that apply. a. The slope on a velocity-time graph is representative of the acceleration of the object. b. The area on a velocity -time graph is representative of the change in position of the object. c. An accelerated object's motion will be represented by a curved line on a velocity-time graph. d. Objects with positive acceleration will be represented by upwardly-curved lines on a velocity-time graph. e. If an object is at rest, then the velocity-time graph will be a line with zero slope. f. A line with zero slope on a velocity-time graph will be representative of an object which is at rest. g. A line with a negative slope on a velocity-time graph is representative of an object with negative velocity. h. If an object changes its direction, then the line on the velocity-time graph will have a changing slope. i. An object which is slowing down is represented by a line on a velocity-time graph which is moving in the downward direction.

ABE (and almost D) a. TRUE - Now this is important! It is the beginning point of much of our discussion of velocity-time graphs. The slope equals the acceleration. b. TRUE - This is equally important. The area is the displacement. c. FALSE - An object which has an acceleration will be represented by an line that has a slope. It may or may not curve, but it must have a slope other than zero. d. FALSE - An object with positive acceleration will have an positive or upward slope on a v-t graph. It does not have to be a curved line. A curved line indicates an object that is accelerating at a changing rate of acceleration. e. TRUE - An object that is at rest has a 0 velocity and maintains that zero velocity. The permanence of its velocity (not the fact that it is zero) gives the object a zero acceleration. and as such, the line on a v-t graph would have a slope of 0 (i.e., be horizontal). f. FALSE - A line with zero slope is representative of an object with an acceleration of 0. It could be at rest or it could be moving at a constant velocity. g. FALSE - A negative slope indicates a negative acceleration. The object could be moving in the positive direction and slowing down (a negative acceleration). h. FALSE - An object which changes its direction will be represented by a line on a v-t graph that crosses over the time-axis from the + velocity region into the - velocity region. i. FALSE - An object which is slowing down has a velocity which is approaching 0 m/s. And as such, on a v-t graph, the line must be approaching the v=0 m/s axis.

Which of the following statements about acceleration are TRUE? List all that apply. a. Acceleration is a vector quantity. b. Accelerating objects MUST be changing their speed. c. Accelerating objects MUST be changing their velocity. d. Acceleration units include the following; m/s2, mi/hr/sec, cm/s2, km/hr/m. e. The direction of the acceleration vector is dependent upon two factors: the direction the object is moving and whether the object is speeding up or slowing down. f. An object which is slowing down has an acceleration. g. An object which is moving at constant speed in a circle has an acceleration. h. Acceleration is the rate at which the velocity changes. i. An object that is accelerating is moving fast. j. An object that is accelerating will eventually (if given enough time) be moving fast. k. An object that is moving rightward has a rightward acceleration. l. An object that is moving rightward and speeding up has a rightward acceleration. m. An object that is moving upwards and slowing down has an upwards acceleration.

ACEFGHL (and maybe J) a. TRUE - Yes it is. Acceleration is direction-conscious. b. FALSE - Accelerating objects could be changing their speed; but it is also possible that an accelerating object is only changing its direction while maintaining a constant speed. The race car drivers at Indy might fit into this category (at least for certain periods of the race). c. TRUE - Accelerating object MUST be changing their velocity -either the magnitude or the direction of the velocity. d. FALSE - The first three sets of units are acceleration units - they include a velocity unit divided by a time unit. The last set of units is a velocity unit divided by a length unit. This is definitely NOT an acceleration. e. TRUE - This is the case and something important to remember. Consider its application in the last three parts of this question. f. TRUE - Accelerating objects are either slowing down, speeding up or changing directions. g. TRUE - To move in a circle is to change one's direction. As such, there is a change in the velocity (not magnitude, but the direction part); this constitutes an acceleration. h. TRUE - This is the very definition of acceleration. Know this one - its the beginning point of all our thoughts about acceleration. i. FALSE - Accelerating objects are not necessarily moving fast; they are merely changing how fast they are moving (or the direction they are moving). j. FALSE - If the accelerating object is slowing down, then it will eventually stop and not reach a fast speed. And if that doesn't convince you, then consider an object that is accelerating by moving in a circle at constant speed forever; it will accelerate the entire time but never being going any faster than at the beginning. k. FALSE - If an object is moving rightward and slowing down, then it would have a leftward acceleration. l. TRUE - If an object is speeding up, then the direction of the acceleration vector is in the direction which the object is moving. m. FALSE - If an object is slowing down, then the acceleration vector is directed opposite the direction of the motion; in this case the acceleration is directed downwards.

3. Which of the following statements about velocity and/or speed are TRUE? List all that apply. Velocity is a vector quantity and speed is a scalar quantity. a. Both speed and velocity refer to how fast an object is moving. b. Person X moves from location A to location B in 5 seconds. Person Y moves between the same two locations in 10 seconds. Person Y is moving with twice the speed as person X. c. The velocity of an object refers to the rate at which the object's position changes. d. For any given motion, it is possible that an object could move very fast yet have an abnormally small velocity. e. The phrase "30 mi/hr, west" likely refers to a scalar quantity. f. The average velocity of an object on a round-trip journey would be 0. g. The direction of the velocity vector is dependent upon two factors: the direction the object is moving and whether the object is speeding up or slowing down. h. The diagram below depicts the path of a person walking to and fro from position A to B to C to D. i. The entire motion takes 8 minutes. The average speed for this motion is approximately 11.3 yds/min. j. For the same diagram below, the average velocity for this motion is 0 yds/min.

ADEGI a. TRUE - Yes! Speed is a scalar and velocity is the vector. Know this one! b. FALSE - Speed refers to how fast an object is moving; but velocity refers to the rate at which one's motion puts an object away from its original position. A person can move very fast (and thus have a large speed); but if every other step leads in opposite directions, then that person would not have a large velocity. c. FALSE - Person Y has one-half the speed of Person X. If person Y requires twice the time to do the same distance, then person Y is moving half as fast. d. TRUE - Yes! That is exactly the definition of velocity - the rate at which velocity changes. e. TRUE - An Indy Race car driver is a good example of this. Such a driver is obviously moving very fast but by the end of the race the average velocity is essentially 0 m/s. f. FALSE - The presence of the direction "west" in this expression rules it out as a speed expression. Speed is a scalar quantity and direction is not a part of it. g. TRUE - For a round trip journey, there is no ultimate change in position. As such, the average velocity is 0 m/t seconds. Regardless of the time, the average velocity will be 0 m/s. h. FALSE - The direction of the velocity vector depends only upon the direction that the object is moving. A westward moving object has a westward velocity. i. TRUE - As discussed in #2g, the distance traveled is 90 meters. When divided by time (8 minutes), the average speed is 11.25 yds/min. j. FALSE - The average velocity would be 0 yds/min only if the person returns to the initial starting position. In this case, the average velocity is 50 yds/8 min, west (6.25 yds/min, west).

7. Which of the following statements about free fall and the acceleration of gravity are TRUE? List all that apply. a. An object that is free-falling is acted upon by the force of gravity alone. b. A falling skydiver which has reached terminal velocity is considered to be in a state of free fall. c. A ball is thrown upwards and is rising towards its peak. As it rises upwards, it is NOT considered to be in a state of free fall. d. An object in free fall experiences an acceleration which is independent of the mass of the object. e. A ball is thrown upwards, rises to its peak and eventually falls back to the original height. As the ball rises, its acceleration is upwards; as it falls, its acceleration is downwards. f. A ball is thrown upwards, rises to its peak and eventually falls back to the original height. The speed at which it is launched equals the speed at which it lands. (Assume negligible air resistance.) g. A very massive object will free fall at the same rate of acceleration as a less massive object. h. The value of g on Earth is approximately 9.8 m/s2. i. The symbol g stands for the force of gravity.

ADFGH a. TRUE - Yes! This is the definition of free fall. b. FALSE - Skydivers which are falling at terminal velocity are acted upon by large amounts of air resistance. They are experiencing more forces than the force of gravity. As such, they are NOT free-falling. c. FALSE - Any object - whether rising, falling or moving horizontally and vertically simultaneously - can be in a state of free fall if the only force acting upon it is the force of gravity. Such objects are known as projectiles and often begin their motion while rising upwards. d. TRUE - The unique feature of free-falling objects is that the mass of the object does not effect the trajectory characteristics. The acceleration, velocity, displacement, etc. is independent of the mass of the object. e. FALSE - The acceleration of all free-falling objects is directed downwards. A rising object slows down due to the downward gravity force. An upward-moving object which is slowing down is said to have a downwards acceleration. f. TRUE - If the object is truly in free-fall, then the speed of the object will be the same at all heights - whether its on the upward portion of its trajectory or the downwards portion of its trajectory. For more information, see the Projectiles page at The Physics Classroom. g. TRUE - The acceleration of free-falling objects (referred to as the acceleration of gravity) is independent of mass. On Earth, the value is 9.8 m/s/s (the direction is down). All objects - very massive and less massive - experience this acceleration value. h. TRUE - Yes! Know this one! i. FALSE - Nope. A careful physics teacher will never call g the force of gravity. g is known as the acceleration of gravity. It might be best to call it the acceleration caused by gravity. When it comes to the force of gravity, we have yet another symbol for that - Fgrav. But that's a topic to be discussed in a later unit.

5. Which of the following statements are true about conservative and non-conservative forces? Include all that apply. a. A force is regarded as a conservative force if it does work but does not remove mechanical energy from a system of objects. b. A force is regarded as a non-conservative force if it does not add mechanical energy to a system of objects. c. The force of gravity and elastic (spring) force are both examples of a conservative forces. d. Applied forces, air resistance, friction forces, and tension are common examples of non-conservative forces. e. Physicists envy biologists' ability to instill order on the world of animal species through their taxonomic system. So physicists have made a habit of identifying forces as conservative and non-conservative forces in order to instill order on the world of forces. f. If a non-conservative force acts upon an object, then the object will either gain or lose mechanical energy. g. If the only forces which do work upon an object are conservative forces, then the object will conserve its mechanical energy. h. If the sum of an object's KE and PE is remaining constant, then non-conservative forces are NOT doing work. i. If work is NOT done on an object by a non-conservative force, then the object will experience a transformation of energy from kinetic to potential energy (or vice versa). j. An object starts from an elevated position with 50 J of potential energy and begins its fall towards the ground. If non-conservative forces can be assumed to NOT do work, then at some point during the fall the object will have 20 J of potential energy and 30 J of kinetic energy.

