Momentum and Impulse

Which of the following objects have momentum? Include all that apply. a. An electron is orbiting the nucleus of an atom. b. A UPS truck is stopped in front of the school building. c. A Yugo (a compact car) is moving with a constant speed. d. A small flea walking with constant speed across Fido's back. e. The high school building rests in the middle of town.

A,C, and D-Momentum can be thought of as mass in motion. An object has momentum if it has its mass in motion. It matters not whether the object is of large mass or small mass, moving with constant speed or accelerating; if the object is MOVING, then it has momentum!

Suppose that you're driving down the highway and a moth crashes into the windshield of your car. Which undergoes the greater acceleration? a. the moth b. your car c. both the same

A-In any collision, there are always four quantities which are the same for both objects involved in the collision. Each object experiences the same force (Newton's third law) for the same amount of time, leading to the same impulse, and subsequently the same momentum change. Only the acceleration and the velocity change can differ for the two objects. The object with the least mass always receives the greatest velocity change and acceleration.

A 4 kg object has a momentum of 12 kg•m/s. The object's speed is ___ m/s. a. 3 b. 4 c. 12 d. 48 e. none of these.

A-This is a relatively simple plug-and-chug into the equation p=m*v with m=4 kg and p=12 kg•m/s.

In a physics experiment, two equal-mass carts roll towards each other on a level, low-friction track. One cart rolls rightward at 2 m/s and the other cart rolls leftward at 1 m/s. After the carts collide, they couple (attach together) and roll together with a speed of _____________. Ignore resistive forces. a. 0.5 m/s b. 0.33 m/s c. 0.67 m/s d. 1.0 m/s e. none of these

A-Use 1 kg as the mass of the carts (or any number you wish) and then set the expression for initial total momentum equal to the expression for the final total momentum: (1 kg)*(2) + (1 kg) *(-1) = (1 kg) *v + (1 kg) *v Now solve for v using the proper algebraic steps. (2 kg•m/s) - (1 kg•m/s) = (2 kg) v 1 kg•m/s = (2 kg)v (1 kg•m/s) / (2 kg) = v 0.5 m/s = v

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. A.)True B.)False

A.)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.

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. A.)True B.)False

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.

Two objects of different mass are moving at the same speed; the more massive object will have the greatest momentum. A.)True B.)False

A.)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.

If an object has momentum, then it must also have mechanical energy. A.)True B.)False

A.)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.

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. A.)True B.)False

A.)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.

Impulse is a vector quantity. A.)True B.)False

A.)TRUE - Impulse is a vector quantity Like momentum, impulse is not fully described unless a direction is associated with it.

During a collision, an object always encounters an impulse and a change in momentum. A.)True B.)False

A.)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.

Two colliding objects will exert equal forces upon each other even if their mass is significantly different. A.)True B.)False

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.

Elastic collisions occur when the collision force is a non-contact force. A.)True B.)False

A.)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.

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). A.)True B.)False

A.)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.

The momentum of an object varies directly with the speed of the object. A.)True B.)False

A.)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.

An object with a changing speed will have a changing momentum. A.)True B.)False

A.)TRUE - Objects with a changing speed also have a changing velocity. As such, an object with a changing speed also has a changing momentum.

The kg•m/s is equivalent to the units on impulse. A.)True B.)False

A.)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.

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. A.)True B.)False

A.)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.

An object which is moving at a constant speed has momentum. A.)True B.)False

A.)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.

In a collision, the two colliding objects could have different acceleration values. A.)True B.)False

A.)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.

Two objects of varying mass have the same momentum. The least massive of the two objects will have the greatest kinetic energy. A.)True B.)False

A.)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.

In a collision, the net impulse experienced by an object is equal to its momentum change. A.)True B.)False

A.)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.

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

A.)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.

A relatively large force acting for a relatively long amount of time on a relatively small mass will produce a relatively ______. List all that apply. a. small velocity change b. large velocity change c. small momentum change d. small acceleration

B-A large force acting upon a small mass will result in a large acceleration (a=F/m) and subsequently a large velocity change (Delta v = a*t). This rules out choices A and D. A large force and for a long time will result in a large impulse and therefore a large momentum change. This rules out choice C.

A wad of chewed bubble gum is moving with 1 unit of momentum when it collides with a heavy box that is initially at rest. The gum sticks to the box and both are set in motion with a combined momentum that is ___. a. less than 1 unit b. 1 unit c. more than 1 unit d. not enough information

B-Before the collision, the total system momentum is 1 unit - all due to the motion of the wad of gum. Since momentum must be conserved, the total momentum of the box and gum after the collision must also be 1 unit.

