Physics lecture final
A box sliding on a frictionless flat surface runs into a fixed spring, which compresses a distance x to stop the box. If the initial speed of the box were doubled, how much would the spring compress in this case? a) half the height b) the same height c) square root 2 times the height d) twice the height e) four times the height
Use energy conservation: -initial energy: E=KE=1/2mv>2 -final energy: Ef= PE=1/2kx>2 conservation of energy: Ei= 1/2mv>2= Ef=1/2kx>2 so mv>2=kx>2 so if v doubles, x doubles
An object at rest begins to rotate with a constant angular acceleration. If this object has angular velocity w at the same time t, what was its angular velocity at time 1/2t? a) 1/2w b) 1/4w c) 3/4w d) 2w e) 4w
a) 1/2w linear dependence on time.
A plane is taking off from Houston airport and is coming back after going around the Earth (radius= 6353 km) a) 39897 km b) 0 km
a) 39897 km Here, total displacement = 2 * pi * r= 2 * 3.14 * 6353 = 39897 km
You throw a ball straight up into the air. After it leaves your hand, at what point in its flight does it have the maximum value of acceleration? a) Its acceleration is constant everywhere b) At the top of its trajectory c) Halfway to the top of its trajectory d) Just after it leaves your hand e) Just before it returns to your hand on the way down
a) Its acceleration is constant everywhere a accelaration is constant everywhere because a=g
The dimensional equivalent of the quantity impulse in terms of the fundamental quantities (mass, length, time) is which of the following? a. MLT-1 b. ML2T-2 c. MLT d. MLT-2
a) MLT-1
Two paths lead to the top of a big hill. One is steep and direct, while the other is twice as long but less steep. How much more potential energy would you gain if you take the longer path? a) the same b) twice as much c) four times as much d) half as much e) you gain no PE in either case
a) The same Since your vertical position (height) changes by the same amount in each case, the gain in potential energy is the same.
Given than A+B=C, and that A2+B2=C2, how are vectors A & B oriented with respect to each other? a) They are perpendicular to each other b) They are parallel and in the same direction c) They are parallel but in the opposite direction d) They are at 45 degrees to each other e) They can be at any angle to each other
a) They are perpendicular to each other Note that the magnitudes of the vectors satisfy the Pythagorean Theorem. This suggests that they form a right triangle, with vector C as the hypotenuse. Thys A and B are the legs of the right triangle and are therefore perpendicular
Is it possible for the gravitational PE of an object to be negative? a) Yes b) No
a) Yes Gravitational PE is mgh, where height h is measured relative to some arbitrary reference level where PE=0. For example, a book on a table has positive PE if the zero reference level is chosen to be the floor. However, if the ceiling is the zero level, then the book has negative PE on the table. It is only differences (or changes) in PE that have any physical meaning
If the distance to the Moon were doubled, then the force of attraction between Earth and the Moon would be: a) one quarter b) one half c) the same d) two times e) four times
a) one quarter The gravitational force depends inversely on the distance squared (F=G(Mm/R>2). So if you increase the distance by a factor of 2, the force will decrease by a factor of 4
Bonnie sits on the outer rim of a merry-go-round, and Klyde sits midway between the center and the rim. The merry-go-round makes one revolution every 2 seconds. Klyde's angular velocity is a) same as Bonnie's b) twice Bonnie's c) half of Bonnie's d) 1/4 of Bonnie's e) four times Bonnie's
a) same as Bonnie's
You and your dog go for a walk to a nearby park. On the way, your dog may take short side trips to chase squirrels, examine fire hydrants, and so on. When you arrive at the park, do you and your dog have the same displacement? a) Yes b) No
a) yes
If the velocity of a particle is 0 can the particles acceleration be 0? a) Yes b) No
a) yes if a particle is at rest, then its velocity is 0 and so is its acceleration hence if a particle's velocity is 0 , its acceleration can be 0
The number 0.000 17 has how many significant figures? a. 2 b. 3 c. 5 d. 6
a. 2
The first displacement is 6 m and the second displacement is 3 m. They cannot add together to give a total displacement of: a. 2 m. b. 3 m. c. 6 m. d. 9 m.
