Quick Quizzes, Reading Quizzes, Comprehensive Quizzes (Exam II)

How to calculate work done by varying force, given a curve of displacement vs force?

Work done is equal to the area under the curve between xi and xf

The feet of a standing person of mass m exert a force equal to mg on the floor, and the floor exerts an equal and opposite force upwards on the feet, which we call the normal force. During the extension phase of a vertical jump, the feet exert a force on the floor that is greater than mg, so the normal force is greater than mg. Using energy ideas, we know that work is performed on the jumper to give him or her kinetic energy. But the normal force can't perform any work here because the feet don't undergo any displacement. How is energy transferred to the jumper?

Work is actually performed by the thigh bone (the femur) on the hips as the torso moves upwards a distance h. The force on the torso is approximately the same as the normal force (since the legs are relatively light and are not moving much), and the work done by minus the work done by gravity is equal to the change in kinetic energy of the torso. At full extension the torso would continue upwards, leaving the legs behind on the ground (!), except that the torso now does work on the legs, increasing their speed (and decreasing the torso speed) so that both move upwards together.

b). Starting at the time of collision, the door exerts a leftward force on you.

You are a passenger in a car and not wearing your seat belt. Without increasing or decreasing its speed, the car makes a sharp left turn, and you find yourself colliding with the right-hand door. Which is the correct analysis of the situation? a). Before and after the collision, there is a rightward force pushing you into the door. b). Starting at the time of collision, the door exerts a leftward force on you. c). both of the above. d). neither of the above

2 > 1 = 4 > 3

You are using a wrench and trying to loosen a rusty nut (see figure). List in order of descending efficiency the arrangements shown in a figure.

during a stress test of the cardiovascular system, a patient walks and runs on a treadmill. a) is the energy expended by the patient equivalent to the energy of walking and running on the ground? b) if the treadmill is tilted upward, what effects does this have?

a) effects are the same (except for air resistance) b) effect of running uphill

a) can the kinetic energy of a system be negative? b) can the gravitational potential energy of a system be negative?

a) no b) yes

discuss whether any work is being done by each of the following agents, and if so, whether the work is positive or negative: a) chicken scratching the ground b) person studying c) crane lifting a bucket of concrete d) gravity on the bucket in part c e) leg muscles of a person in the act of sitting down

a) positive b) no work c) positive d) negative e) negative

as a simple pendulum swings back and forth, the forces acting on the suspended object are the force of gravity, the tension in the supporting cord, and air resistance. a) which of these forces, if any, does no work on the pendulum? b) which of these forces does negative work at all times during its motion? c) describe the work done by the force of gravity while the pendulum is swinging

a) tension in supporting cord b) air resistance always does negative work c) as the pendulum moves to equilibrium (middle), it loses gravitational potential energy and as the pendulum moves away from equilibrium (middle), it gains potential energy. Recall: the work done by gravity is the negative of change in PE

Describe the path of a moving object in the event that the object's acceleration is constant in magnitude at all times and perpendicular to its velocity.

a. If the acceleration is constant in magnitude and perpendicular to the velocity, the object is moving in a circular path at constant speed b. If the acceleration is parallel to the velocity, the object is either speeding up, v and a in the same direction, or slowing down, v and a in opposite directions

a bowling ball is suspended from the ceiling of a lecture hall by a strong cord. the ball is drawn away from its equilibrium position and released from rest at the tip of the demonstrator's nose. if the demonstrator remains stationary, why wouldn't the ball hit her? would she be safe if the ball were given a push from its starting position at her nose?

a. the ball wouldn't hit her because of energy lost to air resistance. if there was no air resistance, it would swing back up to starting position b. probably not, because positive work is done on the ball, and because of that, it will tend to reach a higher level than its initial position before coming to rest again

If someone told you that astronauts are weightless in Earth orbit because they are beyond the force of gravity, would you accept the statement?

no Explanation: The statement is wrong for two reasons. First, gravity is the centripetal force that keeps the astronauts and their spacecraft in orbit around the Earth, so the astronauts aren't beyond gravity's influence. Second, weight is the magnitude of the gravitational force, so astronauts inEarth orbit have weight, although it's lower than on Earth's surface. Because they are freely falling around the Earth along with their spacecraft environment, gravity doesn't press them against the cabin's walls or floor, giving rise to the feeling of weightlessness. The same feeling of weightlessness would occur in a freely falling elevator.

in most circumstances, the normal force acting on an object and the force of static friction do no work on the object. however, the reason that the work is zero is different for the two cases. explain why each does zero work

normal force is perpendicular to direction of motion; there is no change in kinetic energy for static friction, since the object remains at rest

A batter bunts a pitched baseball, blocking the ball without swinging. (a) Can the baseball deliver more kinetic to the bat and batter than the ball carries initially? (b) Can the baseball deliver more momentum to the bat and batter than the ball carries initially? Explain.

(a) No. It cannot carry more kinetic energy than it possesses. That would violate the law of energy conservation. (b) Yes. By bouncing from the object it strikes, it can deliver more momentum in a collision than it possess in its flight.

If two objects collide and one is initially at rest, (a) is it possible for both to be at rest after the collision? (b) Is it possible for only one to be at rest after the collision? Explain.

(a) No. One of the objects was in motion before collision, so the system consisting of the two particles had a nonzero momentum before impact. Since momentum is always conserved in collisions, the system must have nonzero momentum after impact, meaning that at least on of the particles must be in motion. (b) Yes. It is possible for one of the particles to be at rest after collision, provided the other particle leaves the collision with a momentum equal to the total momentum of the two-particle system before impact.

In golf, novice players are often advised to be sure to "follow through" with their swing. (a) Why does this make the ball travel a longer distance? (b) If a shot is taken near the green, very little follow-through is required. Why?