When a mass M experiences a velocity change of v in a time of t, it experiences a force of F. Assuming the same velocity change of v, the force experienced by a mass of 2M in a time of (1/2)t is ____. a. 2F b. 4F c. (1/2)*F d. (1/4)*F e. none of these

B-The impulse-momentum change theorem states that F*t = m*(Delta vel.). This equation can be rearranged to locate the F by itself on one side of the equation; rearranging yields F = m*(Delta vel.)/t The equation shows that force is directly related to the mass, directly related to the change in velocity, and inversely related to the time. So any change in mass will result in the same change in force; and any change in time will result in the inverse effect upon the force. In this case, doubling the mass (from M to 2M) will double the force and halving the time (from t to 1/2-t) will double the force. The combined effect of these two changes will make the new force four times bigger than the old force. This is a case of where equations can be a guide to thinking about how a change in one variable (or two variables) impacts other dependent variables.

When a mass M experiences a velocity change of v in a time of t, it experiences a force of F. Assuming the same velocity change of v, the force experienced by a mass of 2M in a time of (1/4)t is ____. a. 2F b. 8F c. (1/2)*F d. (1/8)*F e. none of these

B-The impulse-momentum change theorem states that F*t = m*(Delta vel.). This equation can be rearranged to locate the F by itself on one side of the equation; rearranging yields F = m*(Delta vel.)/t The equation shows that force is directly related to the mass, directly related to the change in velocity, and inversely related to the time. So any change in mass will result in the same change in force; and any change in time will result in the inverse effect upon the force. In this case, doubling the mass (from M to 2M) will double the force and quartering the time (from t to 1/4-t) will quadruple the force. The combined effect of these two changes will make the new force eight times bigger than the old force. This is a case of where equations can be a guide to thinking about how a change in one variable (or two variables) impacts other dependent variables.

The standard unit on momentum is the Joule. A.)True B.)False

B.) FALSE - The Joule is the unit of work and energy. The kg m/s is the standard unit of momentum.

A less massive object can never have more momentum than a more massive object. A.)True B.)False

B.)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.

An object with mass will have momentum. A.)True B.)False

B.)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.

An object which is traveling east would experience a westward directed impulse in a collision. A.)True B.)False

B.)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.

Object A has more momentum than object B. Therefore, object A will also have more kinetic energy. A.)True B.)False

B.)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.

Most collisions tend to be partially to completely elastic. A.)True B.)False

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.

If an object does not have momentum, then it definitely does not have mechanical energy either. A.)True B.)False

B.)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.

Impulse is a force. A.)True B.)False

B.)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.

The kinetic energy of an object remains constant during an elastic collision. A.)True B.)False

B.)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.

A moving object collides with a stationary object; the stationary object has significantly less mass. The stationary object encounters the greater collision force. A.)True B.)False

B.)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.

When a moving object collides with a stationary object of identical mass, the stationary object encounters the greater collision force. A.)True B.)False

B.)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.

A moving object collides with a stationary object; the stationary object has significantly less mass. The stationary object encounters the greater momentum change. A.)True B.)False

B.)FALSE - In any collision, the colliding objects will experience equal (and opposite) momentum changes, provided that the collision occurs in an isolated system.

When a moving object collides with a stationary object of identical mass, the stationary object encounters the greater momentum change. A.)True B.)False

B.)FALSE - In any collision, the colliding objects will experience equal (and opposite) momentum changes, provided that the collision occurs in an isolated system.

In a collision between two objects of identical mass, the acceleration values could be different. A.)True B.)False

B.)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.

Momentum is conserved in an elastic collision but not in an inelastic collision. A.)True B.)False

B.)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.

Momentum is a form of energy. A.)True B.)False

B.)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.

The Newton is the unit for impulse. A.)True B.)False

B.)FALSE - The Newton is the unit of force. The standard metric unit of impulse is the N•s.

An object can be traveling eastward and slowing down; its momentum is westward. A.)True B.)False

B.)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.

During a collision, the impulse which an object experiences is equal to its velocity change. A.)True B.)False

B.)FALSE - The impulse encountered by an object is equal to mass multiplied by velocity change - that is, momentum change.

While individual objects may change their velocity during a collision, the overall or total velocity of the colliding objects is conserved. A.)True B.)False

B.)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.

Momentum is a conserved quantity; the momentum of an object is never changed. A.)True B.)False

B.)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.