Answer: A(sort of) CDGH I(sort of) J a. TRUE (sort of) - If a force does work, yet does not remove mechanical energy from an object, then it is definitely a conservative force. The sort of indicates that a force is also considered a conservative force if it does work and does not add mechanical energy to an object. b. FALSE - If a force does not add mechanical energy to a system of objects, then it is likely a conservative force (provided it doesn't remove mechanical energy either). Non-conservative forces are those which either add or remove energy from a system of objects. c. TRUE - You must know this! d. TRUE - These are all non-conservative forces. You can add normal force to the list as well. e. FALSE - Whether there is envy in a physicist's heart is not for us to tell; the evil found within one's heart is often vast and mysterious ... . We can however definitively say that a physicist classifies forces in order to analyze physical situations in accord with the classification. If only conservative-classified forces do work, then KEi + PEi = KEf + PEf. On the other hand if one or more non-conservative-classified forces are doing work, then KEi + PEi + Wnc = KEf + PEf. f. FALSE - Not only must the force act upon the object, it must also be doing work upon the object. As you sit in your chair, there is a non-conservative force (normal force) acting upon your body. But since it does not do work (it's being assumed that you are not sitting in one of those fancy lounge chairs that has more controls than a TV set), your mechanical energy is not changing. g. TRUE - This is a big principle. You must know this one! h. TRUE - Non conservative forces would alter the total mechanical energy; that is, the PE + KE would not be a constant value. i. TRUE (sort of) - This statement is true (sort of); when only conservative forces are doing work, an object has its kinetic energy transformed into potential energy (or vice versa) without the total amount of the two being altered. It would however be possible that work is not done by a non-conservative force and there be no transformation of energy at all; i.e., the object remains at rest. A conservative force must be doing work in order for there to be a transformation of energy. j. TRUE - One would notice that the PE would begin to drop from 50 J to 0 J and that the KE would increase from 0 J to 50 J. And of course there would be a point at which the PE/KE would be distributed with 20 J to PE and 30 J to KE.

3. Which of the following statements are true of the quantity weight? List all that apply. a. The weight of an object is dependent upon the value of the acceleration of gravity. b. Weight refers to a force experienced by an object. c. The weight of an object would be less on the Moon than on the Earth. d. A person could reduce their weight significantly by taking an airplane ride to the top of Mount Everest. e. Two objects of the same mass can weigh differently. f .To gain weight, one must put on more mass. g. The weight of an object can be measured in kilograms. h. The weight of an object is equal to the force of gravity acting upon the object. i. When a chemistry student places a beaker on a balance and determines it to be 84.3 grams, they have weighed the beaker.

Answer: ABCH and possibly EF a. True - The weight of an object is equal to the force of gravity acting upon the object. It is computed by multiplying the object's mass by the acceleration of gravity (g) at the given location of the object. If the location of the object is changed, say from the Earth to the moon, then the acceleration of gravity is changed and so is the weight. It is in this sense that the weight of an object is dependent upon the acceleration of gravity. b. True - This statement is true in the sense that the weight of an object refers to a force - it is the force of gravity. c. True - The weight of an object depends upon the mass of the object and the acceleration of gravity value for the location where it is at. The acceleration of gravity on the moon is 1/6-th the value of g on Earth. As such, the weight of an object on the moon would be 6 times less than that on Earth. d. False - A trip from sea level to the top of Mount Everest would result in only small alterations in the value of g and as such only small alterations in a person's weight. Such a trip might cause a person to lose a pound or two. e. Mostly True - Two objects of the same mass can weigh differently if they are located in different locations. For instance, person A and person B can both have a mass of 60 kg. But if person A is on the Earth, he will weigh ~600 N, whereas person B would weight ~100 N on the moon. f. Kinda True (Mostly False) - Weight is the product of mass and the acceleration of gravity (g). To gain weight, one must either increase their mass or increase the acceleration of gravity for the environment where they are located. So the statement is true if one disregards the word MUST which is found in the statement. g. False - By definition, a free-falling object is an object upon which the only force is gravity. Such an object is accelerating at a rate of 9.8 m/s/s (on Earth) and as such cannot be experiencing a balance of forces. h. True - This statement is the precise definition of weight. Weight is the force of gravity. i. False - This student has determined the mass of the beaker, not the weight. As such, he/she has massed the beaker, not weighed it.

6. Which of the following statements are true of projectiles? List all that apply. a. A projectile is a free-falling object. b. A projectile experiences negligible or no air resistance. c. A projectile must be moving in the downward direction. d. A projectile must be accelerating in the downward direction. e. A projectile does not have to have horizontal motion. f. A projectile could begin its projectile motion with a downward velocity. g. A projectile does not need to be "falling."

Answer: ABDEF and possibly G a. TRUE - Free-falling objects, like projectiles, are objects upon which the only significant force is gravity. b. TRUE - The only force on a projectile is gravity; air resistance must not be present or must not have an influence upon the motion of the projectile. c. FALSE - Projectiles can be moving either upward or downward or at an angle to the vertical. They must however be accelerating downward, consistent with gravity's effect on an object. d. TRUE - The force of gravity acts directly downwards upon an object, causing a downward acceleration. Any projectile must be accelerating downwards regardless of other features of its motion. e. TRUE - A projectile could be moving strictly in a vertical direction with no horizontal motion. A ball thrown straight up in the air would be such a case. f. TRUE - There is no rule about which direction a projectile must be moving at the instant it is projected. It could begin its motion with a initial downward velocity. g. TRUE - The word "falling" can mean different things to different people. If "falling" involves moving in the downward direction at all instants in time, then a projectile does not need to be "falling." To many, "falling" means being pulled downward by gravity's force. In this case, a projectile must be "falling."

2. Which of the following statements are true about power? Include all that apply. a. Power is a time-based quantity. b. Power refers to how fast work is done upon an object. c. Powerful people or powerful machines are simply people or machines which always do a lot of work. d. A force is exerted on an object to move it at a constant speed. The power delivered by this force is the magnitude of the force multiplied by the speed of the object. e. The standard metric unit of power is the Watt. f. If person A and person B do the same job but person B does it faster, then person A does more work but person B has more power. g. The Newton•meter is a unit of power. h. A 60-kg boy runs up a 2.0 meter staircase in 1.5 seconds. His power is approximately 80 Watt. i. A 300-Newton force is applied to a skier to drag her up a ski hill at a constant speed of 1.5 m/s. The power delivered by the toe rope is 450 Watts.

Answer: ABDEI a. TRUE - Power is a rate quantity and thus time-based. b. TRUE - This is the definition of power. c. FALSE - This is not always the case. A machine can do a lot of work but if it fails to do it rapidly, then it is not necessarily powerful. In fact two machines can do the same task (and therefore the same work), yet they can have drastically different power ratings. d. TRUE - An equation for computing work in constant speed situations is P=F•v. e. TRUE - Watt is the unit of power? Yes!! f. FALSE - Vice versa. If two people do the same job, then they're doing the same amount of work. The person who does it fastest generates more power. g. FALSE - A N•m is a Joule and that is a unit of work (not power). Think force (N) times distance (m); that's work (J). h. FALSE - The work would be (m•g)•d or approximately 1200 J. The power is work divided by time - 1200 J/1.5 s = 800 W. i. TRUE - Since force and speed are given, use Power = F•v. The calculation yields 450 W.

4. Which of the following statements are true about collisions? a. Two colliding objects will exert equal forces upon each other even if their mass is significantly different. b. During a collision, an object always encounters an impulse and a change in momentum. c. During a collision, the impulse which an object experiences is equal to its velocity change. d. The velocity change of two respective objects involved in a collision will always be equal. e. While individual objects may change their velocity during a collision, the overall or total velocity of the colliding objects is conserved. f. In a collision, the two colliding objects could have different acceleration values. g. In a collision between two objects of identical mass, the acceleration values could be different. h. Total momentum is always conserved between any two objects involved in a collision. i. When a moving object collides with a stationary object of identical mass, the stationary object encounters the greater collision force. j. When a moving object collides with a stationary object of identical mass, the stationary object encounters the greater momentum change. k. A moving object collides with a stationary object; the stationary object has significantly less mass. The stationary object encounters the greater collision force. l. A moving object collides with a stationary object; the stationary object has significantly less mass. The stationary object encounters the greater momentum change.

Answer: ABF a. TRUE - In any collision between two objects, the colliding objects exert equal and opposite force upon each other. This is simply Newton's law of action-reaction. b. TRUE - In a collision, there is a collision force which endures for some amount of time to cause an impulse. This impulse acts upon the object to change its momentum. c. FALSE - The impulse encountered by an object is equal to mass multiplied by velocity change - that is, momentum change. d. FALSE - Two colliding objects will only experience the same velocity change if they have the same mass and the collision occurs in an isolated system. However, their momentum changes will be equal if the system is isolated from external forces. e. FALSE - This statement is mistaking the term velocity for momentum. It is momentum which is conserved by an isolated system of two or more objects. f. TRUE - Two colliding objects will exert equal forces upon each other. If the objects have different masses, then these equal forces will produce different accelerations. g. FALSE - It the colliding objects have different masses, the equal force which they exert upon each other will lead to different acceleration values for the two objects. h. FALSE - Total momentum is conserved only if the collision can be considered isolated from the influence of net external forces. i. FALSE - In any collision, the colliding objects exert equal and opposite forces upon each other as the result of the collision interaction. There are no exceptions to this rule. j. FALSE - In any collision, the colliding objects will experience equal (and opposite) momentum changes, provided that the collision occurs in an isolated system. k. FALSE - In any collision, the colliding objects exert equal and opposite forces upon each other as the result of the collision interaction. There are no exceptions to this rule. l. FALSE - In any collision, the colliding objects will experience equal (and opposite) momentum changes, provided that the collision occurs in an isolated system.