a. 2 m
According to Kepler's second law, Halley's Comet circles the Sun in an elliptical path with the Sun at one focus of the ellipse. What is at the other focus of the ellipse? a. nothing b. the Earth c. The comet itself passes through the other focus. d. The tail of the comet stays at the other ellipse
a. nothing
In a 2 dimensional Cartesian coordinate system the y-component of a given vector is equal to that vector's magnitude multiplied by which trigonometric function, with respect to the angle between vector and y-axis? a. sine b. cosine c. tangent d. cotangent
a. sine
Which of the following is not a vector quantity? a. temperature b. velocity c. acceleration d. displacement
a. temperature
Displacement is which of the following types of quantities? a. vector b. scalar c. magnitude d. dimensional
a. vector
Which of the following is an example of a vector quantity? a. velocity b. temperature c. volume d. mass
a. velocity
A cannon sits on a stationary railroad flatcar with a total mass of 1000 kg. When a 10-kg cannon ball is fired to the left at a speed of 50 m/s, what is the recoil speed of the flatcar? a) 0 m/s b) 0.5 m/s to the right c) 1 m/s to the right d) 20 m/s to the right e) 50 m/s to the right
b) 0.5 m/s to the right Since the initial momentum of the system was zero, the final total momentum must also be zero. Thus the final momenta of the cannon ball and the flatcar must be equal and opposite Pcannonball= (10kg)(50 m/s)=500 kg-m/s Pflatcar= 500 kg-m/s= (1000 kg) (0.5 m/s)
Two satellites A and B of the same mass are going around Earth in concentric orbits. The distance of satellite B from Earth's center is twice that of satellite A. What is the ratio of the centripetal force acting on B compared to that acting on A? a) 1/2 b) 1/4 c) 1/2 d) same e) 2
b) 1/4 using the law of gravitation: F=G(Mm/R>2)
An object at rest begins to rotate with a constant angular acceleration. If this object rotates through an angle theta in the time t, through what angle did it rotate in time 1/2t? a) 1/2 theta b) 1/4 theta c) 3/4 theta d) 2 theta e) 4 theta
b) 1/4 theta the angular displacement is theta= 1/2 at>2 (starting from rest), and there is a quadratic dependence on time.
You throw a ball upward with an initial speed of 10 m/s. Assuming that there is no air resistance, what is its speed when it returns to you? a) More than 10 m/s b) 10 m/s c) Less than 10 m/s d) Zero e) Need more information
b) 10 m/s The ball is slowing down on the way up due to gravity. Eventually it stops. Then it accelerates downward due to gravity (again). Since a=g on the way up and on the way down, the ball reaches the same speed when it gets back to you as it had when it left.
A projectile is launched from the ground at an angle of 30 degrees. At what point in its trajectory does this projectile have the least speed? a) Just after it is launched b) At the highest point in its flight c) Just before it hits the ground d) Halfway between the ground and the highest point e) Speed is always constant
b) At the highest point in its flight the speed is smallest at the highest point of its flight path because the y-component of the velocity is zero
Bonnie sits on the outer rim of a merry-go-round, and Klyde sits midway between the center and the rim. The merry-go-round makes one revolution every 2 seconds. Who has the larger linear (tangential) velocity? a) Klyde b) Bonnie c) both the same d) liner velocity is zero for both
b) Bonnie linear speeds v will be different because Bonnie is located further out (larger radius)
The straight-line distance and direction between two points is called a) Velocity b) Displacement c) Distance d) Speed e) Length
b) Displacement
The magnitude of a displacement, compared with that of a distance is: a) None of these; the two cannot be compared b) Less than or equal to it c) Always equal to it d) Greater than or equal to it
b) Less than or equal to it
You and your dog go for a walk to a nearby park. On the way, your dog may take short side trips to chase squirrels, examine fire hydrants, and so on.Have you traveled the same distance? a) Yes b) No
b) No
Two objects are known to have the same momentum. Do these two objects necessarily have the same KE? a) Yes b) No
b) No If object #1 has mass m and speed v, and object #2 has mass 1/2m and speed 2v, they will both have the same momentum. However, since KE=1/2mv>2, we see that object #2 has twice the KE of object #1, due to the fact that the velocity is squared.
A system of particles is known to have a total momentum of zero. Does it necessarily follow that the total kinetic energy of the system is also zero? a) Yes b) No
b) No Momentum is a vector, so the fact that ptot=0 does not mean that the particles are at rest! THey could be moving such that their momenta cancel out when you add up all of the vectors. In that case, since they are moving, the particles would have non-zero KE.