Total momentum is always conserved between any two objects involved in a collision. A.)True B.)False

B.)FALSE - Total momentum is conserved only if the collision can be considered isolated from the influence of net external forces.

The velocity change of two respective objects involved in a collision will always be equal. A.)True B.)False

B.)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.

Two identical objects are movinA.)Tg in opposite directions at the same speed. The forward moving object will have the greatest momentum. A.)True B.)False

B.)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.

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. a. True b. False

B.)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.

Consider the concepts of work and energy (presuming you have already studied it) and those of impuse and momentum. Force and time is related to momentum change in the same manner as force and displacement pertains to ___________. a. impulse b. work c. energy change d. velocity e. none of these.

C-A force multiplied by a time gives an impulse which will cause (and be equal to) a momentum change. In the same manner, a force multiplied by a displacement gives work which will cause (and be equal to) an energy change. Take the time to reread those two sentences because it relates two big concepts.

A 5-N force is applied to a 3-kg ball to change its velocity from +9 m/s to +3 m/s. This impulse causes the momentum change of the ball to be ____ kg•m/s. a. -2.5 b. -10 c. -18 d. -45 e. none of these

C-Don't make this harder than it is; the momentum change of an object can be found if the mass and the velocity change are known. In this equation, m=3 kg and the velocity change is -6 m/s. When finding the velocity change, always subtract the initial velocity from the final velocity (vf - vi). There is a second means of determining the momentum change of an object (though it does not need to be used in this problem). The momentum change can also be found if the force and the time are known. Multiplying force*time yields the impulse and the impulse equals the momentum change.

A 5-N force is applied to a 3-kg ball to change its velocity from +9 m/s to +3 m/s. The impulse experienced by the ball is ____ N•s. a. -2.5 b. -10 c. -18 d. -45 e. none of these

C-Impulse is defined as a force acting upon and object for a given amount of time. Impulse can be computed by multiplying force*time. But in this problem, the time is not known. Never fear - the impulse equals the momentum change. The momentum change in this problem is -18 kg•m/s (see question #27). Thus, the impulse is -18 N•s.

Suppose that you're driving down the highway and a moth crashes into the windshield of your car. Which undergoes the greater change is momentum? a. the moth b. your car c. both the same

C-In any collision, there are always four quantities which are the same for both objects involved in the collision. Each object experiences the same force (Newton's third law) for the same amount of time, leading to the same impulse, and subsequently the same momentum change. Only the acceleration and the velocity change can differ for the two objects. The object with the least mass always receives the greatest velocity change and acceleration.

Suppose that you're driving down the highway and a moth crashes into the windshield of your car. Which undergoes the greater force? a. the moth b. your car c. both the same

C-In any collision, there are always four quantities which are the same for both objects involved in the collision. Each object experiences the same force (Newton's third law) for the same amount of time, leading to the same impulse, and subsequently the same momentum change. Only the acceleration and the velocity change can differ for the two objects. The object with the least mass always receives the greatest velocity change and acceleration.

Suppose that you're driving down the highway and a moth crashes into the windshield of your car. Which undergoes the greater impulse? a. the moth b. your car c. both the same

C-In any collision, there are always four quantities which are the same for both objects involved in the collision. Each object experiences the same force (Newton's third law) for the same amount of time, leading to the same impulse, and subsequently the same momentum change. Only the acceleration and the velocity change can differ for the two objects. The object with the least mass always receives the greatest velocity change and acceleration.

In order to catch a ball, a baseball player naturally moves his or her hand backward in the direction of the ball's motion once the ball contacts the hand. This habit causes the force of impact on the players hand to be reduced in size principally because ___. A.)the resulting impact velocity is lessened B.)the momentum change is decreased C.)the time of impact is increased D.)the time of impact is decreased E.)none of these

C-Increasing the time over which the ball's momentum is brought to 0 will decrease the force required to stop it. Suppose a ball is coming at you with 100-units of momentum. An impulse of 100-units would be required to stop the ball. Regardless of how the impulse is accomplished (big F, little t or little F, big t), there must be 100-units of it. Imparting such an impulse over a long time results in a small force.

The firing of a bullet by a rifle causes the rifle to recoil backwards. The speed of the rifle's recoil is smaller than the bullet's forward speed because the ___. a. force against the rifle is relatively small b. speed is mainly concentrated in the bullet c. rifle has lots of mass d. momentum of the rifle is unchanged e. none of these

C-Please don't answer A (for it will make Newton roll over in his grave and he's getting quite tired of that). Perhaps you've heard that "for every action, there is an equal and opposite ...". Choice B is invalid; speed is not something that becomes concentrated or squeezed into an object. Choice D is invalid; ask anyone who's fired a rifle if the rifle is set into motion by the firing of the bullet. (Of course, since it is set in motion, its momentum is not unchanged.) Because of the large mass of the rifle, the acceleration and the recoil speed of the rifle is small.