7. Consider Newton's second law of motion to determine which of the following statements are true? List all that apply. a. If an object is accelerating to the right, the net force on the object must be directed towards the right. b. If an object is moving to the right and slowing down, then the net force on the object is directed towards the left. c. Accelerating objects are either slowing down or speeding up. d. The acceleration of an object is directly dependent upon its mass and inversely dependent upon its net force. e. An object has an acceleration of 8 m/s/s. If the net force acting upon the object is increased by a factor of 2, then the new acceleration would be 10 m/s/s. f. An object has an acceleration of 8 m/s/s. If the net force acting upon the object is increased by a factor of 3, then the new acceleration would be 11 m/s/s. g. An object has an acceleration of 8 m/s/s. If the mass of the object is increased by a factor of 2, then the new acceleration would be 16 m/s/s. h. An object has an acceleration of 8 m/s/s. If the mass of the object is increased by a factor of 4, then the new acceleration would be 2 m/s/s. i. An object has an acceleration of 8 m/s/s. If the net force acting upon the object is increased by a factor of 2 and the mass of the object is decreased by a factor of 2, then the two factors would offset each other and the acceleration would still be 8 m/s/s. j. An object has an acceleration of 8 m/s/s. If the net force acting upon the object is increased by a factor of 2 and the mass of the object is increased by a factor of 4, then the new acceleration would be 4 m/s/s. k. An object has an acceleration of 8 m/s/s. If the net force acting upon the object is decreased by a factor of 2 and the mass of the object is increased by a factor of 4, then the new acceleration would be 1 m/s/s. l. An object has an acceleration of 8 m/s/s. If the net force acting upon the object is increased by a factor of 4 and the mass of the object is increased by a factor of 2, then the new acceleration would be 16 m/s/s. m. A 2-kg object accelerates from rest to a final velocity of 6 m/s in 3 seconds. The magnitude of the net force acting upon the object is 12 N. n. A 10-kg object slows down from 24 m/s to a final velocity of 9 m/s in 3 seconds. The magnitude of the net force acting upon the object is 80 N.

Answer: ABHJKL a. True - The acceleration is directly related to the net force and the direction of the acceleration is always the same as the direction of the net force. When it comes to force, objects can be thought of as being in the middle of a tug-of-war between the individual forces. The force that wins the tug-of-war is the force which determines the direction of the acceleration. So if a rightward force wins over a leftward force, the acceleration will be to the right. b. True - An object which is slowing down has an acceleration which is directed opposite the motion of the object. So an object which moves to the right and slows down experiences a leftward acceleration and therefore a leftward net force. c. False - Acceleration involves a change in velocity and velocity is a vector with a magnitude (15 m/s, 22 m/s, etc.) and a direction (east, northeast, etc.). Accelerating objects are either changing the magnitude of the velocity by speeding up or slowing down or changing the direction of the velocity by turning. d. False - Vice Versa. The acceleration of an object is inversely dependent upon the mass and directly dependent upon the net force. e. False - Acceleration is directly dependent upon the net force. Whatever alteration is made in the net force, the same alteration must be made in the acceleration. So if the net force is increased by a factor of 2, then the acceleration is increased by a factor of 2 from 8 m/s/s to 16 m/s/s. f. False - Whatever alteration is made in the net force, the same alteration must be made in the acceleration. So if the net force is increased by a factor of 3, then the acceleration is increased by a factor of 3 from 8 m/s/s to 24 m/s/s. g. False - Acceleration is inversely dependent upon the mass. Whatever alteration is made in the mass, the inverse must be made of the acceleration. So if the mass is increased by a factor of 2, then the acceleration is decreased by a factor of 2 from 8 m/s/s to 4 m/s/s. h. True - Acceleration is inversely dependent upon the mass. Whatever alteration is made in the mass, the inverse must be made of the acceleration. So if the mass is increased by a factor of 4, then the acceleration is decreased by a factor of 4 from 8 m/s/s to 2 m/s/s. i. False - Acceleration is inversely dependent upon the mass and directly dependent upon the net force. If the net force is increased by a factor of 2, then the acceleration is increased by a factor of 2. If the mass is decreased by a factor of 2, then the acceleration is increased by a factor of 2. The overall result of the two changes is to increase acceleration by a factor of 4 from 8 m/s/s to 32 m/s/s. j. True - Acceleration is inversely dependent upon the mass and directly dependent upon the net force. If the net force is increased by a factor of 2, then the acceleration is increased by a factor of 2. If the mass is decreased by a factor of 4, then the acceleration is decreased by a factor of 4. The overall result of the two changes is to decrease acceleration by a factor of 2 from 8 m/s/s to 4 m/s/s. k. True - Acceleration is inversely dependent upon the mass and directly dependent upon the net force. If the net force is decreased by a factor of 2, then the acceleration is decreased by a factor of 2. If the mass is decreased by a factor of 4, then the acceleration is decreased by a factor of 4. The overall result of the two changes is to decrease acceleration by a factor of 8 from 8 m/s/s to 1 m/s/s. l. True - Acceleration is inversely dependent upon the mass and directly dependent upon the net force. If the net force is increased by a factor of 4, then the acceleration is increased by a factor of 4. If the mass is increased by a factor of 2, then the acceleration is decreased by a factor of 2. The overall result of the two changes is to increase acceleration by a factor of 2 from 8 m/s/s to 16 m/s/s. m. False - The net force is the product m•a. Acceleration (a) can be calculated as the velocity change per time. The velocity change is +6 m/s (from 0 m/s to 6 m/s), so the acceleration is (+6 m/s) / (3 s) = +2 m/s/s. Therefore the net force is (2 kg)•(+2 m/s/s) = +4 N. The + indicates information about the direction; the 4 N is the magnitude. n. False - The net force is the product m•a. Acceleration (a) can be calculated as the velocity change per time. The velocity change is -15 m/s (from 24 m/s to 9 m/s), so the acceleration is (-15 m/s) / (3 s) = -5 m/s/s. Therefore the net force is (10 kg)•(-5 m/s/s) = -50 N. The - indicates information about the direction; the 50 N is the magnitude.

1. Which of the following statements are true about work? Include all that apply. a. Work is a form of energy. b. A Watt is the standard metric unit of work. c. Units of work would be equivalent to a Newton times a meter. d. A kg•m2/s2 would be a unit of work. e. Work is a time-based quantity; it is dependent upon how fast a force displaces an object. f. Superman applies a force on a truck to prevent it from moving down a hill. This is an example of work being done. g. An upward force is applied to a bucket as it is carried 20 m across the yard. This is an example of work being done. h. A force is applied by a chain to a roller coaster car to carry it up the hill of the first drop of the Shockwave ride. This is an example of work being done. i. The force of friction acts upon a softball player as she makes a headfirst dive into third base. This is an example of work being done. j. An eraser is tied to a string; a person holds the string and applies a tension force as the eraser is moved in a circle at constant speed. This is an example of work being done. k. A force acts upon an object to push the object along a surface at constant speed. By itself, this force must NOT be doing any work upon the object. l. A force acts upon an object at a 90-degree angle to the direction that it is moving. This force is doing negative work upon the object. m. An individual force does NOT do positive work upon an object if the object is moving at constant speed. n. An object is moving to the right. A force acts leftward upon it. This force is doing negative work. o. A non-conservative force is doing work on an object; it is the only force doing work. Therefore, the object will either gain or lose mechanical energy.

Answer: ACDHIKNO a. TRUE - Work is a form of energy, and in fact it has units of energy. b. FALSE - Watt is the standard metric unit of power; Joule is the standard metric unit of energy. c. TRUE - A N•m is equal to a Joule. d. TRUE - A kg•m2/s2 is a mass unit times a speed squared unit, making it a kinetic energy unit and equivalent to a Joule. e. FALSE - Work is not dependent on how rapidly the force displaces an object; power is time-based and calculated by force multiplied by speed. f. FALSE - Since Superman does not cause a displacement, no work is done; he is merely holding the car to prevent its descent down the hill. g. FALSE - The upward force does not cause the horizontal displacement so this is a NON-example of work. h. TRUE - There is a component of force in the direction of displacement and so this is an example of work. i. TRUE - There is a force and a displacement; the force acts in the opposite direction as the displacement and so this force does negative work. j. FALSE - For uniform circular motion, the force acts perpendicular to the direction of the motion and so the force never does any work upon the object. k. FALSE - This is clearly work - a force is causing an object to be displaced. l. FALSE - If a force acts at a 90-degree angle to the direction of motion, then the force does not do any work at all. Negative work is done when there is a component of force opposite the direction of motion. m. FALSE - There are many instances in which an individual force does positive work and yet the object maintains a constant speed. Consider a force applied to lift an object at constant speed. The force does positive work. Consider a car moving at constant speed along a level surface. The force of the road on the tires does positive work while air resistance does and equal amount of negative work. n. TRUE - A force which acts in a direction opposite the motion of an object will do negative work. o. TRUE - When non-conservative forces do work upon an object, the object will either gain or lose mechanical energy. Mechanical energy is conserved (neither gained nor lost) only when conservative forces do work upon objects.

3. Which of the following are never true of an object that is at equilibrium? Include all that apply. a. The object is accelerating. b. The object is at rest. c. The object is moving in a circle at constant speed. d. All the forces acting upon the object are equal. e. The object is in free-fall. f. The object is falling and has reached its terminal velocity. g. There is a net force acting upon the object. h. The object is moving and moving with a constant velocity.

Answer: ACEG An object that is at equilibrium can never be accelerating; its acceleration MUST be 0 m/s/s. Thus, A is an answer; and because an object in free-fall (E) and an object moving in a circle (C) are also accelerating, they must be counted as answers as well. (NOTE: an object moving in a circle is changing its direction and as such has an acceleration.) If there is a net force (G), then by definition the object is not at equilibrium. Choices B, D, F and H could be true of an object at equilibrium (though none of them are always true).

3. Numerical values and directions are stated for a variety of quantities. Which of these statements represent a vector description? Include all that apply. a. 20 meters, west b. 9.8 m/s/s c. 35 mi/hr, south d. 16 years old e. 60 minutes f. 3.5 m/s/s, south g. -3.5 m/s/s h. +20 degrees C

Answer: ACFG Expressions of vector quantities would include a magnitude (number, value, etc.) and a direction. The direction could be described as being north, south, east, west or left, right, up, down. On occasion, a "+" or "-" is used to describe the direction. Since mathematical computations on calculators do not fare well with the typing of "south," a - sign is often substituted for a given direction. In the case of g, the units indicate an acceleration quantity. The "-" sign indicates a direction. One must be careful in assuming that a "+" or "-" sign is a sure sign of a quantity being a direction for other non-vector quantities can use such signs as well (as is the case in h).

1. Which of the following statements are true of scalars and vectors? List all that are TRUE. a. A vector quantity always has a direction associated with it. b. A scalar quantity can have a direction associated with it. c. Vectors can be added together; scalar quantities cannot. d. Vectors can be represented by an arrow on a scaled diagram; the length of the arrow represents the vector's magnitude and the direction it points represents the vector's direction.