(a) The follow-through keep the club in contact with the ball as long as possible, maximizing the impulse. Thus, the ball accrues a larger change in momentum than without the follow-through, and it leaves the club with a higher velocity and travels farther. (b) With a short shot to the green, the primary factor is control, not distance. Hence, there is little of no follow-through, allowing the golfer to have a better feel for how hard he/she is striking the ball.

b). The ball undergoes the same acceleration as Earth c). The magnitude of the force the Earth exerts on the ball is greater than the magnitude of the force the ball exerts on the Earth

A ball is falling toward the ground. Which of the following statements are false? a). The force that the ball exerts on Earth is equal in magnitude to the force that Earth exerts on the ball b). The ball undergoes the same acceleration as Earth c). The magnitude of the force the Earth exerts on the ball is greater than the magnitude of the force the ball exerts on the Earth

The maximum kinetic energy occurs at the point of release and the maximum gravitational potential energy occurs at the top of the ball's trajectory

A ball is thrown straight up in the air. At what position is its kinetic energy a maximum? At what position is the gravitational potential energy of the ball a maximum? Consider only the trip up.

d). 4

A block initially at rest is allowed to slide down a frictionless ramp and attains speed V at the bottom. To achieve a speed 2V at the bottom, how many times as high must a new ramp be? a). 1 b). 2 c). 3 d). 4 e). 5 f). 6

b). The combined net work done by all three forces is zero.

A block slides at constant speed down a ramp while acted on by gravity, normal force and kinetic friction. Which of the following statements is correct? a). Each force does negative work on the block as it slides. b). The combined net work done by all three forces is zero. c). Each force does a positive work on the block as it slides. d). Each force does zero work on the block as it slides.

c). It's smaller on the tilted surface (the decrease in mechanical energy of they system is fkdeltax. this has a smaller value on the tilted surface for two reasons. (1) the force of kinetic friction fk is smaller b/c the normal force, and (2) the displacement deltax is smaller b/c a component of the gravitational force is pulling on the book in the direction opposite to its velocity.)

A book of mass m is projected with a speed v across a horizontal surface. The book slides until it stops due to the friction force between the book and the surface. The surface is now tilted 30 degrees, and the book is projected up the surface with the same initial speed v. When the book has come to rest, how does the decrease in mechanical energy of the book-Earth system compare with that when the book slid over the horizontal surface? a). It's the same b). It's larger on the tiled surface c). It's smaller on the tilted surface d). More information is needed

C If the box is about to tip over, its weight will be resting mainly on its leftmost corner. Assume that this is the starting point. Make that the pivot, then the only torque comes from gravity on the box. In cases A, B, and D, the gravitation torque makes it rotate clockwise, which increases its stability. In the case of C, the torque is counterclockwise, which makes it tip over

A box, with its center of mass of -center as indicated by the dot in the figure, is placed on an incline plane. In which of the four orientations shown, does the box tip over?

a). The tension increases to four times its original value. everything stays the same except the speed (v) which doubles. When v doubles it quadruples bc (2)^2 = 4

A boy is whirling a stone at the end of a string around his head. The string makes one complete revolution every second, and the tension in the string is T. The boy increases the speed of the stone, keeping the radius of the circle unchanged, so that the string makes two complete revolutions per second. What happens to the tension in the sting? a). The tension increases to four times its original value. b). The tension increases to twice its original value. c). The tension is unchanged. d). The tension is reduced to one half of its original value. e). The tension is reduced to one fourth of its original value.

c). moves toward the shore

A boy standing at one end of a floating raft that is stationary relative to the shore walks to the opposite end of the raft, away from the shore. As a consequence, the raft... a). remains stationary b). moves away from the shore c). moves toward the shore

c). Both vehicles experience the same magnitude change in momentum.

A car and a large truck make a head-on collision and stick together. Prior to the collision, the truck's velocity was twice that of the car. Which vehicle experiences the larger change of its momentum? a). the car. b). the truck. c). Both vehicles experience the same magnitude change in momentum. d). Impossible to determine without knowing the speeds.

c). the change in the magnitude of momentum is the same for both

A car and a large truck traveling at the same speed collide head-on and stick together. Which vehicle undergoes the larger change in the magnitude of its momentum? a). the car b). the truck c). the change in the magnitude of momentum is the same for both d). impossible to determine without more information

b). Yes Acceleration is a change in the speed and/or direction of an object. Thus, because its direction has changed, the car has accelerated and a force must have been exerted on it.

A car rounds a curve while maintaining a constant speed. Is there a net force on the car as it rounds the curve? a). No-its speed is constant. b). Yes. c). It depends on the sharpness of the curve. d). It depends on the speed of the car.

a). Yes; both can be larger. The cart's momentum has magnitude mv and its kinetic energy is ½mv². If the cart's speed increases, its momentum and kinetic energy will increase. It is not possible for the kinetic energy but not the magnitude of momentum to increase, or vice versa. Thus, answers (2) and (3) are impossible. But is it possible for the speed to increase, thus causing momentum and kinetic energy to increase? Yes! For example, the cart could be rammed from behind by something moving faster. Not all collisions are head-on! Or, it could collide head-on with an object having a much larger momentum. Even if it sticks to the object, its final speed can be larger than its initial speed (though in the opposite direction). For instance, if the cart collides head-on with a cart of mass 3m and speed v moving to the left, and energy is conserved, then the 3m cart is at rest after the collision, and the m cart is moving to the left with speed 2v. You may be thinking that momentum is always conserved in a collision, and kinetic energy is either conserved or lost depending on whether the collision is elastic or inelastic. This is true, but for the entire system, not for each individual object involved. Key Points: •If an object's kinetic energy increases, the magnitude of its momentum must also increase. •Energy and momentum can be transferred between objects during a collision, and sometimes one object ends up with more than it had to start. •When trying to figure out whether some general statement about physics is possible, think of extreme examples. For Instructors Only Most collision problems students encounter in physics are head-on and in many cases cause both objects to slow down, so students might erroneously generalize. This question helps to remedy that. Ask your students how many considered a rear-end (or even side-on) collision. Another common mistake is for students to automatically apply "momentum is conserved" or "energy is conserved or lost" ideas without thinking through what system or bodies these apply to. Some confusion is possible about whether "larger", for momentum, depends on the sign as well as the magnitude. We intend this question to be about the magnitude only, but as with all ambiguities, the best result is to have the confusion articulated and discuss how the choice of interpretation would affect students' answers.