Is it possible to do work on an object that remains at rest? a) Yes b) No
b) No Work requires that a force acts over a distance. If an object does not move at all, there is no displacement, and therefore no work done.
Two forces produce the same torque. Does it follow that they have the same magnitude? a) Yes b) No c) depends
b) No because torque is the product of force times distance, two different forces that act at different distances could still give the same torque.
Can the equation of kinematics be used in a situation where the acceleration varies with time? a) Yes b) No
b) No the basic kinematics equation such as v^2 = u^2 + 2ad cannot be used with varying acceleration. They can be used with 0 or constant acceleration
From the same height (and at the same time), one ball is dropped and another ball is fired horizontally. Which ball has the greater velocity at ground level? a) The dropped ball b) The fired ball c) Neither- they both have the same velocity on impact d) It depends on how hard the ball was thrown
b) The fired ball Both balls have the same vertically velocity when they hit the ground (since they are both acted on by gravity for the same time). However, the fired ball also has a horizontal velocity. When you add the two components vectorially the fired ball has a larger net velocity when it hits the ground
In a baseball game, the catcher stops a 90-mph pitch. What can you say about the work done by the catcher on the ball? a) catcher has done positive work b) catcher has done negative work c) catcher has done zero work
b) catcher has done negative work The force exerted by the catcher is opposite in direction to the displacement of the ball, so the work is negative. Or using the definition of work (W=Fd cos theta), since theta=180, then W<0. Note that because the work done on the ball is negative, its speed decreases.
Two spheres have the same radius and equal masses. One is made of solid aluminum, and the other is made from a hollow shell of gold. Which one has the bigger moment of inertia about an axis through its center? a) solid aluminum b) hollow gold c) same
b) hollow gold Moment of inertia depends on mass and distance from the axis squared. It is bigger for the shell since its mass is located farther from the center
A figure skater spins with her arms extended. When she pulls in her arms, she reduces her rotational inertia and spins faster so that her angular momentum is conserved. Compared to her initial rotational kinetic energy, her rotational kinetic energy after she pulls in her arms must be: a) the same b) larger because she is rotating faster c) smaller because her rotational inertia is smaller
b) larger because she is rotating faster
You weigh yourself on a scale inside an airplane that is flying with constant speed at an altitude of 20,000 feet. How does your measured weight in the airplane compare with your weight as measured on the surface of the Earth? a) greater than b) less than c) same
b) less than At a high altitude, you are farther away from the center of Earth. therefore, the gravitational force in the airplane will be less than the force that you would experience on the surface of the earth
a net force of 200 N acts on a 100 kg boulder, and a force of the same magnitude acts on a 130 g pebble. How does the rate of change of the boulder's velocity compare to the rate of change of the pebble's velocity? a) greater than b) less than c) equal to
b) less than The rate of change of velocity is the acceleration. Remember that a= v/t. The acceleration is related to the force by Newton's 2nd law (F=ma), so the acceleration of the boulder is less than that of the pebble (for the same applied force) because the boulder is much more massive
Consider two elastic collisions: 1) a golf ball with speed v hits a stationary bowling ball head-on. 2) a bowling ball with speed v hits a stationary golf ball head-on. In which case does the golf ball have the greater speed after the collision? a) situation 1 b) situation 2 c) both the same
b) situation 2 Remember that the magnitude of the relative velocity has to be equal before and after the collision! case 1= the bowling ball will almost remain at rest, and the golf ball will bounce back with speed close to v Case 2= the bowling ball will keep going with speed close to v, hence the golf ball will rebound with speed close to 2v
Suppose that the speedometer of a truck is set to read the linear speed of the truck, but uses a device that actually measures the angular speed of the tires. If larger diameter tires are mounted on the truck instead, how will that affect the speedometer reading as compared to the true linear speed of the truck? a) speedometer reads a higher speed than the true linear speed b) speedometer reads a lower speed than the true linear speed c) speedometer still reads the true linear speed
b) speedometer reads a lower speed than the true linear speed tire radius is larger than before
Two boxes, one heavier than the other, are initially at rest on a horizontal frictionless surface. The same constant force F acts on each one for exactly 1 second. Which box has the larger velocity after the force acts? a) the heavier one b) the lighter one c) both the same
b) the lighter one The force is related to acceleration by Newton's 2nd law (F=ma). The lighter box therefore has the greater acceleration, and will reach a higher speed after the 1 sec time interval
A small beanbag and a bouncy rubber ball are dropped from the same height above the floor. They both have the same mass. Which one will impart the greater impulse to the floor when it hits? a) the beanbag b) the rubber ball c) both the same
b) the rubber ball Both objects reach the same speed at the floor. However, while the beanbag comes to rest on the floor, the ball bounces back up with nearly the same speed as it hit. Thus, the change in momentum for the ball is greater, because of the rebound. The impulse delivered by the ball is twice that of the beanbag beanbag= P=pf-pi=0-(-mv)=mv rubber ball= P= pf-pi= mv- (-mv)= 2mv
Starting from rest, a wheel undergoes constant angular acceleration for a period of time T. At what time after the start of rotation does the wheel reach an angular speed equal to its average angular speed for this interval? a. 0.25 T b. 0.50 T c. 0.67 T d. 0.71 T
b. 0.50 T
An object moves at a constant velocity of 11 m/s to the southwest for an interval of 20 s. Halfway through this interval, what is the magnitude of its instantaneous velocity? a. It can be any value from 0 to 22 m/s. b. 11 m/s c. 5.5 m/s d. More information is needed.