Answer: AD a. TRUE - Vectors are defined as quantities which are fully described by both their magnitude and direction. By definition, a vector has a direction associated with it. If it didn't, then it would NOT be a vector. b. FALSE - Scalars are defined as quantities which are fully described by their magnitude alone. Scalars have no regard for direction and it is meaningless to associate a direction with such a quantity. If a quantity did have a direction associated with it, then that quantity would not be a vector. c. FALSE - Both vectors and scalars can be added together. The rules for adding vectors together are unique to vectors and cannot be used when adding scalars together. The direction of a vector must be considered when adding two vectors together. Direction is of no importance when adding scalars. d. TRUE - This is exactly the case and exactly what is done throughout the unit.

1. Which of the following statements are true about momentum? a. Momentum is a vector quantity. b. The standard unit on momentum is the Joule. c. An object with mass will have momentum. d. An object which is moving at a constant speed has momentum. e. An object can be traveling eastward and slowing down; its momentum is westward. f. Momentum is a conserved quantity; the momentum of an object is never changed. g. The momentum of an object varies directly with the speed of the object. h. Two objects of different mass are moving at the same speed; the more massive object will have the greatest momentum. i. A less massive object can never have more momentum than a more massive object. j. Two identical objects are moving in opposite directions at the same speed. The forward moving object will have the greatest momentum. k. An object with a changing speed will have a changing momentum.

Answer: ADGHK a. TRUE - Momentum is a vector quantity. Like all vector quantities, the momentum of an object is not fully described until the direction of the momentum is identified. Momentum, like other vector quantities, is subject to the rules of vector operations. b. FALSE - The Joule is the unit of work and energy. The kg m/s is the standard unit of momentum. c. FALSE - An object has momentum if it is moving. Having mass gives an object inertia. When that inertia is in motion, the object has momentum. d. TRUE - This is true. However, one should be quick to note that the object does not have to have a constant speed in order to have momentum. e. FALSE - The direction of an object's momentum vector is in the direction that the object is moving. If an object is traveling eastward, then it has an eastward momentum. If the object is slowing down, its momentum is still eastward. Only its acceleration would be westward. f. FALSE - To say that momentum is a conserved quantity is to say that if a system of objects can be considered to be isolated from the impact of net external forces, then the total momentum of that system is conserved. In the absence of external forces, the total momentum of a system is not altered by a collision. However, the momentum of an individual object is altered as momentum is transferred between colliding objects. g. TRUE - Momentum is calculated as the product of mass and velocity. As the speed of an object increases, so does its velocity. As a result, an increasing speed leads to an increasing momentum - a direct relationship. h. TRUE - For the same speed (and thus velocity), a more massive object has a greater product of mass and velocity; it therefore has more momentum. i. FALSE - A less massive object would have a greater momentum owing to a velocity which is greater than that of the more massive object. Momentum depends upon two quantities * mass and velocity. Both are equally important. j. FALSE - When comparing the size of two momentum vectors, the direction is insignificant. The direction of any vector would never enter into a size comparison. k. TRUE - Objects with a changing speed also have a changing velocity. As such, an object with a changing speed also has a changing momentum.

8. Which of the following statements are true about mechanical energy? Include all that apply. a. The total amount of mechanical energy of an object is the sum of its potential energy and the kinetic energy. b. Heat is a form of mechanical energy. c. The mechanical energy of an object is always conserved. d. When non-conservative forces do work, energy is transformed from kinetic to potential (or vice versa), but the total mechanical energy is conserved. e. A bowling ball is mounted from a ceiling by way of a strong cable. It is drawn back and released, allowed to swing as a pendulum. As it swings from its highest position to its lowest position, the total mechanical energy is mostly conserved. f. When a friction force does work on an object , the total mechanical energy of that object is changed. g. The total mechanical energy of an object remains constant if the only forces doing work on the object are conservative forces. h. If an object gains mechanical energy, then one can be certain that a non-conservative force is doing work.

Answer: AEFGH a. TRUE - This is the definition of mechanical energy. b. FALSE - Heat or thermal energy is a non-mechanical form of energy. Potential and kinetic energy are the only forms of mechanical energy. c. FALSE - The mechanical energy of an object is only conserved if non-conservative forces do not do work upon the object. d. FALSE- If a non-conservative force does work upon an object, then the total mechanical energy of that object is changed. Energy will not be conserved. e. TRUE - Tension does not do work upon the object and so the total mechanical energy is conserved. The presence of air resistance (a non-conservative force) does a little work and so one might notice a very slight change in mechanical energy. f. TRUE - Friction is a non-conservative force and thus alters the total mechanical energy of an object. g. TRUE - This is the conservation of energy principle and one that you need to firmly understand. h. TRUE - If there is any change in the total mechanical energy of an object (whether a gain or a loss), then you know for certain that there is a non-conservative force doing work.

5. Which of the following statements are true about elastic and inelastic collisions? a. Perfectly elastic and perfectly inelastic collisions are the two opposite extremes along a continuum; where a particular collision lies along the continuum is dependent upon the amount kinetic energy which is conserved by the two objects. b. Most collisions tend to be partially to completely elastic. c. Momentum is conserved in an elastic collision but not in an inelastic collision. d. The kinetic energy of an object remains constant during an elastic collision. e. Elastic collisions occur when the collision force is a non-contact force. f. Most collisions are not inelastic because the collision forces cause energy of motion to be transformed into sound, light and thermal energy (to name a few). g. A ball is dropped from rest and collides with the ground. The higher that the ball rises upon collision with the ground, the more elastic that the collision is. h. A moving air track glider collides with a second stationary glider of identical mass. The first glider loses all of its kinetic energy during the collision as the second glider is set in motion with the same original speed as the first glider. Since the first glider lost all of its kinetic energy, this is a perfectly inelastic collision. i. The collision between a tennis ball and a tennis racket tends to be more elastic in nature than a collision between a halfback and linebacker in football.

Answer: AEFGI a. TRUE - A perfectly elastic collision is a collision in which the total kinetic energy of the system of colliding objects is conserved. Such collisions are typically characterized by bouncing or repelling from a distance. In a perfectly inelastic collision (as it is sometimes called), the two colliding objects stick together and move as a single unit after the collision. Such collisions are characterized by large losses in the kinetic energy of the system. b. FALSE - Few collisions are completely elastic. A completely elastic collision occurs only when the collision force is a non-contact force. Most collisions are either perfectly inelastic or partially inelastic. c. FALSE - Momentum can be conserved in both elastic and inelastic collisions provided that the system of colliding objects is isolated from the influence of net external forces. It is kinetic energy that is conserved in a perfectly elastic collision. d. FALSE - In a perfectly elastic collision, in an individual object may gain or lose kinetic energy. It is the system of colliding objects which conserves kinetic energy. e. TRUE - Kinetic energy is lost from a system of colliding objects because the collision transforms kinetic energy into other forms of energy - sound, heat and light energy. When the colliding objects don't really collide in the usual sense (that is when the collision force is a non-contact force), the system of colliding objects does not lose its kinetic energy. Sound is only produced when atoms of one object make contact with atoms of another object. And objects only warm up (converting mechanical energy into thermal energy) when their surfaces meet and atoms at those surfaces are set into vibrational motion or some kind of motion. f. TRUE - See above statement. g. TRUE - If large amounts of kinetic energy are conserved when a ball collides with the ground, then the post-collision velocity is high compared to the pre-collision velocity. The ball will thus rise to a height which is nearer to its initial height. h. FALSE - This is a perfectly elastic collision. Before the collision, all the kinetic energy is in the first glider. After the collision, the first glider has no kinetic energy; yet the second glider has the same mass and velocity as the first glider. As such, the second glider has the kinetic energy which the first glider once had. i. TRUE - There is significant bounce in the collision between a tennis racket and tennis ball. There is typically little bounce in the collision between a halfback and a linebacker (though there are certainly exceptions to this one). Thus, the ball-racket collision tends to be more elastic.

6. Which of the following statements are true of the concept of force? List all that apply. a. A force is a push or pull exerted upon an object which results from the interaction of that object with its environment. b. Bubba approaches Billie and gives him a swift shove. Timid little Billie keeps his hands in his pocket during this interaction. Subsequently, while Bubba places a force upon Billie, Billie does not place a force upon Bubba. c. A quarterback throws a football down field. Once thrown, the force from the quarterback persists upon the ball to cause it to continue on its upward trajectory towards its peak. d. A sled slides down the hill and reaches the bottom where it gradually slows to a stop. Once on the level ground, the force of the hill persists upon the sled to allow it to continue its forward motion. e. Forces always cause objects to move. f. An object can experience two or more forces and not accelerate. g. A contact force results from the physical contact between two objects. h. A field force results from the action of two objects which are positioned some distance away. i. Spring and tension forces are examples of field forces. j. A force is a vector quantity; there is always a direction associated with it. k. Force can be measured in kilograms or Newtons depending upon the system of measurement (metric or otherwise).

Answer: AFGJ and sort of H. a. True - This is a great definition of force. b. False - According to Newton's third law, one cannot push on an object without being pushed back. The force on Billie is the result of an interaction of Bubba's hands with Billie's body. That force on Billie might cause Billie to go flying, but the reaction force offers resistance to the motion of Bubba's hands and slows them down. In general, forces will always (without exception) come in pairs. c. False - The force of the quarterback on the football is a contact force which can only exist during the interaction (i.e., the contact) between the quarterback's hands and the football. Once thrown, the football continues its horizontal motion due to its own inertia and its vertical motion is effected by the force of gravity. d. False - Be careful if you answered true to this one. If you did, perhaps you believe in the fatal misconception that a rightward force is required to sustain a rightward motion. The sleds motion to the right can be described as a leftward accelerated motion. Such a leftward acceleration demands that there is a leftward force (despite its rightward force). This leftward force slows the rightward-moving sled down. The hill cannot push on the sled unless the hill is in contact with the sled. e. False - Forces, if unbalanced, can cause objects to accelerate (one form of moving; the other form is moving at a constant velocity). But by no means can one say that forces always cause objects to move. For instance, as you sit in your chair, the chair pushes up on your body but your body does not move. f. True - Certainly! As you sit in your chair, the chair pushes up on your body but your body does not accelerate. This upward force (known as the normal force) is balanced by the downward force of gravity. Many objects experience a force yet do not accelerate. g. True - There are two broad categories of forces - contact forces and field forces. Contact forces, by definition, are those which result from the physical contact of two forces. h. True (mostly) - A field force is a force which can acts between two objects even when they are separated by a distance. Field forces have magnitudes which are dependent upon the distance of separation between the two interacting objects. For instance, the force of gravity between the Sun and the earth is a field force whose value depends upon the distance of separation between the center of the Earth and the center of the Sun. In this sense, the force of gravity is a force which acts when two objects are separated in space from each other. Yet field forces can also occur when the two objects are touching each other. In this sense, one can be skeptical of the wording of the statement. i. False - Spring and tension are examples of contact forces. The spring or the rope/cable/wire are in contact with the object upon which it exerts its push or pull. The field forces are electric force, magnetic force, and gravity force. j. True - Forces always have a direction associated with them. As such, force is a vector quantity - a quantity which is fully described by both a magnitude (size, value) and a direction. k. False - Force is measured in Newtons in the metric system and in pounds in the British system. Kilograms is a unit of mass.