A cart of mass m is moving with speed v. Is it possible for the cart's kinetic energy or the magnitude of its momentum to be larger after it collides with something? a). Yes; both can be larger. b). Yes; the momentum can be larger. c). Yes; the kinetic energy can be larger. d). No; it is impossible.

c). car (Newton's Second Law, ↓m, ↑ a)

A compact car and a large truck collide head on and stick together. Which vehicle undergoes the larger acceleration during the collision? a). Both experience the same acceleration. b). truck c). car d). Can't tell without knowing the final velocity of combined mass.

If two automobiles collide, they usually do not stick together. Does this mean the collision is elastic? (b) Explain why a head-on collision is likely to be more dangerous than other types of collisions.

A greater portion of the incident kinetic energy is transformed to other forms of energy in a head-on collision than in a glancing collision. Thus, the expectation of damage to passengers is greatest in head-on collisions.

b). the same as ladybug's.

A ladybug sits at the outer edge of a merry-go-round, and a gentleman bug sits halfway between her and axis of rotation (see a figure). The merry-go-round makes a complete revolution once each second. The gentleman bug's angular speed is... a). half the ladybug's. b). the same as ladybug's. c). twice the ladybug's. d). impossible to determine.

a). half the ladybug's.

A ladybug sits at the outer edge of a merry-go-round, and a gentleman bug sits halfway between her and axis of rotation (see a figure). The merry-go-round makes a complete revolution once each second. The gentleman bug's tangential speed is... a). half the ladybug's. b). the same as ladybug's. c). twice the ladybug's. d). impossible to determine.

e). +z direction

A ladybug sits at the outer edge of a merry-go-round, and a gentleman bug sits halfway between her and axis of rotation (see figure below). The merry-go-round makes a complete revolution once each second. The vector expressing ladybug's angular velocity is in the... a). +x direction b). -x direction c). +y direction d). -y direction e). +z direction f). -z direction

d). the rubber ball Because momentum is conserved in these interactions, more momentum is transferred to the bowling pin from the rubber ball than from the putty ball. Hence, the rubber ball is more likely to knock the pin over.

A person attempts to knock down a large wooden bowling pin by throwing a ball at it. The person has two balls of equal size and mass, one made of rubber and the other of putty. The rubber ball bounces back, while the ball of putty sticks to the pin. Which ball is more likely to topple the bowling pin? a). need more information. b). makes no difference. c). the ball of putty d). the rubber ball

e). one-fourth as large as the gravitational force exerted by the planet on moon 1

A planet has two moons with identical mass. Moon 1 is in a circular orbit of radius r. Moon 2 is in a circular orbit of radius 2r. The magnitude of the gravitational force exerted by the planet on Moon 2 is... a). 4 times as large b). twice as large c). the same d). half as large e). one-fourth as large as the gravitational force exerted by the planet on moon 1

e). the tangential acceleration is zero at both points

A racetrack is constructed such that two arcs of radius 80m at A and 40m at B are joined by two stretches of straight track. In a particular trial run, a driver travels at a constant speed of 50m/s for one complete lap. 1. The ratio of the tangential acceleration at A to that at B is... a). 1/2 b). 1/4 c). 2 d). 4 e). the tangential acceleration is zero at both points

a). 1/2

A racetrack is constructed such that two arcs of radius 80m at A and 40m at B are joined by two stretches of straight track. In a particular trial run, a driver travels at a constant speed of 50m/s for one complete lap. 2. The ratio of the centripetal acceleration at A to that at B is... a). 1/2 b). 1/4 c). 2 d). 4 e). the centripetal acceleration is zero at both points

b). B

A racetrack is constructed such that two arcs of radius 80m at A and 40m at B are joined by two stretches of straight track. In a particular trial run, a driver travels at a constant speed of 50m/s for one complete lap. 3. The angular speed is greatest at... a). A b). B c). It is equal at both A and B

1

A rider in a "barrel of fun" finds herself stuck with her back to the wall. Which diagram correctly shows the forces acting on her?

c). 1 rad, 5 rad

A rigid body is rotating counterclockwise about a fixed axis. Each of the following pairs of quantities represents an initial angular position and a final angular position of the rigid body. Which of the sets can occur only if the rigid body rotates through more than 180 degrees? a). 3 rad, 6 rad b). -1 rad, 1 rad c). 1 rad, 5 rad

a). perfectly inelastic b). inelastic c). inelastic

A skater is using very low-friction rollerblades. A friend throws a frisbee at her, on the straight line along which she is coasting. Describe each of the following events as an elastic, inelastic, or perfectly inelastic collision between the skater and the frisbee. a). She catches the frisbee and holds it b). She tries to catch the Frisbee, but it bounces off her hands and falls to the ground in front of her c). She catches the Frisbee and immediately throws it back with the same speed (relative to the ground) to her friend

e). The final kinetic energy is one half of the initial kinetic energy.

A sled of mass m is coasting at a constant velocity on the ice covered surface of a lake. Three birds, with a combined mass 0.5m, gently land at the same time on the sled. The sled and birds continue sliding along the original direction of motion. How does the kinetic energy of the sled and birds compare with the initial kinetic energy of the sled before the birds landed? a). The final kinetic energy is equal to the initial kinetic energy. b). The final kinetic energy is one quarter of the initial kinetic energy. c). The final kinetic energy is one third of the initial kinetic energy. d). The final kinetic energy is one ninth of the initial kinetic energy. e). The final kinetic energy is one half of the initial kinetic energy.

b). The force on B is half the force on A. F = mv^2/r. For car B traveling on the outside, the radius is 2r: FB = mv^2/ (2r) . For car A traveling on the inside, the radius is r: FA = mv^2/ r. Here m and v are constant. Therefore the force on B is 1/2 that of the force on A.