b. 11 m/s instantaneous velocity is the same as constant velocity
A student adds two vectors with magnitudes of 200 and 40. Which one of the following is the only possible choice for the magnitude of the resultant? a. 100 b. 200 c. 260 d. 40
b. 200
Consider a point on a bicycle wheel as the wheel turns about a fixed axis, neither speeding up nor slowing down. Compare the linear and angular velocities of the point. a. Both are constant. b. Only the angular velocity is constant. c. Only the linear velocity is constant. d. Neither is constant.
b. Only the angular velocity is constant.
Jeff throws a ball straight up. For which situation is the vertical velocity zero? a. on the way up b. at the top c. on the way back down d. none of the above
b. at the top
In a 2 dimensional Cartesian coordinate system the x-component of a given vector is equal to that vector's magnitude multiplied by which trigonometric function, with respect to the angle between vector and x-axis? a. sine b. cosine c. tangent d. cotangent
b. cosine
Vector points north and vector points east. If = - , then vector points: a. north of east. b. south of east. c. north of west. d. south of west.
b. south of east. to add vectors, take the tail end of one arrow and line it up in the arrowhead end of the other. Then you draw a line from the tail of one arrow to the head of the second arrow and that is the result. when subtracting a vector, its the same thing as adding a vector pointing in the opposite direction. just take the arrow, reverse it 180 degrees and add to the other one. to find C= B-A, first find the arrow opposite to A which is south. Then line this arrow up tai 2head with arrow B pointing East, and draw the resulting arrow from the tail of the first to the head of the second
A v vs. t graph is drawn for a ball moving in one direction. The graph starts at the origin and at t = 5 s the acceleration of the ball is zero. We know that at t = 5 s, a. the slope of the curve is non zero. b. the velocity of the ball is not changing. c. the curve is not crossing the time axis. d. the curve is at v = 0, t = 0.
b. the velocity of the ball is not changing.
The kinetic energy of an object is quadrupled. Its momentum will change by what factor? a. zero b. two c. eight d. four
b. two KE= 1/2mv>2
Which type of quantity is characterized by both magnitude and direction? a. scalar b. vector c. trigonometric d. algebraic variable
b. vector
You tie a rope to a tree and you pull on the rope with a force of 100 N. What is the tension in the rope? a) 0 N b) 50 N c) 100 N d) 150 N e) 200 N
c) 100 N The tension in the rope is the force that the rope feels across any section of it (or that you wouls feel if you replaced a piece of the rope). Since you are pulling with a force of 100 N that is the tension in the rope
Two tug-of-war opponents each pull with a force of 100 N on opposite ends of a rope. What is the tension in the rope? a) 0 N b) 50 N c) 100 N d) 150 N e) 200 N
c) 100 N The tension is not 200!! whether the other end of the rope is pulled by a person, or pulled by a tree, the tension in the rope is still 100 N!!