5. Consider Newton's first law of motion to determine which of the following statements are true? List all that apply. a. Newton's first law of motion is applicable to both moving and nonmoving objects. b. If a football is moving upwards and rightwards towards the peak of its trajectory, then there are both rightwards and upwards forces acting upon it. c. It would take an unbalanced force to keep an object in motion. d. If an object is at rest, then there are no forces acting upon the object. e. It would take an unbalanced force to keep an object in motion at a constant velocity. f. It is the natural tendency of all objects to eventually come to a rest position. g. A pendulum bob is set into its usual back-and-forth periodic motion. After some time (perhaps 10 minutes), the pendulum bob comes to a rest position. This is best explained by the idea of inertia - all objects eventually resist motion. h. If a 3-kg rock is thrown at a speed of 2 m/s in a gravity-free environment (presuming one could be found), then an unbalanced force of 6 N would be required to keep the rock moving at a constant speed. i. It would take an unbalanced force to cause an object to accelerate from rest.

Answer: AI a. True - Absolutely true. Like all true scientific laws, they govern all objects. In the case of Newton's first law of motion: An object that is nonmoving remains at rest (unless acted upon by an unbalanced force); and a moving object will continue in its motion at a constant velocity (unless acted upon by an unbalanced force). b. False - A football which is moving upwards and rightwards towards its peak, then it has both an upward and a rightward velocity; it does not however have an upward and a rightward force. In fact, if acting as a projectile, it has no horizontal force and maintains a constant horizontal velocity; similarly, it would have a downward force of gravity and a slowing down motion as it rises. If the football were not a projectile, then the horizontal force would be leftward (air resistance opposing its motion) and the vertical force would be gravity and air resistance, both directed downward. c. False - An unbalanced force would accelerate an object. If directed against its motion, then it would actually slow it down rather than keep is motion going. A balance of forces is all that is required to keep an object going at a constant velocity. An unbalanced force directed in the direction of motion would be required to keep an object going with an increasing speed. d. False - If an object is at rest, then there are no unbalanced forces acting upon it. There is a force of gravity and at least one other upward force capable of balancing the force of gravity. e. False - This is dead wrong. It would take a balance of forces to keep an object in motion at constant velocity. An unbalanced force would cause some form of acceleration. f. False - If you answered TRUE, then Galileo and Newton just rolled over in their grave. It is the natural tendency of all objects to maintain their velocity and to resist changes in whatever state of motion that they have. This is the law of inertia. g. False - All objects resist changes in their state of motion. In the absence of unbalanced forces, they maintain their velocity (whether zero or nonzero). The pendulum changes its state of motion due to an unbalanced force - the force of air resistance. h. False - For an object to maintain a constant velocity, 0 Newtons of net force (i.e., a balance of forces) is required. i. True - Unbalanced forces cause stationary objects to accelerate from rest. In the absence of an unbalanced force, a stationary object would remain at rest.

9. Which of the following statements are true of the time of flight for a projectile? List all that apply. a. The time that a projectile is in the air is dependent upon the horizontal component of the initial velocity. b. The time that a projectile is in the air is dependent upon the vertical component of the initial velocity. c. For a projectile which lands at the same height that it is projected from, the time to rise to the peak is equal to the time to fall from its peak to the original height. d. For the same upward launch angles, projectiles will stay in the air longer if the initial velocity is increased. e. Assume that a kicked ball in football is a projectile. If the ball takes 3 seconds to rise to the peak of its trajectory, then it will take 6 seconds to fall from the peak of its trajectory to the ground.

Answer: BCD a. FALSE - The time for a projectile to rise vertically to its peak (and subsequently fall back to the ground) is dependent upon the initial vertical velocity. Alteration in the horizontal velocity will only cause the projectile to have a greater horizontal displacement (x). b. TRUE - Absolutely true. Projectiles with a greater vertical component of initial velocity will be in the air for longer amount of times (assuming that the direction of viy is upward). An alteration in the viy value will alter the time of flight of the projectile, regardless of the direction of viy. c. TRUE - For projectiles launched at upward angles and landing at the original height, the time to the rise to the peak equals the time to fall from the peak. If it takes 3 seconds to rise upward, it will take 3 seconds to fall. d. TRUE - For a constant launch angle, an increase in the initial velocity (vi) will increase the vertical velocity (viy). This results in an increased time for the projectile to decelerate to 0 m/s as it rises towards its peak. So the projectile takes longer to get to the peak, longer to fall from the peak and overall is in the air for a longer time. e. FALSE - Close, but very false. If it takes 3 seconds to rise to the peak, then it takes 3 seconds to fall from the peak; The 6 seconds is the total time of flight of the projectile.

2. Which of the following statements are true of the quantity mass? List all that apply. a. The mass of an object is dependent upon the value of the acceleration of gravity. b. The standard metric unit of mass is the kilogram. c. Mass depends on how much stuff is present in an object. d. The mass of an object is variable and dependent upon its location. e. An object would have more mass on Mount Everest than the same object in the middle of Lake Michigan. f. People in Weight Watcher's are really concerned about their mass (they're mass watchers). g. The mass of an object can be measured in pounds. h. If all other variables are equal, then an object with a greater mass would have a more difficult time accelerating. i. If all other variables are equal, then it would require less exerted force to stop a less massive object than to stop a more massive object. j. The mass of an object is mathematically related to the weight of the object.

Answer: BCFHIJ a. False - Mass is independent of the gravitational environment that an object is in and dependent solely upon the number of atoms in the object and the type of atoms (Carbon: ~12 g/mol; Hydrogen: ~1 g/mol ; Oxygen: ~16 g/mol). Because of this, mass is said to be invariable (unless of course, an object loses some of its atoms) - a constant quantity which is independent of the acceleration of gravity and therefore independent of location. (Weight on the other hand depends upon the gravitational environment.) b. True - Know this one. Kilograms is for mass and Newtons is for force. c. True - This is kind of a simple definition of mass but it does do the job (provided stuff means atoms or material). d. False - See explanation to #2d. e. False - An object has the same mass on Mount Everest as it does at sea level (or near sea level); only the weight of the object would be slightly different in these two locations. f. True - Weight Watcher's participants only use a measurement of their weight as a reflection of how many atoms of flesh that they have burned from their bodies. Their real interest is in losing mass for reasons related to health, appearance, etc. g. False - Pounds is a unit of force commonly used in the British system of measurement. It is not a metric unit and it is not a unit of mass. Kilogram is the standard metric unit of mass and slug is the British unit. h. True - Weight and force of gravity are synonymous terms. You should quickly become comfortable with the terms mass, weight and force of gravity; it will save you many headaches as we continue through the course. i. True - A less massive object has less inertia and as such would offer less resistance to changes in their velocity. For this reason, a less massive object requires less force to bring from a state of motion to a state of rest. j. True - The weight of an object is the mass of the object multiplied by the acceleration of gravity of the object. Mass and weight are mathematically related by the equation: Weight (or Fgrav) = m•g

2. Which of the following quantities are vectors? Include all that apply. a. distance traveled b. displacement c. average speed d. average velocity e. instantaneous velocity f. acceleration

Answer: BDEF Of the five kinematic quantities listed here (distance, displacement, speed, velocity and acceleration), three of them are vectors. Displacement, velocity (both average and instantaneous), and acceleration all require the mention of a direction in order to fully describe the quantity.

7. Which of the following statements are true about potential energy? Include all that apply. a. Moving objects cannot have potential energy. b. Potential energy is the energy stored in an object due to its position. c. Both gravitational and elastic potential energy are dependent upon the mass of an object. d. The gravitational potential energy of an object is dependent upon the mass of the object. e. If the mass of an elevated object is doubled, then its gravitational potential energy will be doubled as well. f. Gravitational potential energy is lost as objects free-fall to the ground. g. The higher that an object is, the more potential energy which it will have. h. The unit of measurement for potential energy is the Joule. i. A 1-kg mass at a height of 1 meter has a potential energy of 1 Joule. j. A 1-kg object falls from a height of 10 m to a height of 6 m. The final potential energy of the object is approximately 40 J. k. If work is done on an object by a non-conservative force, then the object will either gain or lose potential energy.

Answer: BDEFGH a. FALSE - Potential energy has nothing to do with speed; an object could be moving at an elevated position. It is this elevation above zero level which gives an object potential energy. b. TRUE - This is the definition of potential energy. c. FALSE - Gravitational potential energy is dependent upon the mass of the object (PEgrav = m•g•h) but elastic potential energy is dependent upon the spring constant and the compression or stretch length of the spring (PEelastic = 0.5•k•x2). d. TRUE - The equation states that PEgrav = m•g•h; PE is dependent upon mass. e. TRUE - The equation states that PEgrav = m•g•h; if the h is doubled, then the PE will be doubled as well. f. TRUE - As objects free-fall, the height (h) decreases; subsequently, the PE decreases. g. TRUE - The equation states that PEgrav = m•g•h; PE is directly related to height. h. TRUE - The Joule (abbrev. J) is the standard metric unit of energy - all forms of energy. i. FALSE - The final potential energy is calculated as PE = m•g•h = (1 kg)•(~10 m/s/s)•(1 m) = ~10 J. j. FALSE - The final potential energy is calculated as PE = m•g•h = (1 kg)•(~10 m/s/s)•(6 m) = ~60 J; the loss in potential energy during this 4-m fall is -40 J. k. FALSE - The object will either gain or lose mechanical energy, but not necessarily potential energy.

3. Which of the following statements are true about impulse? a. Impulse is a force. b. Impulse is a vector quantity. c. An object which is traveling east would experience a westward directed impulse in a collision. d. Objects involved in collisions encounter impulses. e. The Newton is the unit for impulse. f. The kg•m/s is equivalent to the units on impulse. g. An object which experiences a net impulse will definitely experience a momentum change. h. In a collision, the net impulse experienced by an object is equal to its momentum change. i. A force of 100 N acting for 0.1 seconds would provide an equivalent impulse as a force of 5 N acting for 2.0 seconds.