A split highway has a number of lanes for traffic. For traffic going in one direction, the radius for the inside of the curve is half the radius for the outside. One car, car A, travels on the inside while another car of equal mass, car B, travels at equal speed on the outside of the curve. Which statement about resultant forces on the cars is correct? a). The force on A is half the force on B. b). The force on B is half the force on A. c). The force on A is four times the force on B. d). The force on B is four times the force on A. e). There is no net resultant force on either as long as they stay on the road while turning.

It does not matter, her speed would be the same for each slide.

A young girl wishes to select on of the frictionless playground slides illustrated below to give her the greatest possible speed when she reaches the bottom of the side. Which of the slides should she chose?

a). The boat will move off on a line tangent to the circle because there is no force on it.

An iceboat is traveling in a circle on the ice. Halfway around the circle the sail and the steering mechanism fall off the boat. Which statement is correct? a). The boat will move off on a line tangent to the circle because there is no force on it. b). The boat will continue traveling in the circle because there is no friction. c). The boat will continue to travel in the circle because its velocity exerts a force on it d). The boat will move off tangent to the circle because there is a force on it perpendicular to the boat directed to the outside of the circle. e). The boat will move off to the outside perpendicular to the tangent line since a force directed to the outside of the circle always acts on the boat.

c). Both its velocity and acceleration are changing

An object moves in a circular path with constant speed v. Which of the following statements is true concerning the object? a). Its velocity is constant, but its acceleration is changing b). Its acceleration is constant, but its velocity is changing c). Both its velocity and acceleration are changing d). Its velocity and acceleration remain constant

a). 0

An object of mass m moves to the right with a speed v. It collides head-on with an object of mass 3m moving with speed v/3 in the opposite direction. If the two objects stick together, what is the speed of the combined object, of mass 4m, after the collision? a). 0 b). v/2 c). v d). 2v

b). the same as Chuck's

Andrea and Chuck are riding on a merry-go-round. Andrea rides on a horse at the outer rim of the circular platform, twice as far from the center of the circular platform as Chuck, who rides on an inner horse. When the merry-go-round is rotating at a constant angular speed, Andrea's angular speed is... a). twice Chuck's b). the same as Chuck's c). half of Chuck's d). impossible to determine

A more ordinary example of conservation of momentum than a rocket ship occurs in a kitchen dish-washing machine. In this device, water at high pressure is forced out of small holes on the spray arms. Use conservation of momentum to explain why the arms rotate, directing water to all dishes.

As the water is forced out of hole in the arm, the arm imparts a horizontal impulse to the water. The water then exerts an equal and opposite impulse on the spray arm, causing the spray arm to rotate in the direction opposite that of the spray.

c). The clown is trying to keep the center of mass of the ladder directly above his head so that the torque due to the gravitational force is zero.

At the circus, a clown balances a step ladder on his forehead. A few people in the audience notice that he is continually moving to keep the ladder from falling off his forehead. Why is this movement necessary? a). By rocking the ladder on his forehead, the ladder will be more stable than if it were stationary. This is similar to riding a bicycle. You can easily balance a bicycle when it's rolling, but not when it's stationary. b). This movement is not necessary. The clown is trying to make this look harder than it really is for entertainment value. The ladder will easily balance in the clown's forehead. c). The clown is trying to keep the center of mass of the ladder directly above his head so that the torque due to the gravitational force is zero. d). The clown is trying to apply a torque to the ladder in the direction opposite to other torques on the ladder.

c). They have the same kinetic energy

Bob, of mass m, drops from a tree limb at the same time that Esther, also of mass m, begins her descent down a frictionless slide. If they both start at the same height above the ground, which of the following is true about their kinetic energies as they reach the ground? a). Bob's kinetic energy is greater than Esther's b). Esther's kinetic energy is greater than Bob's c). They have the same kinetic energy d). The answer depends on the shape of the slide

One commentator remarked that the force of the explosion at the Twin Towers of the World Trade Center was strong enough to blow glass and parts of the steel structure to small fragments. Yet the television coverage showed thousands of sheets of paper floating down, many still intact. Explain how that could be.

Both the paper and the steel/glass structures experience the same Impulse(momentum) from the force of explosion. Due to the elasticity, paper experiences the force of explosion for a longer period of time which reduces the magnitude of force experienced. The steel/glass structure feels the full force because it has limited elasticity and cannot move with the force of explosion. Therefore the many remain intact.

A pendulum consists of a small object called a bob hanging from a light cord of fixed length, with the top end of the cord fixed, as represented in the figure. The bob moves without friction, swinging equally high on both sides. It moves from its turning point A through point B and reaches its maximum speed at point C. (a) At what point does the bob have nonzero radial acceleration and zero tangential acceleration? What is the direction of its total acceleration at this point? (b) At what point does the bob have nonzero tangential acceleration and zero radial acceleration? What is the direction of its total acceleration at this point? (c) At what point does the bob have both nonzero tangential and radial acceleration?What is the direction of its total acceleration at this point?