You are adding vectors of length 20 and 40 units. What is the only possible resultant magnitude that you can obtain out of the following choices? a) 0 b) 18 c) 37 d) 64 e) 100
c) 37 The minimum resultant occurs when the vectors are opposite, giving 20 units. The maximum resultant occurs when the vectors are aligned, giving 60 units. Anything in between is also possible, for angles between 0 and 180
The spring-loaded gun can launch projectiles at different angles with the same launch speed. At what angle should the projectile be launched in order to travel the greatest distance before landing? a) 15 degrees b) 30 degrees c) 45 degrees d) 60 degrees e) 75 degrees
c) 45 degrees a steeper angle lets the projectile stay in the air longer, but it does not travel so far because it has a small x-component of velocity. on the other hand, a shallow angle gives a large x-velocity, but the projectile is not in the air for very long. the compromise comes at 45 degrees, although the result is best seen in a calculation of the range formula
You kick a smooth flat stone out on a frozen pond. The stone slides, slows down, and eventually stops. You conclude that: a) The force pushing the stone forward finally stopped pushing on it b) No net force acted on the stone c) A net force acted on it all along d) The stone simply ran out of steam e) The stone has a natural tendency to be at rest
c) A net force acted on it all along after the stone was kicked, no force was pushing it along! However, there must have been some force acting on the stone to slow it down and stop it. This would be friction
When we add a displacement vector to another displacement vector, the result is: a) A velocity b) An acceleration c) Another displacement d) A scalar
c) Another displacement
If each component of a vector is doubled, what happens to the angle of that vector? a) It doubles b) It increases, but by less than double c) It does not change d) It is reduced by half e) It decreases, but not as much as half
c) It does not change The magnitude of the vector clearly doubles if each of its components is doubled. But the angle of the vector is given by tan theta=2y/2x, which is the same as tan theta= y/s (the original angle)
Alice and Bill are at the top of a building. Alice throws her ball downward. Bill simply drops his ball., which ball has the greater acceleration just after release? a) Alice's ball b) It depends on how hard the ball was thrown c) Neither- they both have the same acceleration d) Bills ball
c) Neither- they both have the same acceleration Both balls are in free fall once they are released, therefore they both feel the acceleration due to gravity. This acceleration is independent of the initial velocity of the ball.
Consider a cart on a horizontal frictionless table. What would have to be done in order to have the cart continue with constant acceleration? a) Push the cart harder before release b) Push the cart longer before release c) Push the cart continuously d) Change the mass of the cart e) It is impossible to do that
c) Push the cart continuously In order to achieve a non-zero acceleration, it is necessary to maintain the applied force. The only way to do this would be to continue pushing the cart as if moves down the track. This will lead us to a discussion of Newton's second law
From the same height (and at the same time), one ball is dropped and another ball is fired horizontally. Which one will hit the ground first? a) The dropped ball b) The fired ball c) They both hit at the same time d) It depends on how hard the ball was fired e) It depends on the initial height
c) They both hit at the same time Both of the balls are falling vertically under the influence of gravity. They both fall from the same height. Therefore, they will hit the ground at the same time. The fact that one is moving horizontally is irrelevant- remember that the x and y motions are completely independent
Paul and Kathleen start from rest at the same time and the same height on frictionless water slides with different shapes. At the bottom, whose velocity is greater? a) Paul b) Kathleen c) both the same
c) both the same conservation of energy: Ef=mgh=Ef=1/2mv>2 Since they both start from the same height, they have the same velocity at the bottom
Two boxes, one heavier than the other, are initially at rest on a horizontal frictionless surface. The same constant force F acts on each one for exactly 1 second. Which box has more momentum after the force acts? a) the heavier one b) the lighter one c) both the same
c) both the same we know Fav= change in P/ change in t so impulse P=Fave (change in t) In this case F and change in t are the same for both boxes! Both boxes will have the same final momentum
a net force of 200 N acts on a 100 kg boulder, and a force of the same magnitude acts on a 130 g pebble. How does the rate of change of the boulder's momentum compare to the rate of change of the pebble's momentum? a) greater than b) less than c) equal to
c) equal to The reate of change of momentum is, in fact, the force. Remember that F= change in P/change in t. Since the force exerted on the boulder and the pebble is the same, then the reate of change of momentum is the same.