Answer: BDFGHI a. FALSE - Impulse is NOT a force. Impulse is a quantity which depends upon both force and time to change the momentum of an object. Impulse is a force acting over time. b. TRUE - Impulse is a vector quantity Like momentum, impulse is not fully described unless a direction is associated with it. c. FALSE - An object which is traveling east could encounter a collision from the side, from behind (by a faster-moving object) or from the front. The direction of the impulse is dependent upon the direction of the force exerted upon the object. In each of these scenarios, the direction of the force would be different. d. TRUE - In a collision, there is a collision force which endures for some amount of time. The combination of force and time is what is referred to as an impulse. e. FALSE - The Newton is the unit of force. The standard metric unit of impulse is the N•s. f. TRUE - The N•s is the unit of momentum. The Newton can be written as a kg•m/s^2. When substituted into the N•s expression, the result is the kg m/s. g. TRUE - In a collision, there is a collision force which endures for some amount of time to cause an impulse. This impulse acts upon the object to change its velocity and thus its momentum. h. TRUE - Yes!!! This is the impulse-momentum change theorem. The impulse encountered by an object in a collision causes and is equal to the momentum change experienced by that object. i. TRUE - A force of 100 N for 0.10 s results in an impulse of 10 N•s. This 10 N•s impulse is equivalent to the impulse created by a force of 5 N for 2.0 seconds.

2. Which of the following are true about the relationship between momentum end energy? a. Momentum is a form of energy. b. If an object has momentum, then it must also have mechanical energy. c. If an object does not have momentum, then it definitely does not have mechanical energy either. d. Object A has more momentum than object B. Therefore, object A will also have more kinetic energy. e. Two objects of varying mass have the same momentum. The least massive of the two objects will have the greatest kinetic energy.

Answer: BE a. FALSE - No. Momentum is momentum and energy is energy. Momentum is NOT a form of energy; it is simply a quantity which proves to be useful in the analysis of situations involving forces and impulses. b. TRUE - If an object has momentum, then it is moving. If it is moving, then it has kinetic energy. And if an object has kinetic energy, then it definitely has mechanical energy. c. FALSE - If an object does NOT have momentum, then it definitely does NOT have kinetic energy. However, it could have some potential energy and thus have mechanical energy. d. FALSE - Consider Object A with a mass of 10 kg and a velocity of 3 m/s. And consider Object B with a mass of 2 kg and a velocity of 10 m/s. Object A clearly has more momentum. However, Object B has the greatest kinetic energy. The kinetic energy of A is 45 J and the kinetic energy of B is 100 J. e. TRUE - When comparing the momentum of two objects to each other, one must consider both mass and velocity; both are of equal importance when determining the momentum value of an object. When comparing the kinetic energy of two objects, the velocity of an object is of double importance. So if two objects of different mass have the same momentum, then the object with the least mass has a greater velocity. This greater velocity will tip the scales in favor of the least massive object when a kinetic energy comparison is made.

6. Which of the following statements are true about kinetic energy? Include all that apply. a. Kinetic energy is the form of mechanical energy which depends upon the position of an object. b. If an object is at rest, then it does not have any kinetic energy. c. If an object is on the ground, then it does not have any kinetic energy. d. The kinetic energy of an object is dependent upon the weight and the speed of an object. e. Faster moving objects always have a greater kinetic energy. f. More massive objects always have a greater kinetic energy. g. Kinetic energy is a scalar quantity. h. An object has a kinetic energy of 40 J. If its mass were twice as much, then its kinetic energy would be 80 J. i. An object has a kinetic energy of 40 J. If its speed were twice as much, then its kinetic energy would be 80 J. j. Object A has a mass of 1 kg and a speed of 2 m/s. Object B has a mass of 2 kg and a speed of 1 m/s. Objects A and B have the same kinetic energy. k. An object can never have a negative kinetic energy. l. A falling object always gains kinetic energy as it falls. m. A 1-kg object is accelerated from rest to a speed of 2.0 m/s. This object gains 4.0 Joules of kinetic energy. n. If work is done on an object by a non-conservative force, then the object will either gain or lose kinetic energy.

Answer: BGHK a. FALSE - Kinetic energy depends upon the speed of the object; potential energy depends upon the position of the object. b. TRUE - Kinetic energy depends upon speed. If there is no speed (the object is at rest), then there is no kinetic energy. c. FALSE - If an object is on the ground, then it does not have potential energy (relative to the ground). d. FALSE (sort of) - Kinetic energy depends upon mass and speed. Two objects of the same mass could have different weights if in a different gravitational field; so it is not appropriate to say that kinetic energy depends upon weight. e. FALSE - Faster moving objects would have more kinetic energy than other objects of the same mass. However, another object could have less speed and make up for this lack of speed in terms of a greater mass. f. FALSE - More massive objects would have more kinetic energy than other objects with the same speed. However, another object could have less mass and make up for this lack of mass in terms of a greater speed. g. TRUE - Kinetic energy does not have a direction associated with it; it is a scalar quantity. h. TRUE - Kinetic energy is directly related to the mass of an object. i. FALSE - Kinetic energy is directly related to the square of the speed of an object. So a doubling of the speed would result in a quadrupling of the kinetic energy - the new KE would be 160 J. j. FALSE - When it comes to kinetic energy, speed is doubly important (recall v2). So in this case, object A would have more kinetic energy. Doing the calculation yields 2 J for object A and 1 J for object B. k. TRUE - Kinetic energy is determined by the equation 0.5•m•v2. the quantity m is always positive. And even if v is negative, v2 will always be positive. Therefore, kinetic energy can never be a negative value. l. FALSE - If an object is falling at a constant velocity (i.e., the air resistance force equals the downward force of gravity), then there is not an increase in kinetic energy. It is true however that free-falling objects always increase their kinetic energy as they fall. m. FALSE - The kinetic energy increases from 0 J to 2 J (0.5•1•22); that's an increase by 2 J. n. FALSE - Such an object will definitely gain or lose mechanical energy but not necessarily kinetic energy.

8. Which of the following statements are true of the vertical motion of projectiles? List all that apply. a. The vertical component of a projectile's velocity is a constant value of 9.8 m/s. b. The vertical component of a projectile's velocity is constant. c. The vertical component of a projectile's velocity is changing. d. The vertical component of a projectile's velocity is changing at a constant rate. e. A projectile with an upward component of motion will have a upward component of acceleration. f. A projectile with an downward component of motion will have a downward component of acceleration. g. The magnitude of the vertical velocity of a projectile changes by 9.8 m/s each second. h. The vertical velocity of a projectile is 0 m/s at the peak of its trajectory. i. The vertical velocity of a projectile is unaffected by the horizontal velocity; these two components of motion are independent of each other. j. The final vertical velocity of a projectile is always equal to the initial vertical velocity. k. The vertical acceleration of a projectile is 0 m/s/s when it is at the peak of its trajectory. l. As a projectile rises towards the peak of its trajectory, the vertical acceleration will decrease; as it falls from the peak of its trajectory, its vertical acceleration will decrease. m. As a projectile rises towards the peak of its trajectory, the vertical acceleration is directed upward; as it falls from the peak of its trajectory, its vertical acceleration is directed downward. n. The peak height to which a projectile rises above the launch location is dependent upon the initial vertical velocity. o. As a projectile rises towards the peak of its trajectory, the vertical velocity will decrease; as it falls from the peak of its trajectory, its vertical velocity will decrease. p. Consider a projectile launched from ground level at a fixed launch speed and a variable angle and landing at ground level. The vertical displacement of the projectile during the first half of its trajectory (i.e., the peak height) will always increase as the angle of launch is increased from 0 degrees to 90 degrees. q. Consider a projectile launched from ground level at a fixed launch angle and a variable launch speed and landing at ground level. The vertical displacement of the projectile during the first half of its trajectory (i.e., the peak height) will always increase as the launch speed is increased.

Answer: CDFGHINPQ a. FALSE - The vertical component of a projectile's velocity is constantly changing. It is the acceleration which has a value of 9.8 m/s/s. b. FALSE - Projectiles are objects being acted upon by gravity alone. As such, there is a vertical acceleration; the vertical velocity is not constant, but changing. c. TRUE - See part b above. d. TRUE - A projectile has a vertical acceleration of 9.8 m/s/s throughout the entire trajectory. This acceleration value is constant. This means that the vertical velocity changes by the same amount - 9.8 m/s - during each second of its motion. There is a change in the vertical velocity by a constant amount. e. FALSE - All projectiles experience a downward acceleration, whether they are moving upward or downward. The upward-moving projectiles have an upward velocity, but the actual velocity values are getting smaller; that is, the projectile is slowing down on the way to its peak. f. TRUE - This is a true statement. It could also be said that a projectile with an upward component of motion also has a downward acceleration. All projectiles accelerate in the downward direction. Period. g. TRUE - This is absolutely true . h. TRUE - At the peak of its trajectory, a projectile is in the process of changing directions. The vertical velocity must change from a positive value (+ for upward) to a negative value (- for downward). This transition means that the value for the vertical velocity must at sometime be in between a + and - number. The in-between number is 0 m/s and this occurs at the peak. i. TRUE - For any two dimensional motion (whether projectile motion or riverboat problems or ...), perpendicular components of the motion are independent of each other. Any alteration in a vertical component will not effect the horizontal components of motion. j. FALSE - A projectile launched at an angle forms a parabolic trajectory. Suppose that one were to trace a projectile's motion forward in time from the peak and backwards in time from the peak. If done, one would find that the vertical velocity value has the same magnitude for equal amounts of times traced forward and backward from the peak. So for the same time before and after the peak, a projectile has the same speed. However, some projectiles are not launched from the same height at which they land. The final height is not the same as the initial height and as such the time to rise to the peak is not equal to the time to fall from the peak. In such instances, the initial vertical velocity is not equal to the final vertical velocity. k. FALSE - No! No! No! The vertical velocity is 0 m/s at the peak and the vertical acceleration is -9.8 m/s/s throughout the entire trajectory. l. FALSE - This would be a true description of the vertical velocity. But the vertical acceleration is a constant value of 9.8 m/s/s throughout the entire trajectory. m. FALSE - Not only is the magnitude of the vertical acceleration a constant value throughout a projectile's trajectory, the direction is constant as well. Projectile's at all times regardless of any other variable will accelerate downwards at 9.8 m/s/s. This is perhaps the most important truth to digest about projectiles. n. TRUE - The initial vertical velocity has an effect on the time taken by a projectile to rise towards its peak. It also effects the average speed of the projectile as it rises towards its peak. As a result, any alteration in the vertical velocity will alter the peak height of the projectile. o. FALSE - Upward-rising projectiles have a downward acceleration; this means they are slowing down as they rise. The magnitude of their velocity is decreasing. Downward-moving projectiles also have a downward acceleration; this means they are speeding up. The magnitude of their velocity is increasing. p. TRUE - An increase in the angle of launch (from 0 to 90 degrees) will always increase the vertical component of the initial velocity (viy). This increase in viy will lead to increased times for the projectile rising towards its peak. And an increased angle causes the projectile to move with a greater average speed during its path towards its peak. Both of these effects lead to the outcome that the peak height of a projectile will increase as the angle of launch increases from 0 to 90 degrees. q. TRUE - As the launch speed is increased, the components of the initial velocity (both the horizontal and the vertical) increase as well. This causes the projectile to stay in the air for a longer period of time and to be moving faster in the vertical direction. The result is that increased launch speeds always lead to increased heights for projectiles.