C, up Explanation: No tangential acceleration, there is no net force acting on it, component of mg along tangential direction is zero and just by looking at it you can clearly see the direction of total acceleration is upwards A, to the right downward and perpendicular to the cord Explanation: Component of mg along the rope will balance the tension but component of mg perpendicular to rope will provide acceleration so circular motion stops at that position B, to the right and upward Explanation: both tension and the component of mg perpendicular to rope is providing net force and hence acceleration

b). -1 rad, 1 rad The object arrives at the final position with the same angular speed W(Af) = W(Bf) = W (Cf) = 5 rad (for instant) Wf = Wi + (alpha x time) Acceleration (Alpha) = (Wf - Wi)/timeA (5-3)/t = 2/t B. (5 - (-1)/t = 6/t C. (5-1)/t = 4/t The correct answer is B. -1 rad, 1 rad

Consider again the pairs of angular positions below (rigid object). If the object starts from rest at the initial angular position, moves counterclockwise with constant angular acceleration, and arrives at the final angular position with the same angular speed in all three cases, for which choice is the angular acceleration the highest? a). 3 rad, 6 rad b). -1 rad, 1 rad c). 1 rad, 5 rad

It has been suggested that rotating cylinders about 10 miles long and 5 miles in diameter be placed in space for colonies. The purpose of their rotation is to simulate gravity for the inhabitants. Explain the concept behind this proposal.

Consider an individual standing against the inside wall of the cylinder with her head pointed toward the axis of the cylinder. As the cylinder rotates, the person tends to move in a straight line path tangent to the circular path followed by the cylinder wall. As a result, the person is forced against the wall, and the normal force exerted on her provides the radial force required to keep her moving in a circular path. If the rotational speed is adjusted such that this normal force is equaling magnitude to her weight on Earth, she would not be able to distinguish between the artificial gravity of the colony and ordinary gravity.

C only Can't be A because the position where force is applied matters!

Consider the three situations shown in the figure. Three forces act on the triangular object in different ways. Two of the forces have magnitude F and one of the forces has a magnitude 2F. In which case(s), if any, will the object be in equilibrium? A only B only A and B A and C C only

e. It is equal to the momentum of the heavy cart. Momentum is equal to force times time. Because the forces on the carts are equal, as are the times over which the forces act, the final momenta of the two carts are equal. Momentum = mass * velocity-We don't know velocity Momentum also = Force * timeForces are same for both, time is same fro bothMomentums are equal

Consider two carts, of masses m and 2m, at rest on a frictionless track. If you push first cart for 3s and then the other for same length of time, exerting equal force on each, how does the momentum of the light cart compare to the momentum of the heavy cart? a). It is one-half of the momentum of the heavy cart. b). It is four times larger. c). It is two time larger. d). It is one-quarter of the momentum of the heavy cart. e). It is equal to the momentum of the heavy cart.

d). it is larger (by 2 times) KE = 0.5mv² We don't know velocities, but we know momentum of both carts are equal If momentums of both are equal, then SPEED of light cart must be twice that of heavy cart. Light Cart: 0.5mv² ---- 0.5(m)((2v)²) = 2mv²Heavy Cart: 0.5mv² ----- 0.5(2m)(v²) = 1mv²

Consider two carts, of masses m and 2m, at rest on a track with negligible friction . If you push first one cart for 3s and then the other for the same length of time, exerting equal forces on each, how does the kinetic energy of the light cart compare to the kinetic energy of the heavy cart? a). can not be determined from the information given. b). It is smaller c). They are equal. d). It is larger.

d). all of the above.

Effectiveness of the force F in opening a door in Figure 8.1 is determine by... a). the force magnitude. b). the position of the application of the force. c). the angle at which the force is applied. d). all of the above.

b). relative velocities before and after collision.

Equation 6.14 in the textbook describes: a). kinetic energies before and after collision. b). relative velocities before and after collision. c). momenta before and after collision. d). none of the above.

Why do astronauts feel weightless?

First, gravity is the centripetal force that keeps the astronauts and their spacecraft in orbit around the Earth, so the astronauts aren't beyond gravity's influence. Second, weight is the magnitude of the gravitational force, so astronauts inEarth orbit have weight, although it's lower than on Earth's surface. Because they are freely falling around the Earth along with their spacecraft environment, gravity doesn't press them against the cabin's walls or floor, giving rise to the feeling of weightlessness. The same feeling of weightlessness would occur in a freely falling elevator.

d). the sum of the torques about any point must equal zero

For a body to be equilibrium under the combined action of several forces: a). all the forces must be applied at the same point b). all of the forces are composed of pairs of equal and opposite forces c). any two of these forces must be balanced by a third d). the sum of the torques about any point must equal zero

In most situations we have encountered in this chapter, frictional forces tend to reduce the KE of an object. However, frictional forces can sometimes increase an object's KE. Describe a few situations in which friction causes an increase in KE.

If a crate is located on the bed of a truck, and the truck accelerates, the friction force exerted on the crate causes it to undergo the same acceleration as the truck, assuming that the crate doesn't slip. Another example is a car that accelerates because of the frictional forces between the road surface and its tires. This force is in the direction of the motion of the car and produces an increase in the car's kinetic energy.

b). r

If a force F acts at a pivot (or at an axis of rotation), torque that F exerts on a rotating object is zero. Which of the three quantities in the formula τ = r F sin ⁡ θ is zero in this situation? a). F b). r c). θ d). both F and r are zero.

c). the collisions are all nearly elastic.

If ball 1 in the arrangement shown here is pulled back and then let go, ball 5 bounces forward. If balls 1 an 2 are pulled back and released, balls 4 and 5 bounce forward, and so on. The number of balls bouncing on each side is equal because: a). neither of the above. b). of conservation of energy only. c). the collisions are all nearly elastic. d). of conservation of momentum only.

b). 0 Joules of work.

If you displace a bucket of water weighing 100 N horizontally by 10 m your hand does... a). -100 Joules of work. b). 0 Joules of work. c). -1000 Joules of work d). 1000 Joules of work. e). 100 Joules of work.

c). c, a, d, b

In Figure 5.5 (a) - (d), a block moves to the right in the positive x-direction through the displacement Δx(vector) while under the influence of a force with the same magnitude F(vector). Which of the following is the correct order of the amount of work done by the force F(vector), from most positive to most negative? a). d, c, a, b b). c, a, b, d c). c, a, d, b

a). the objects must have momenta with the same magnitude but opposite directions

In a perfectly inelastic one-dimensional collision between two objects, what condition alone is necessary so that all of the original kinetic energy of the system is gone after the collision? a). the objects must have momenta with the same magnitude but opposite directions b). the objects must have the same mass c). the objects must have the same velocity d). the objects must have the same speed, with velocity vectors in opposite directions

d). the area under the curve.