You throw a ball straight up into the air. In addition to gravity, the ball feels a force due to air resistance. Compared to the time it takes the ball to go up, the time it takes to come back down is: a) smaller b) the same c) greater
c) greater Due to air friction, the ball is continuously losing mechanical energy. Therefore it has less KE (and consequently a lower speed) on the way down. Thismeans it will take more time on the way down
When a bullet is fired from a gun, the bulled and the gun have equal and opposite momenta. If this is true, then why is the bullet deadly? (whereas it is safe to hold the gun while it is fired) a) it is much sharper than the gun b) it is smaller and can penetrate your body c) it has more KE than the gun d) it goes a longer distance and gains speed e) it has more momentum than the gun
c) it has more KE than the gun While it is true that the magnitudes of the momenta of the gun and the bullet are equal, the bullet is less massive and so it has much higher velocity. Since KE is related to V2, the bullet ahs considerably more KE and therefore can do more damage on impact
A system of particles is known to have a total kinetic energy of zero. What can you say about the total momentum of the system? a) momentum of the system is positive b) momentum of the system is negative c) momentum of the system is zero d) you cannot say anything about the momentum of the system
c) momentum of the system is zero Since the total KE is 0, this means that all of the particles are ar rest (v=0). Therefore, since nothing is moving, the total momentum of the system must also be zero
Two stones, one twice the mass of the other, are dropped from a cliff. In the previous question, just before hitting the ground, what is the final speed of the heavy stone compared to the light one? a) quarter as much b) half as much c) the same d) twice as much e) four times as much
c) the same all freely falling objects fall at the same rate, which is g. Since the acceleration is the same for both, and the distance is the same, then the final speeds will be the same for both stones
If a glass of water is on a table with a piece of paper under it, it is relatively easy to pull the paper out without disturbing the glass very much if the pull is done very quickly. This is because, with a quick pull: a. the force on the glass will be less. b. the momentum of the paper will be greater. c. the time for the pull will be less d. the coefficient of kinetic friction will be less.
c) the time for the pull will be less
Which is stronger, Earth's pull on the Moon, or the Moon's pull on Earth? a) the Earth pulls harder on the Moon b) the Moon pulls harder on the Earth c) they pull on each other equally d) there is no force between the Earth and the Moon e) it depends upon where the Moon is in its orbit at that time
c) they pull on each other equally By Newton's 3rd law, the forces are equal and opposite
If the displacement of an object, x, is related to velocity, v, according to the relation x=Av, the constant, A, has the dimension of which of the following? a) acceleration b) length c) time d) area
c) time
If a is acceleration, v is velocity, x is position, and t is time, then which equation is not dimensionally correct? a) t= x/v b) a=v>2/x c) v=a/t d) t>2= 2x/a
c) v=a/t
The prefixes which are abbreviated p, n, and G represent which of the following? a. 10-2, 10-6, and 1015 b. 10-9, 106, and 1010 c. 10-12, 10-9, and 109 d. 10-15, 10-6, and 1012
c. 10-12, 10-9, and 109 Pico, nano, giga
The ratio M/m of the prefixes M and m has what value? a. 10>3 b. 10>6 c. 10>9 d. 10>18
c. 10>9
A crate of weight W is being pushed across a horizontal surface by a force directed at an angle of 20° below the horizontal. What is the magnitude of the normal force on the crate? a. It is less than W. b. It equals W. c. It is more than W. d. None of the above since the coefficient of kinetic friction is not given.
c. It is more than W.
The quantity "moment of inertia" (in terms of the fundamental quantities of mass, length, and time) is equivalent to: a. ML2T2. b. ML. c. ML2. d. ML1T2.
c. ML2.
Consider a point on a bicycle wheel as the wheel makes exactly four complete revolutions about a fixed axis. Compare the linear and angular displacement of the point. a. Both are zero. b. Only the angular displacement is zero. c. Only the linear displacement is zero. d. Neither is zero.
c. Only the linear displacement is zero.