1. Which of the following statements are true of inertia? List all that apply. a. Inertia is a force. b. Inertia is a force which keeps stationary objects at rest and moving objects in motion at constant velocity. c. Inertia is a force which brings all objects to a rest position. d. All objects have inertia. e. A more massive object has more inertia than a less massive object. f. Fast-moving objects have more inertia than slow-moving objects. g. An object would not have any inertia in a gravity-free environment (if there is such a place). h. Inertia is the tendency of all objects to resist motion and ultimately stop. i. In a gravity-free environment (should there be one), a person with a lot of inertia would have the same ability to make a turn as a person with a small amount of inertia.

Answer: DE a. False - Inertia is not a force. b. False - Inertia is NOT a force. c. False - Inertia is NOT a force. Inertia is simply the tendency of an objects to resist a change in whatever state of motion that it currently has. Put another way, inertia is the tendency of an object to "keep on doing what it is doing." Mass is a measure of an object's inertia. The more mass which an object has, the more that it sluggish towards change. d. True - Bet money on this one. Any object with mass has inertia. (Any object without mass is not an object, but something else like a wave.) e. True - Mass is a measure of an object's inertia. Objects with greater mass have a greater inertia; objects with less mass have less inertia. f. False - The speed of an object has no impact upon the amount of inertia that it has. Inertia has to do with mass alone. g. False - Inertia (or mass) has nothing to do with gravity or lack of gravity. In a location where g is close to 0 m/s/s, an object loses its weight. Yet it still maintains the same amount of inertia as usual. It still has the same tendency to resist changes in its state of motion. h. False - Inertia is NOT the tendency to resist motion, but rather to resist changes in the state of motion. For instance, its the tendency of a moving object to keep moving at a constant velocity (or a stationary object to resist changes from its state of rest). i. False - Once more (refer to g), inertia is unaffected by alterations in the gravitational environment. An alteration in the g value effects the weight of an object but not the mass or inertia of the object.

2. Which of the following are always true of an object that is at equilibrium? Include all that apply. a. All the forces acting upon the object are equal. b. The object is at rest. c. The object is moving and moving with a constant velocity. d. The object has an acceleration of zero. e. There is no change in the object's velocity. f. The sum of all the forces is 0 N. g. All the forces acting upon an object are balanced.

Answer: DEFG These (DEFG) statements are always true. Statements ABC might be true but are not always true.

5. Which of the following descriptions of moving objects accurately portray a projectile? List all that apply. a. an object which is moving through the air and not touching any surface b. a falling skydiver with an open parachute c. any object upon which air resistance is negligible d. a free-falling object e. an object upon which the only significant force is the force of gravity f. a falling feather g. a falling feather in a vacuum chamber h. a falling feather in a falling vacuum chamber.

Answer: DEGH A projectile is an object upon which the only force is gravity. Air resistance must be negligible or nonexistent. Other forces resulting from people or things pulling or pushing, attached strings or contact with surfaces must not be present. a. NO - A plane moves through the air and is not touching any surface. Yet, a plane is clearly not a projectile. b. NO - A falling skydiver typically experiences considerable air resistance. It is popular to describe such skydivers as being in free fall. This is an erroneous use of the term. c. NO - As you sit in your chair, air resistance is negligible. You are certainly not a projectile (at least, we hope not). d. YES - A projectile is an object in free fall. e. YES - An object upon which the only significant force is gravity fits the definition of a projectile (provided that significant means "having an influence"). f. NO - Falling feathers encounter air resistance which impedes the downward acceleration and causes the feather to fall at nearly a constant velocity. g. YES - When a feather is allowed to fall in a vacuum, air resistance is eliminated and the feather can free fall. h. YES - When a feather is allowed to fall in a vacuum and the vacuum is free-falling as well, air resistance is eliminated and an observer would notice that both the vacuum chamber and the feather are in free fall.

7. Which of the following statements are true of the horizontal motion of projectiles? List all that apply. a. A projectile does not have a horizontal velocity. b. A projectile with a rightward component of motion will have a rightward component of acceleration. c. The horizontal velocity of a projectile changes by 9.8 m/s each second. d. A projectile with a horizontal component of motion will have a constant horizontal velocity. e. The horizontal velocity of a projectile is 0 m/s at the peak of its trajectory. f. The horizontal velocity of a projectile is unaffected by the vertical velocity; these two components of motion are independent of each other. g. The horizontal displacement of a projectile is dependent upon the time of flight and the initial horizontal velocity. h. The final horizontal velocity of a projectile is always equal to the initial horizontal velocity. i. As a projectile rises towards the peak of its trajectory, the horizontal velocity will decrease; as it falls from the peak of its trajectory, its horizontal velocity will decrease. j. Consider a projectile launched from ground level at a fixed launch speed and a variable angle and landing at ground level. The horizontal displacement (i.e., the range) of the projectile will always increase as the angle of launch is increased from 0 degrees to 90 degrees. k. Consider a projectile launched from ground level at a fixed launch angle and a variable launch speed and landing at ground level. The horizontal displacement (i.e., the range) of the projectile will always increase as the launch speed is increased.

Answer: DFGHK a. FALSE - Many projectiles are moving from left to right and from right to left as they simultaneously free fall. Such projectiles have a horizontal motion. While a projectile can have a horizontal motion, it cannot have a horizontal acceleration. Whatever motion which it has in the horizontal dimension, must be motion with a constant velocity. b. FALSE - A projectile with a rightward motion (in addition to a vertical motion) will have a constant velocity in the rightward direction. This is to say that it has no horizontal acceleration. c. FALSE - A projectile has a constant horizontal velocity. The vertical velocity will change by 9.8 m/s each second. d. TRUE - Absolutely true! Projectiles are objects being acted upon by gravity alone. As such, there is a vertical acceleration but no horizontal acceleration. The horizontal velocity of a projectile is either zero or a constant nonzero value. e. FALSE - The vertical velocity of a projectile is 0 m/s at the peak of its trajectory; but the horizontal component of the velocity at the peak is whatever the value was when first launched. f. TRUE - For any two dimensional motion (whether projectile motion or riverboat problems or ...), perpendicular components of the motion are independent of each other. Any alteration in a vertical component will not effect the horizontal components of motion. g. TRUE - The horizontal displacement (x) can be calculated with the formula x = vox • t, where vox is the initial horizontal velocity and t is the time. These are the two variables which effect the horizontal displacement of a projectile. h. TRUE - Since there is no horizontal acceleration for a projectile, the initial horizontal velocity is equal to the final horizontal velocity. i. FALSE - This is a true description for the vertical component of the velocity. The horizontal velocity is unchanging throughout the trajectory of a projectile. j. FALSE - The range (or horizontal displacement) will increase as the angle is increased from 0 degrees to 45 degrees. The maximum range occurs at 45 degrees. As the angle is further increased to values greater than 45 degrees, the horizontal displacement decreases. k. TRUE - As the launch speed is increased, the components of the initial velocity (both the horizontal and the vertical) increase as well. This causes the projectile to stay in the air for a longer period of time and to be moving faster in the horizontal direction. The result is that increased launch speeds always lead to increased horizontal displacements.

4. Which of the following statements are true of vector addition, vector subtraction, and vector addition diagrams? List all that apply. a. Vectors A, B, and C are added together as A + B + C. If the order in which they are added is changed to C + B + A, then the result would be different. b. Vectors A, B, and C are added together as A + B + C. If the order in which they are added is reversed to C + B + A, then the result would be a vector with the same magnitude but the opposite direction. c. When constructing a vector diagram for A + B + C, it is not absolutely necessary that vectors B and C use the same scale that is used by vector A. d. The resultant in a vector addition diagram always extends from the head of the last vector to the tail of the first vector. e. If vectors A and B are added at right angles to each other, then one can be sure that the resultant will have a magnitude that is greater than the magnitudes of either one of the individual vectors A and B. f. If vectors A and B are added at right angles to each other, then one can be sure that the resultant will have a magnitude that is less than the arithmetic sum of the magnitudes of A and B. g. Vector addition diagrams cannot be used to determine the resultant when there is a vector subtraction operation.

Answer: EF a. FALSE - Altering the order in which three vectors are added does not alter the result of the addition process. A + B + C = C + B + A. Each order of operation yields a resultant with the same magnitude and direction. b. FALSE - As mentioned above in a, altering the order in which three vectors are added does not alter the result of the addition process. Reversing the order produces a resultant with the same magnitude and the same direction. c. FALSE - When constructing a vector addition diagram, a scale must be chosen and adhered to. The scale which used to draw vector A must also be used for vectors B and C. One cannot switch horses in the middle of the stream. d. FALSE - The resultant in a vector addition diagram is drawn from the tail of the first vector (the starting point) to the head of the last vector (the finishing point). e. TRUE - Suppose that A = 3 units and B = 4 units and that the two vectors are directed at right angles to each other. The vector sum or resultant of A + B is 5 units, which is clearly greater than either one of the vectors being added. In general, the resultant in such a case will be represented on a vector addition diagram as the hypotenuse of a right triangle. The hypotenuse is always greater than the other two legs of the triangle. So this statement is always true. f. TRUE - Suppose that A = 3 units and B = 4 units and that the two vectors are directed at right angles to each other. The vector sum or resultant of A + B is 5 units whereas the arithmetic sum is 7 units. In this case and in all cases, the vector sum of two right angle vectors will always be less than the arithmetic sum. That is, Sqrt(a2 + b2) will always be less than a + b. g. FALSE - When a vector subtraction operation is performed, it is usually advisable to simply convert it into a vector addition operation. This is accomplished by adding the negative of the vector which is being subtracted. So A - B would be equivalent to A + (-B). By so doing, a vector addition diagram can be used to determine the resultant.