In the case of a force varying with position, what feature of the graph of force vs. position represents the work done during a displacement? a). the beginning force times the total displacement b). none of the above. c). the maximum force times the maximum position d). the area under the curve.

A ball of clay of mass M is thrown with a speed V against a brick wall. The clay sticks to the wall and stops. Is the principle of conservation of momentum violated in this example?

Initially, the clay has momentum directed toward the wall. When it collides and sticks to the wall, neither the clay nor the wall appears to have any momentum. Thus, it is tempting to (wrongfully) conclude that momentum is not conserved. However, the "lost" momentum is actually imparted to the wall and Earth, causing both to move. Because of Earth's enormous mass, its recoil speed is too small to detect.

The earth moves in a closed almost circular orbit around the sun. Since its path is a circular orbit, the Earth is also experiencing an acceleration all the time. But this force/acceleration being at right angles to the pathof the earth does not change magnitude of the velocity or the speed with which earth revolves around the sun. So, yes the earth does have an acceleration.

Is the Earth accelerating?

A sharpshooter fires a rifle while standing with the butt of the gun against his shoulder. If the forward momentum of a bullet is the same as the backward momentum of the gun, why isn't it as dangerous to be hit by the gun as by the bullet?

It is the product mv that is the same for both the bullet and the gun. The bullet has a larger velocity and a small mass, while the gun had a small velocity and a large mass. Furthermore, the bullet carries much more KE than the gun.

Use Kepler's second law to convince yourself that Earth must move faster in its orbit during the northern hemisphere winter, when it is closest to the Sun than during the summer, when it is farthest from the Sun.

Kepler's second law says that equal areas are swept out in equal times by a line drawn from the Sun to the Earth. For this to be so, the planet must move fastest when it is closest to the Sun. This, surprisingly, occurs during the winter in the northern hemisphere.

Does a larger net force exerted on an object always produce a larger change in the momentum of the object, compared to a smaller net force? Explain.

No. Impulse (Fdeltatime) depends on the force and the time interval during which it is applied.

Does a larger net force always produce a larger change in kinetic energy than a smaller net force? Explain.

No. The change in kinetic energy of an object is equal to the net work done on it. This net work is the product of the net force acting on the object and the displacement in the direction of the force. Thus, a small magnitude force acting through a large distance may do more work (and hence produce a greater change in kinetic energy) than a large force acting through a small distance.

Relate net work done on an object, center of mass, and a person jumping into the air with arms outstretched

Note: An alternative way to think about problems that involve internal motions of an object is to note that the net work done on an object is equal to the net force times the displacement of the center of mass. Using this idea, the effect of throwing the arms upwards during the extension phase is accounted for by noting that the position of the center of mass is higher on the body with the arms extended, so that total displacement of the center of mass is greater.

d). not enough information given to tell

Object 1 has more kinetic energy than Object 2. How do the magnitudes of their momenta compare? a). p1=p2 b). p1 > p2 c). p1 < p2 d). not enough information given to tell

Your physical education teacher throws you a tennis ball at a certain velocity, and you catch it. You are now given the following choice: The teacher can throw you a medicine ball (which is much more massive than the tennis ball) with the same velocity, the same momentum, or the same kinetic energy as the tennis ball. Which option would you choose in order to make the easiest catch, and why?

Same momentum (slowest speed/velocity)

A skater is standing on a frictionless ice rink. Her friend throws a Frisbee straight at her. In which of the following cases is the largest momentum transferred to the skater? (a) The skater catches the Frisbee and holds onto it. (b) The skater catches the Frisbee momentarily, but then drops it vertically downward. (c) The skater catches the Frisbee, hold it momentarily, and throws it back to her friend.

Since the total momentum of the skater-Frisbee system is conserved, the momentum transferred to the skater equals the magnitude of the change in the Frisbee's momentum. This is greatest when the skater throws the Frisbee back after catching it.

c). Both take the same time. Because force equals the time rate of change of momentum, the two balls lose momentum at the same rate. If both balls initially have the same momentum, it takes the same amount of time to stop them.

Suppose a ping-pong ball and a bowling ball are rolling toward you. Both have the same momentum, and you exert the same force to stop each. How do the time intervals to stop them compare? a). It takes less time to stop the ping-pong ball. b). Can not be determined from the information given. c). Both take the same time. d). It takes more time to stop the ping-pong ball.

d). 8 years

Suppose an asteroid has a semimajor axis of 4AU. How long does it take the asteroid to go around the Sun? a). 2 years b). 4 years c). 6 years d). 8 years

b). -1 rad, 1 rad

Suppose the change in angular position for each of the pairs of values below occurred in 1s. Which choice represents the lowest average angular speed? a). 3 rad, 6 rad b). -1 rad, 1 rad c). 1 rad, 5 rad

True

T/F: The spring potential energy of a stretched or compressed spring is always positive

False

T/F: The total momentum and the total energy of an isolated system is always conserved in a glancing collision of two objects.

False

T/F: The work done by a force during a displacement is always a positive scalar quantity.

True

T/F: When no external force acts on a system, the total momentum of the system is conserved.

The moon can be considered a projectile that is falling around the earth, for, in fact, the moon does have a velocity that is tangential to its orbital motion. That motion is fast enough for it to fall around the earth, rather than into it.

The Moon does not fall to Earth because...

d). Yes, it is possible.