A baseball is thrown by the center fielder (from shoulder level) to home plate where it is caught (on the fly at an equal shoulder level) by the catcher. At what point is the ball's speed at a minimum? (air resistance is negligible) a. just after leaving the center fielder's hand b. just before arriving at the catcher's mitt c. at the top of the trajectory d. speed is constant during entire trajectory
c. at the top of the trajectory
A baseball is thrown by the center fielder (from shoulder level) to home plate where it is caught (on the fly at shoulder level) by the catcher. At what point does the magnitude of the vertical component of velocity have its minimum value? (air resistance is negligible) a. just after leaving the center fielder's hand b. just before arriving at the catcher's mitt c. at the top of the trajectory d. magnitude of vertical component of velocity is constant
c. at the top of the trajectory velocity slows as the ball changes direction (at the top)
In mechanics, physicists use three basic quantities to derive additional quantities. Mass is one of the three quantities. What are the other two? a. length and force b. power and force c. length and time d. force and time
c. length and time
A moderate force will break an egg. However, an egg dropped on the road usually breaks, while one dropped on the grass usually doesn't break. This is because for the egg dropped on the grass: a. the change in momentum is greater. b. the change in momentum is less. c. the time interval for stopping is greater. d. the time interval for stopping is less.
c. the time interval for stopping is greater. The added padding that is provided by the grass greatly prolongues the time during which the egg is in contact with the grass
In the terminology a 500-N block, the 500-N refers to the block's: a. mass. b. force. c. weight. d. None of the above.
c. weight.
A ball with original momentum +4.0 kgm/s hits a wall and bounces straight back without losing any kinetic energy. The change in momentum of the ball is: a. 0. b. 4.0 kgm/s. c. 8.0 kgm/s. d. -8.0kgm/s.
d) -8.0 kg m/s
Arvin the Ant is on a picnic table. He travels 30 cm eastward, then 25 cm northward, and finally 15 cm westward. What is the magnitude of Arvin's net displacement? a) 70 cm b) 57 cm c) 52 cm d) 29 cm
d) 29 cm
Consider a cart on a horizontal frictionless table. Once the cart has been given a push and released, what will happen to the cart? a) Slowly come to a stop b) Continue with constant acceleration c) Continue with decreasing acceleration d) Continue with constant velocity e) Immediately come to a stop
d) Continue with constant velocity After the cart is released, there is no longer a force acting in the x direction. this does not mean that the cart stops moving!! It simply means that the cart will continue moving with the same velocity it had at the moment of release. The initial push got the cart moving, but that force is not needed to keep the cart in motion
On a frictionless surface, a sliding box collides and sticks to a second identical box which is initially at rest. What is the final KE of the system in terms of the initial KE? a) KEf= KEi b) KEf= KEi/ 4 c) KEf= KEi/ (square rt 2) d) KEf=KEi/ 2 e) KEf= square rt 2 (KEi)
d) KEf=KEi/ 2
If two vectors are given such that A+B=0, what can you say about the magnitude and direction of vectors A & B? a) Same magnitude, but can be in any direction b) Same magnitude, but must be in same direction c) Different magnitudes, but must be in same direction d) Same magnitude, but must be in opposite directions e) Different magnitudes, but must be in opposite directions
d) Same magnitude, but must be in opposite directions The magnitudes must be the same, but one vector must be pointing in the opposite direction of the other, in order for the sume to come out to zero. you can prove this with the tip-to-tail method.
By what factor does the kinetic energy of a car change when its speed is tripled? a) no change at all b) factor of 3 c) factor of 6 d) factor of 9 e) factor of 12
d) factor of 9 Since the kinetic energy is 1/2 mv>2, if the speed increases by a factor of 3, then the KE will increase by a factor of 9.
Two stones, one twice the mass of the other, are dropped from a cliff. Just before hitting the ground, what is the kinetic energy of the heavy stone compared to the light one? a) quarter as much b) half as mush c) the same d) twice as much e) four times as much
d) twice as much consider the work done by gravity to make the stone fall distance d: change in KE=Wnet= Fdcos0 KE =mgh Thus, the stone with the greater mass has the greater KE, which is twice as big for the heavy stone.
Which formula is dimensionally consistent with an expression yielding a value for velocity? a) v=v/t>2 b) v=vx>2 c) v=v>2/t d) v=at
d) v=at
Which one of the choices below represents the preferred practice regarding significant figures when adding the following: 12.4 + 11 + 67.37 + 4.201? a. 94.971 b. 94.97 c. 95.0 d. 95
d. 95
In one-dimensional motion where the direction is indicated by a plus or minus sign, the average velocity of an object has which of the following properties? a. It is positive. b. It is negative. c. It is zero. d. It can be positive, negative, or zero.
d. It can be positive, negative, or zero.