A physics cart rolls along a low-friction track with considerable momentum. If it rolls at the same speed but has twice as much mass, its momentum is ____. a. zero b. four times as large c. twice as large d. unchanged

C-The momentum of an object is calculated as the product of mass and velocity. Thus, the momentum is directly proportional to the mass of the object. If the mass of an object is somehow doubled, the momentum is doubled as well.

Two objects, A and B, have the same size and shape. Object A is twice as massive as B. The objects are simultaneously dropped from a high window on a tall building. (Neglect the effect air resistance.) The objects will reach the ground at the same time but object A will have a greater ___. Choose all that apply. a. speed b. acceleration c. momentum d. none of the above quantities will be greater

C-The two objects free-fall at the same rate of acceleration, thus giving them the same speed when they hit the ground. The heavier object however has more momentum since momentum takes into account both the speed and the mass of the object (p=m*v).

A 0.5-kg ball moving at 5 m/s strikes a wall and rebounds in the opposite direction with a speed of 2 m/s. If the impulse occurs for a time duration of 0.01 s, then the average force (magnitude only) acting upon the ball is ____ Newtons. a. 0.14 b. 150 c. 350 d. 500 e. none of these

C-This is a relatively simple plug-and-chug into the equation F*t = m*(Delta vel.) with m=0.5 kg, t=0.01 s and Delta vel.=-7 m/s. (The change in velocity is -7 m/s since the ball must first slow down from 5 m/s to 0 m/s and then be thrown back in the opposite direction at 2 m/s.) Using these numbers and solving for force yields -350 N. The magnitude of the force is 350 N and the "-" sign indicates the direction of the force.

A 5-N force is applied to a 3-kg ball to change its velocity from +9 m/s to +3 m/s. The impulse is encountered by the ball for a time of ____ seconds. a. 1.8 b. 2.5 c. 3.6 d. 10 e. none of these

C-Use the impulse momentum change theorem with F=5 N, m=3 kg and Delta v=-6 m/s. Solving for time involves the following steps. t = m*(delta v)/F = (3 kg)*(-6 m/s) / (5 N) t = 3.6 s

Suppose that Paul D. Trigger fires a bullet from a gun. The speed of the bullet leaving the muzzle will be the same as the speed of the recoiling gun ____. A.)because momentum is conserved B.)because velocity is conserved C.)because both velocity and momentum are conserved D.)only if the mass of the bullet equals the mass of the gun E.)none of these

D-In any collision or explosion involving two objects, the momentum change for each object is the same. So both the bullet and the gun encounter the same momentum change. The momentum change is simply the mass multiplied by the velocity change. Thus, the velocity change would only be the same if their masses were the same. Otherwise, the smaller-mass object receives a greater velocity change.

Consider a karate expert. During a talent show, she executes a swift blow to a cement block and breaks it with her bare hand. During the collision between her hand and the block, the ___. A.)time of impact on both the block and the expert's hand is the same B.)force on both the block and the expert's hand have the same magnitude C.)impulse on both the block and the expert's hand have the same magnitude D.)all of the above. E.)none of the above.

D-In any collision, there are always four quantities which are the same for both objects involved in the collision. Each object experiences the same force (Newton's third law) for the same amount of time, leading to the same impulse, and subsequently the same momentum change. Only the acceleration and the velocity change can differ for the two colliding objects. The lower mass object always receives the greater velocity change and acceleration.

It is NOT possible for a rocket to accelerate in outer space because ____. List all that apply. A.)there is no air in space B.)there is no friction in space C.)there is no gravity in outer space D.)... nonsense! Rockets do accelerate in outer space.

D-Rockets accelerate in outer space by means of Newton's third law of motion. It does not matter that there is no air outside of the rocket. Rockets produce their own gas by burning fuels. The combustion of rocket fuels produces gaseous products. The rocket's thrusters push these gases backwards (or rightwards, or leftwards, or ...) and the gases push the rocket forwards (or leftwards, or rightwards, or ...). Thus, rockets indeed can and do accelerate in outer space.