The center of gravity is a useful point at which to balance an object. For instance, a ruler can be balanced by placing its center on your finger. Is it possible for the center of gravity of an object to be located at a point where no material exists to balance the object? a). no, never b). only for very unsymmetrical objects c). It is possible in theory, but no objects have been found for which this occurs. d). Yes, it is possible.

c). The centripetal force is the net force acting on an orbiting object that maintains it in uniform circular motion.

The centripetal force is best explained by which of the following statements? a). The centripetal force is the force on an object that is directed radially outward from the center of its orbit. b). The centripetal force is the force on an orbiting object that is directed along a line that is tangent to the circle. c). The centripetal force is the net force acting on an orbiting object that maintains it in uniform circular motion. d). The centripetal force is a fundamental force of nature.

In a force vs. displacement graph, the area under the line gives the work done by the force and the work done will be the change in the K so the largest area is the most K change

The following graphs, all drawn to the same scale, represent the net force F as a function of position x for an object that moves along a straight line. Which graph represents the force that will cause the greatest gain in the kinetic energy of the object from x = 0 to x = x1? [Explain why please]

d). depends on the reference configuration for zero potential energy.

The gravitational potential energy of a system a). is always zero. b). is always positive. c). is always negative. d). depends on the reference configuration for zero potential energy.

In a force versus time curve, how would we determine impulse? What else can we say this is equal to?

The impulse imparted to the particle by the force is the area under the curve of the force versus time curve.This area is also equal to the change in momentum

An object executes circular motion with constant speed whenever a net force of constant magnitude acts perpendicular to the velocity. What happens to the speed if the force is not perpendicular to the velocity? Explain.

The speed changes Explanation: The tangential force component causes tangential acceleration

a). perfectly inelastic collisions

The statement "The momentum is conserved, the kinetic energy is not conserved and the final velocities of the two objects are the same" describes: a). perfectly inelastic collisions b). inelastic collisions c). all of the above d). elastic collisions

A pail of water can be whirled in a vertical circular path such that no water is spilled. Why does the water remain in the pail, even when the pail is upside down above your head?

The tendency of the water is to move in a straight line path tangent to the circular path followed by the container. As a result, at the top of the circular path, the water is forced against the bottom of the pail, and the normal force exerted on the water by the pail provides the radial force required to keep the water moving in its circular path.

you are re shelving books in a library. you lift a book from the floor to the top shelf. the kinetic energy of the book on the floor was zero and the kinetic energy of the book on the top shelf is zero, so there is no change in kinetic energy. yet you did some work in lifting the book. is the work kinetic energy theorem violated?

There is no violation. Choose the book as the system. You did work and the earth did work on the book. The average force you exerted just counterbalanced the weight of the book. The total work on the book is zero, and is equal to its overall change in kinetic energy, which is also zero.

b). The one with the highest mass.

Three different-mass balls are launched from the top of a building each at different angles of elevation. Each particle has the same initial kinetic energy. Which particle has the greatest kinetic energy just as it impacts with the ground? a). The one launched at the highest angle of elevation. b). The one with the highest mass. c). The one with the lowest mass. d). They all will have the same kinetic energy on impact.

d). All three balls strike the ground at the same speed

Three identical balls are thrown from the top of a building, all with the same initial speed. The first ball is thrown horizontally, the second at some angle above the horizontal, and the third at some angle below the horizontal. Neglecting air resistance, rank the speeds of the balls as they reach the ground, from fastest to slowest. a). 1, 2, 3 b). 2, 1, 3 c). 3, 1, 2 d). All three balls strike the ground at the same speed

Only 3 1 and 2 will never be in static equilibrium because the edges create non-zero net torque. RECALL - the force doesn't need to be applied in the opposite direction!

Three identical uniform rods are each acted on by two or more forces, all perpendicular to the rods. Which of the rods could be in static equilibrium if an additional force is applied at the center of mass of the rod? All three Only 1 Only 2 Only 3 Only 1 and 2

at night, you are farther away from the sun than during the day. what's more, the force exerted by the sun on you is downward into the earth at night and upward into the sky during the day. if you have a sensitive enough bathroom scale, would you appear to weight more at night than during the day? explain

To a good first approximation, your bathroom scale reading is unaffected because you, the Earth, and the scale are all in free fall in the Sun's gravitational field, in orbit around the Sun. To a precise second approximation, you weigh slightly less at noon and at midnight than you do at sunrise or sunset. The Sun's gravitational field is a little weaker at the center of the Earth than at the surface sub-solar point, and a little weaker still on the far side of the planet. When the Sun is high in your sky, its gravity pulls up on you a little more strongly than on the Earth as a whole. At midnight the Sun pulls down on you a little less strongly than it does on the Earth below you. So you can have another doughnut with lunch, and your bedsprings will still last a little longer.

b). p1 < p2

Two masses m1 and m2, with m1 < m2, have equal kinetic energy. How do the magnitudes of their momenta compare? a). not enough information is given b). p1 < p2 c). p1 = p2 d). p1 > p2

c). The force will be one-sixteenth as great.

Two objects with masses m and M are separated by a distance d. If the distance between the objects is increased to 4d, how does the gravitational force between them change? a). The force will be one-half as great. b). The force will be one-forth as great. c). The force will be one-sixteenth as great. d). The force will be four times as great. e). The force will be sixteen times as great.

b). remembering that momentum is a vector quantity that is conserved in each direction.