An object is dropped from a height. Once it is moving, which of the following statements is true, at least at one point? a. Its velocity is more than its acceleration. b. Its velocity is less than its acceleration. c. Its velocity is the same as its acceleration. d. Its velocity is never equal to its acceleration.
d. Its velocity is never equal to its acceleration.
A hiker walks 200 m west and then walks 100 m north. In what direction is her resulting displacement? a. north b. west c. northwest d. None of the answers is correct.
d. None of the answers is correct. 200 m west and 100 m north would point in a direction that is not directly northwest, which would require you to travel equidescent west and north
A baseball is thrown by the center fielder (from shoulder level) to home plate where it is caught (on the fly at shoulder level) by the catcher. At what point is the magnitude of the acceleration at a minimum? (air resistance is negligible) a. just after leaving the center fielder's hand b. just before arriving at the catcher's mitt c. at the top of the trajectory d. acceleration is constant during entire trajectory
d. acceleration is constant during entire trajectory acceleration of x will be 0 after launch so horizontal velocity remains constant
Starting from rest, a wheel undergoes constant angular acceleration for a period of time T. At which of the following times does the average angular acceleration equal the instantaneous angular acceleration? a. 0.50 T b. 0.67 T c. 0.71 T d. all of the above
d. all of the above
Vector is 3 m long and vector is 4 m long. The length of the sum of the vectors must be: a. 5 m. b. 7 m. c. 12 m. d. some value from 1 m to 7 m.
d. some value from 1 m to 7 m.
As a car moves forward on a level road at constant velocity, the net force acting on the tires is: a. greater than the normal force times the coefficient of static friction. b. equal to the normal force times the coefficient of static friction c. the normal force times the coefficient of kinetic friction. d. zero.
d. zero
Amy (150 lbs) and Gwen (50 lbs) are standing on slippery ice and push off each other. If Amy slides at 6 m/s, what speed does Gwen have? a) 2 m/s b) 6 m/s c) 9 m/s d) 12 m/s e) 18 m/s
e) 18 m/s The initial momentum is zero, so the momenta of Amy and Gwen must be equal and opposite. SInce p=mv, then if Amy has 3 times more mass, we see that Gwen must have 3 times more speed
A certain vector has x & y components that are equal in magnitude. Which of the following is a possible angle for this vector in a standard x-y coordinate system? a) 30 degrees b) 180 degrees c) 90 degrees d) 60 degrees e) 45 degrees
e) 45 degrees The angle of the vector is given by tan theta= y/x. Thus tan theta=1 in this case if x and y are equal, which means that the angle must be 45
A box slides with initial velocity 10 m/s on a frictionless surface and collides inelastically with an identical box. The boxes stick together after the collision. What is the final velocity? a) 10 m/s b) 20 m/s c) 0 m/s d) 15 m/s e) 5 m/s
e) 5 m/s The initial momentum is Mv=(10)M The final momentum must be the same! The final momentum is Mtot(Vf)= (2M)Vi= (2M)(5)
A hockey puck slides on ice at constant velocity. What is the net force acting on the puck? a) More than its weight b) Equal to its weight c) Less than its weight but more than zero d) Depends on the speed of the puck e) Zero
e) Zero The puck is moving at a constant velocity, and therefore is not accelerating. Thus there must be no net force acting on the puck.
A truck initially at rest, rolls down a frictionless hill and attains a speed of 20 m/s at the bottom. To achieve a speed of 40 m/s at the bottom, how many times higher must the hill be? a) half the height b) the same height c) square root 2 times the height d) twice the height e) four times the height
e) four times the height Use energy conservation: -initial energy E=PE=mgh -final energy E=KE=1/2mv>2 Conservation of Energy: E=mgh=1/2mv>2 so gh=1/2v>2 so if V doubles, H qrauruples
You and your friend both solve a problem involving a skier going down a slope, starting from rest. The two of you have chosen different levels for y=0 in this problem. Which of the following quantities will you and your friend agree on? A) skier's PE B) skier's change in PE C) skier's final KE a) only B b) only C c) A, B and C d) only A and C e) only B and C
e) only B and C The gravitational PE depends upon the reference level but the difference PE does not! The work done by gravity must be the same in the two solutions, so PE and KE should be the same
You lift a book with your hand in such a way that it moves up at constant speed. While it is moving, what is the total work done on the book?
zero Since the net force acting on the book is zero. The work done by the hand is positive, while the work done by gravity is negative. The sum of the two is zero.