When a mass M experiences a velocity change of v in a time of t, it experiences a force of F. Assuming the same velocity change of v, the force experienced by a mass of (1/2)M in a time of 4t is ____. a. 2F b. 8F c. (1/2)*F d. (1/8)*F e. none of these

D-The impulse-momentum change theorem states that F*t = m*(Delta vel.). This equation can be rearranged to locate the F by itself on one side of the equation; rearranging yields F = m*(Delta vel.)/t The equation shows that force is directly related to the mass, directly related to the change in velocity, and inversely related to the time. So any change in mass will result in the same change in force; and any change in time will result in the inverse effect upon the force. In this case, halving the mass (from M to 1/2-M) will halve the force and quadrupling the time (from t to 4t) will quarter the force. The combined effect of these two changes will make the new force eight times smaller (i.e., one-eighth the size) than the old force. This is a case of where equations can be a guide to thinking about how a change in one variable (or two variables) impacts other dependent variables.

Three boxes, X, Y, and Z, are at rest on a table as shown in the diagram at the right. The weight of each box is indicated in the diagram. The net or unbalanced force acting on box Y is _____. a. 4 N down b. 5 N down c. 5 N up d. 10 N up e. zero

E-If an object is at rest, then all the forces acting upon the object must be zero. The net force on any one of the boxes is 0 Newtons. Subsequently, in each case, the support force (which we have called the "normal force throughout this course) acting upwards on any of the boxes must be equal to the force of gravity on that box (i.e., the weight) plus the amount of load exerted from above (which would be equivalent to the weight of the other boxes located above the box). So for box Y, the support force acting upward would be equal to 9 N while the net force is still 0 Newtons. And for box Z, the support force is 19 N, sufficient to balance the 10-N gravitational force plus the 9-N of force resulting from the other two boxes bearing down on it.

When a mass M experiences a velocity change of v in a time of t, it experiences a force of F. Assuming the same velocity change of v, the force experienced by a mass of (1/2)M in a time of (1/2)t is ____. a. 2F b. 4F c. (1/2)*F d. (1/4)*F e. none of these

E-The impulse-momentum change theorem states that F*t = m*(Delta vel.). This equation can be rearranged to locate the F by itself on one side of the equation; rearranging yields F = m*(Delta vel.)/t The equation shows that force is directly related to the mass, directly related to the change in velocity, and inversely related to the time. So any change in mass will result in the same change in force; and any change in time will result in the inverse effect upon the force. In this case, halving the mass (from M to 1/2-M) will half the force and halving the time (from t to 1/2-t) will double the force. The combined effect of these two changes will make the new force the same size as the old force. This is a case of where equations can be a guide to thinking about how a change in one variable (or two variables) impacts other dependent variables.

Momentum is a vector quantity. A.)True B.)False

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.

Cars are equipped with padded dashboards. In collisions, the padded dashboards would be safer than non-padded ones because they ____. List all that apply. a. increase the impact time b. decrease an occupant's impulse c. decrease the impact force d. none of the above

A and C-Both A and C are correct. Padded dashboard serve to increase the time over which the momentum of a passenger is reduced to zero. With this increase in time, there is a decrease in force (big T, little f). The impulse acting upon the passenger is not changed. The passenger still must have his/her mass slowed down from the pre-impact velocity to zero velocity. This means the velocity change is the same whether the collision occurs with a padded dashboard, an air bag or a glass windshield. Since the velocity change is independent of the collision time, the momentum change and the required impulse are also independent of the collision time.

An object which experiences a net impulse will definitely experience a momentum change. A.)True B.)False

A.)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.

Objects involved in collisions encounter impulses. A.)True B.)False

A.)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.

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. A.)True B.)False

B.)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.

A truck driving along a highway road has a large quantity of momentum. If it moves at the same speed but has twice as much mass, its momentum is ________________. a. zero b. quadrupled c. doubled d. unchanged

C-Momentum is directly related to the mass of the object. So for the same speed, a doubling of mass leads to a doubling of momentum.

Consider the head-on collision between a lady bug and the windshield of a high speed bus. Which of the following statements are true? List all that apply. A.)The magnitude of the force encountered by the bug is greater than that of the bus. B.)The magnitude of the impulse encountered by the bug is greater than that of the bus. C.)The magnitude of the momentum change encountered by the bug is greater than that of the bus. D.)The magnitude of the velocity change encountered by the bug is greater than that of the bus. E.)The magnitude of the acceleration encountered by the bug is greater than that of the bus.

D and E-In any collision between two objects, the force, impulse, and momentum change are the same for each object. (This makes statements A, B, and C false.) However, the smaller mass object encounters a greater acceleration and velocity change. (This makes statements D and E true).