Two pucks on an air hockey table collide elastically. Complete the following statement: when such a collision occurs in two dimensions, the before and after velocities are best determined by: a). using the fact that momentum is conserved and that the initial speeds of the objects must equal the final speeds of the objects. b). remembering that momentum is a vector quantity that is conserved in each direction. c). making use of the work-energy theorem d). applying Newton's second law of motion and setting the net force equal to zero newtons.

b). sq. root of 1/2

Two satellites A and B of the same mass are going around Earth in concentric orbits. The distance satellite B from Earth's center is twice that of satellite A. What is the ratio of the tangential speed of B to that of A? a). 1/2 b). sq. root of 1/2 c). 1 d). sq. root of 2 e). 2

A conservative force is a force that does zero work done in a closed path. If only these forces act then the mechanical energy of the system remains conserved. Examples of conservative force: Gravitational force, spring force etc. On the other hand, non-conservative forces are those forces which cause loss of mechanical energy from the system. In the above case friction is the non-conservative force. But as we know energy can neither be created nor destroyed hence these forces convert mechanical energy into heat, sound, light etc.

What is a conservative force? What is a nonconservative force?

b). zero.

When a disk rotates counterclockwise at a constant rate about a vertical axis through its center, the tangential acceleration of a point on the rim is... a). positive. b). zero. c). negative. d). impossible to determine without more information.

a). twice Chuck's

When the merry-go-round below is rotating at a constant angular speed, Andrea's tangential speed is... Andrea and Chuck are riding on a merry-go-round. Andrea rides on a horse at the outer rim of the circular platform, twice as far from the center of the circular platform as Chuck, who rides on an inner horse. a). twice Chuck's b). the same as Chuck's c). half of Chuck's d). impossible to determine

c). the sum of the kinetic energy and the potential energy.

Which of the following is (are) conserved in an isolated system? a). the potential energy alone. b). both the potential energy and the kinetic energy c). the sum of the kinetic energy and the potential energy. d). the kinetic energy alone.

b). the force of friction.

Which of the following is not a conservative force? a). the force exerted by a spring on a particle in one dimension. b). the force of friction. c). the force of gravity. d). the electrostatic force.

a). the horizontal component of the normal force

Which one of the following forces holds a car on a frictionless banked curve? a). the horizontal component of the normal force b). the vertical component of the car's weight c). the vertical component of the normal force d). the horizontal component of the car's weight e). the reaction force to the car's weight

c

Which one of the following pictures best represents the forces that prevent the ladder from slipping while someone is standing on it?

a). conservation of kinetic energy

Which one of the following provides a basis to distinguish different types of collisions? a). conservation of kinetic energy b). conservation of mechanical energy c). conservation of impulse d). conservation of linear momentum e). conservation of mass

e). The value of G is the same everywhere in the universe, but the value of g is not.

Which one of the following statements concerning the two "gravitational constants" G, the universal gravitational constant, and g the magnitude of the acceleration due to gravity is true? a). The values of g and G depend on location. b). The values of g and G do not depend on location. c). The value of g is the same everywhere in the universe, but the value of G is not. d). The values of g and G are equal on the surface of any planet, but in general, vary with location in the universe. e). The value of G is the same everywhere in the universe, but the value of g is not.

b). A line that connects a planet to the Sun sweeps out equal areas in the plane of the planet's orbit in equal time intervals.

Which one of the following statements represents Kepler's Second Law? a). In their orbits about the Sun, every planet sweeps out the same equal area in the same equal amount of time. b). A line that connects a planet to the Sun sweeps out equal areas in the plane of the planet's orbit in equal time intervals. c). The surface area of a planet is directly proportional to the square of its orbit about the Sun. d). Every planet sweeps out the same area in a one Earth year period, making one complete orbit about the Sun. e). The area swept by the orbit of the Sun is equal to the sum of the areas swept by the planets during one Earth year period.

when a punter kicks a football, is he doing any work on the ball while the toe of his foot is in contact with it? is he doing any work on the ball after it loses contact with his toe? are any forces doing work on the ball white it is in flight?

punter is only doing work when in contact with the ball gravity and air resistance are also doing work on the ball

in a race like the indianapolis​ 500, a driver circles the track counterclockwise and feels his head pulled to one shoulder. to relieve his neck muscles from having to hold his head erect, the driver fastens a strap to one wall of the car and the other to his helmet. the length of his strap is adjusted to keep his head vertical. which shoulder does his head tend to lean towards?

right/outside of curve

in a race like the indianapolis​ 500, a driver circles the track counterclockwise and feels his head pulled to one shoulder. to relieve his neck muscles from having to hold his head erect, the driver fastens a strap to one wall of the car and the other to his helmet. the length of his strap is adjusted to keep his head vertical. what force produces the centripetal acceleration when there is no strap?

tension in the neck muscles

Δ Velocity

the area under an acceleration curve represents the change in velocity. In other words, the area under the acceleration graph for a certain time interval is equal to the change in velocity during that time interval

Distance

the area under the speed vs. time curve is equal to the distance traveled by an object. If the shape of the graph can be broken into simple geometric shapes, the total area under the line can be calculated by adding the areas of those shapes

Displacement

the area under the velocity vs. time curve is equal to the displacement of the object. If the shape of the graph can be broken into simple geometric shapes, the total area under the line can be calculated by adding the areas of those shapes

Instantaneous acceleration

the instantaneous acceleration of an object at a given time equals the slope of the tangent line to the velocity vs. time graph at that time. In the special case where the velocity vs. time graph of an object's motion is a straight line, the instantaneous acceleration of the object at any point is equal to its average acceleration

Instantaneous speed

the magnitude of the instantaneous velocity is defined as the instantaneous speed

Instantaneous velocity

the slope of the tangent line to the position vs. time graph is defined as the instantaneous velocity at that time

in a race like the indianapolis​ 500, a driver circles the track counterclockwise and feels his head pulled to one shoulder. to relieve his neck muscles from having to hold his head erect, the driver fastens a strap to one wall of the car and the other to his helmet. the length of his strap is adjusted to keep his head vertical. what happens to the force when there is a strap?

with tension in the strap, neck muscles are able to relax

If a car's wheels are replaced with wheels of greater diameter, will the reading of the speedometer change?

yes Explanation: The speedometer will be inaccurate. The speedometer measures the number of tire revolutions per second, so itsreadings will be too low.