4. Which of the following statements are true of an object that experiences balanced forces (or unbalanced forces)? List all that apply. a. If a person is moving to the right, then the forces acting upon it are NOT balanced. b. A balance of forces is demonstrated by an object which is slowing to a stop. c. It would take an unbalanced force to keep an object in motion. d. If an object is moving with a constant speed in a circle, then the forces acting upon the object are balanced. e. If an object is accelerating at a constant rate of acceleration, then the forces acting upon the object are balanced. f. It is NOT possible for just three forces to be acting upon an object and they still balance each other. g. A free-falling object experiences a balance of forces. h. Balanced forces cause stationary objects to remain at rest and moving objects to come to rest. i. Unbalanced forces cause objects to move.

Answer: None of these are true, though one might make a strong argument for I. a. False - An object which is moving to the right could have unbalanced forces, but only if it is accelerating. The presence of unbalanced forces must always be associated with acceleration, not mere motion. In this case, an object moving to the right could have a balance of forces if it is moving with a constant velocity. b. False - An object would never slow to a stop unless the forces acting upon it were unbalanced. In fact, an object which slows down must have a unbalanced force directed in the direction opposite their motion. c. False - An unbalanced force is only required to accelerate an object. A balance of forces is required to keep an object moving at a constant velocity. For instance, a car moving to the right at constant velocity encounters as much rightward force as leftward force. d. False - An object which moves in a circle has a changing direction. As such, there is an acceleration and this acceleration requires that there be an unbalanced force present on the object. e. False - Any object that accelerates has a changing velocity. An object that accelerates at a constant rate has a velocity that changes by the same amount each second. For instance, a free-falling object changes its velocity by -9.8 m/s ever second. It is said to have a constant acceleration of -9.8 m/s2. A free-falling object, or any object with an acceleration (whether constant or non-constant) must be experiencing an unbalanced force. f. False - Consider an object which weighs 1000 N (a 1000 N downward force) which is being pulled on by two people, each exerting 500 N of upward force. Such an object has three forces acting upon it and the three forces together balance each other. g. False - A free-falling object is an object upon which the only force is gravity. As such, there is an unbalanced force acting upon it; this unbalanced force explains its acceleration. h. False - Balanced forces cause stationary objects to stay at rest. However balanced forces would never cause moving objects to stop; an unbalanced force would be required to stop a moving object. i. False - Unbalanced forces do more than cause objects to move; unbalanced forces cause objects to accelerate. Though one could make a strong argument that an object that is accelerating must also be moving (albeit with a changing velocity). In this sense, this statement is true.

2. Which of the following statements about distance and/or displacement are TRUE? List all that apply. Distance is a vector quantity and displacement is a scalar quantity. a. A person makes a round-trip journey, finishing where she started. The displacement for the trip is 0 and the distance is some nonzero value. b. A person starts at position A and finishes at position B. The distance for the trip is the length of the segment measured from A to B. c. If a person walks in a straight line and never changes direction, then the distance and the displacement will have exactly the same magnitude. d. The phrase "20 mi, northwest" likely describes the distance for a motion. e. The phrase "20 m, west" likely describes the displacement for a motion. f. The diagram below depicts the path of a person walking to and fro from position A to B to C to D. g. The distance for this motion is 100 yds. h. For the same diagram below, the displacement is 50 yds. (다이어그램 사진 안넣어짐..)

BDF a. FALSE - Distance is the scalar and displacement is the vector. Know this one! b. TRUE - Displacement is the change in position of an object. An object which finishes where it started is not displaced; it is at the same place as it started and as such has a zero displacement. On the other hand, the distance is the amount of ground which is covered. And if it was truly a journey, then there is definitely a distance. c. FALSE - This would only be the case if the person walk along a beeline path from A to B. But if the person makes a turn and veers left, then right and then ..., then the person has a distance which is greater than the length of the path from A to B. Distance refers to the amount of ground which is covered. d. TRUE - If a person never changes direction and maintains the same heading away from the initial position, then every step contributes to a change in position in the same original direction. A 1 m step will increase the displacement (read as out of place-ness) by 1 meter and contribute one more meter to the total distance which is walked. e. FALSE - Distance is a scalar and is ignorant of direction. The "northwest" on this quantity would lead one to believe that this is a displacement (a vector quantity) rather than a distance. f. TRUE - The unit is an appropriate displacement unit (length units) and the direction is stated. Since there is both magnitude and direction expressed, one would believe that this is likely a displacement. g. FALSE - The distance from A to B is 35 yds; from B to C is 20 yds; and from C to D is 35 yds. The total distance moved is 90 yds. h. FALSE (a rather picky FALSE) - Technically, this is not a displacement since displacement is a vector and fully described by both magnitude and direction. The real expression of displacement is 50 yds, left (or west or -)

1. Which of the following statements about vectors and scalars are TRUE? List all that apply. a. A vector is a large quantity and a scalar is a small quantity. b. A scalar quantity has a magnitude and a vector quantity does not. c. A vector quantity is described with a direction and a scalar is not. d. Scalar quantities are path dependent quantities and vector quantities are not. e. A scalar quantity depends only upon the initial and final values of the quantity; this is not the case for vector quantities. f. The quantity 20 m/s, north is a speed and as such is a scalar quantity. g. The quantity 9.8 m/s/s is an acceleration value and as such is a vector quantity.

CD a. FALSE - This would never be the case. Vectors simply are direction-conscious, path-independent quantities which depend solely upon the initial and final state of an object. Vectors are always expressed fully by use of a magnitude and a direction. b. FALSE - Both scalar and vector quantities have a magnitude or value expressed with a given unit; additionally, a vector quantity requires a direction in order to fully express the quantity. c. TRUE - Vectors are fully described by magnitude AND direction; scalars are not described with a direction. d. TRUE - Scalars such as distance would depend upon the path taken from initial to final location. If you run around the track one complete time, your distance will be different than if you take a step forward and a step backwards. The path MATTERS; distance (like all scalars) depends upon it. On the other hand, the displacement (a vector quantity) is the same for both paths. e. FALSE - Vectors are the types of quantities which depend only upon initial and final state of the object. For instance, the vector quantity displacement depends only upon the starting and final location. f. FALSE - This is certainly not a speed quantity; though the unit is appropriate for speed, the statement of the direction is inconsistent with speed as a scalar quantity. g. FALSE (a rather picky FALSE) - If a direction was included, then this would be an acceleration value. The unit is characteristic of acceleration but the lack of direction is inconsistent with acceleration being a vector quantity.

An object which is moving rightward has a rightward force acting upon it.

False A rightward acceleration would require a rightward net force. But if an object is moving rightward and slowing down (a leftwards acceleration), then there is certainly not a rightward net force and possibly not even a rightward force at all. For instance, if a car is moving rightward and skidding to a stop (with wheels locked), then there is no rightward force upon the car. The only horizontal force is a leftward force of friction which serves to slow the car down. (If you're getting stuck on this question and ones like them, it might be time to read the page titled "The Big Misconceptsion"; use the link below.)

For an object resting upon a non-accelerating surface, the normal force is equal to the weight of the object.

False In this instance, the normal force could be equal to the force of gravity. But all that we can conclusively know is that the all the vertical forces sum up to 0 N. If the object is upon an incline, then the normal force will not be equal to the force of gravity. Or if there is another force with an upward or downward component, then the normal force is not equal to the force of gravity.

A ball is dropped from the same height upon various flat surfaces. For the same collision time, impulses are smaller when the most bouncing take place.

False Since being dropped from the same height, the balls will be moving with the same pre-collision velocity (assuming negligible air resistance). Upon collision with the ground, the velocity will have to be reduced to zero - that is, the ball will cease moving downwards. This decrease in velocity constitutes the first portion of the velocity change. If the ball bounces, then there is an additional velocity change sending the ball back upwards opposite the original direction. Thus, for the same collision time, bouncing involves a greater velocity change, a greater momentum change, and therefore a greater impulse.

35. If mass and collision time are equal, then impulses are greater on objects which rebound (or bounce).

True The impulse is equal to the momentum change. And when there is a rebound, the momentum change is larger since there is a larger velocity change. For instance, a ball thrown at a wall at 5 m/s may rebound at -3 m/s yielding a velocity change of -8 m/s. An egg thrown at the same wall at the same speed of 5 m/s hits and stops, thus yielding a velocity change of -5 m/s. More velocity change means more momentum change and thus more impulse.

Which of the following statements about position-time graphs are TRUE? List all that apply. a. Position-time graphs cannot be used to represent the motion of objects with accelerated motion. b. The slope on a position-time graph is representative of the acceleration of the object. c. A straight, diagonal line on a position-time graph is representative of an object with a constant velocity. d. If an object is at rest, then the position-time graph will be a horizontal line located on the time-axis. e. Accelerated objects are represented on position-time graphs by curved lines. f. An object with a positive velocity will be represented on a position-time graph by a line with a positive slope. g. An object with a negative velocity will be represented on a position-time graph by a line with a negative slope. h. An object with a positive acceleration will be represented on a position-time graph by a line which curves upwards. i. An object with a negative acceleration will be represented on a position-time graph by a line which curves downwards.

a. FALSE - Position-time graphs represent accelerated motion by curved lines. b. FALSE - The slope of a position-time graph is the velocity of the object. Some things in this unit are critical things to remember and internalize; this is one of them. c. TRUE - A straight diagonal line is a line of constant slope. And if the slope is constant, then so is the velocity. d. FALSE - Not necessarily true. If the object is at rest, then the line on a p-t graph will indeed be horizontal. However, it will not necessarily be located upon the time axis. e. TRUE - Accelerating objects (if the acceleration is attributable to a speed change) are represented by lines with changing slope - i.e., curved lines. f. TRUE - Since slope on a p-t graph represents the velocity, a positive slope will represent a positive velocity. g. TRUE - Since slope on a p-t graph represents the velocity, a negative slope will represent a negative velocity. h. FALSE - (This is confusing wording here since we might not all agree on what "curving up" means.) A line that slopes upward and has a curve (perhaps you call that "curving up" as I do) has a positive velocity (due to its positive slope). If the curve is "concave down" (you might say leveling off to a horizontal as time progresses) then the object is slowing down and the acceleration is negative. i. FALSE - (Once more, there is confusing wording here since we might not all agree on what "curving downwards" means.) A line that slopes downwards and has a curve (perhaps you call that "curving downwards " as I do) has a negative velocity (due to its negative slope). If the curve is "concave up" (you might say leveling off to a horizontal as time progresses) then the object is slowing down and the acceleration is positive.