Physics Chapter 7

An airplane is flying horizontally with a constant momentum during a time interval Δt. (a) Is there a net impulse acting on the plane during this time? Use the impulse-momentum theorem to guide your thinking. (b) In the horizontal direction, both the thrust generated by the engines and air resistance act on the plane. Considering your answer to part (a), how is the impulse of the thrust related in magnitude and direction to the impulse of the force due to the air resistance? (a) No. (b) They're equal in magnitude and opposite in direction. (a) No. (b) They're equal in both magnitude and direction. (a) Yes. (b) They're equal in both magnitude and direction. (a) Yes. (b) They're equal in magnitude and opposite in direction.

(a) No. (b) They're equal in magnitude and opposite in direction.

An ice boat is coasting on a frozen lake. Friction between the ice and the boat is negligible, and so is air resistance. Nothing is propelling the boat. From a bridge someone jumps straight down into the boat, which continues to coast straight ahead. (a) Does the total horizontal momentum of the boat plus the jumper change? (b) Does the speed of the boat itself increase, decrease, or remain the same? (a) no (b) decrease (a) yes (b) decrease (a) no (b) increase (a) yes (b) increase (a) yes (b) remain the same (a) no (b) remain the same

(a) no (b) decrease

An object slides along the surface of the earth and slows down because of kinetic friction. If the object alone is considered as the system, the kinetic frictional force must be identified as an external force that, according to Equation 7.4, decreases the momentum of the system. (a) If both the object and the earth are considered to be the system, is the force of kinetic friction still an external force? (b) Can the frictional force change the total linear momentum of the two-body system? (a) yes (b) yes (a) yes (b) no (a) no (b) yes (a) no (b) no

(a) no (b) no

(a) Can a single object have a kinetic energy and no momentum? (b) Can a group of two or more objects have a total kinetic energy that is not zero but a total momentum that is zero? (a) yes; (b) yes (a) yes; (b) no (a) no; (b) yes (a) no; (b) no

(a) no; (b) yes

A sunbather is lying on a floating raft that is staionary. She then gets up and walks to one end of the raft. Consider the sunbather and raft as an isolated system. (a) What is the velocity of the center of mass of this system while she is walking? (b) Does the raft itself move while she is walking? If so, what is the direction of the raft's velocity relative to that of the sunbather? (a) her velocity with respect to the water (b) The raft doesn't move relative to the sunbather. (a) zero (b) The raft moves toward the other end relative to the sunbather. (a) her velocity with respect to the water (b) The raft moves toward the other end relative to the sunbather. (a) zero (b) The raft doesn't move relative to the sunbather.

(a) zero (b) The raft moves toward the other end relative to the sunbather

Object 1 is moving along the x axis with an initial momentum +16 kg·m/s, where the + sign indicates that it is moving to the right. As the drawing shows, object 1 collides with a second object that is initially at rest. The collision is not head-on, so the objects move off in different directions after the collision. The net external force acting on the two-object system is zero. After the collision, object 1 has a momentum whose x component is +6 kg·m/s. What is the x-component of the momentum of object 2 after the collision? +6 kg·m/s -8 kg·m/s 0 kg·m/s +10 kg·m/s The x-component of the momentum of object 2 cannot be determined

+10 kg·m/s

Object 1 is moving along the x axis with an initial momentum +16 kg·m/s, where the + sign indicates that it is moving to the right. As the drawing shows, object 1 collides with a second object that is initially at rest. The collision is not head-on, so the objects move off in different directions after the collision. The net external force acting on the two-object system is zero. After the collision, object 1 has a momentum whose y component is -5 kg·m/s. What is the y-component of the momentum of object 2 after the collision? The y-component of the momentum of object 2 cannot be determined +16 kg·m/s 0 kg·m/s +5 kg·m/s -16 kg·m/s

+5 kg·m/s

Car One is traveling due north and Car Two is traveling due east. After the collision shown, Car One rebounds in the due south direction. Which of the numbered arrows is the only one that can represent the final direction of Car Two? 1 2 3 4 5

4

Immediately before colliding with the sculpture, the ball's speed was 10 m/s. Immediately after the collision, the ball's speed is most nearly 3 m/s. 5 m/s. 7 m/s. 8 m/s.

7 m/s

A particle is moving along the +x axis, and the graph shows its momentum p as a function of time t. Use the impulse-momentum theorem and rank (largest to smallest) the three regions according to the magnitude of the impulse applied to the particle. A, B, C A, C, B A and C (a tie), B B, A, C C, A, B

A and C (a tie), B

Six runners have masses (in multiples of m0), speeds (in multiples of v0) and travel in the directions indicated in the table. Which two runners have identical momenta? RunnerMassSpeedDirection of TravelA m0v0Due northBm0v0Due eastCm02v0Due southD2m0v0Due westEm0 v0Due northF2m02v0Due west B and C C and D A and C A and E D and F

A and E

As the name implies, the impulse-momentum theorem provides a relationship between impulse and momentum. Which one of the following statements correctly describes that relationship? An impulse is equal to the object's momentum divided by the product of the net force and the time interval during which the force acts. An impulse is equal to the product of the net force acting on the object and its momentum. An impulse is equal to the work done on an object when a net force acts on an object and it has a displacement. An impulse is equal to the change in an object's momentum that occurs when a net force acts on it. An impulse is equal to one-half of the object's momentum squared.

An impulse is equal to the change in an object's momentum that occurs when a net force acts on it.

Two objects undergo an elastic collision. The table shows four possible sets of the initial and final kinetic energies of the objects. Which is the only set that could occur? Initial Kinetic Energies(Before Collision)Final Kinetic Energies(After Collision) Object 1Object 2Object 1Object 2a.15 J0 J10 J9 Jb.8 J6 J10 J4 Jc.8 J6 J16 J-2 Jd.3 J8 J2 J6 J b d c a

B

The two objects shown in the drawing are initially moving in opposite directions. They are on a horizontal frictionless surface, so the net external force acting on them is zero. The objects collide and move apart after the collision. The table shows five possible sets of initial and final momenta for the objects. Which is the only set that could occur? Initial Momenta(Before Collision)Final Momenta(After Collision) Object 1Object 2Object 1Object 2a.+16 kg·m/s-16 kg·m/s+8 kg·m/s+12 kg·m/sb.+16 kg·m/s-6 kg·m/s+4 kg·m/s+10 kg·m/sc.+12 kg·m/s-2 kg·m/s-4 kg·m/s+14 kg·m/sd.+12 kg·m/s-28 kg·m/s-8 kg·m/s-10 kg·m/se.+6 kg·m/s-14 kg·m/s-6 kg·m/s+14 kg·m/s c a d e b

C

Two objects are involved in a completely inelastic one-dimensional collision. The net external force acting on them is zero. The table lists four possible sets of the initial momenta and kinetic energies of the two objects, as well as their final momenta and kinetic energies. Which is the only set that could occur? Initial(Before Collision)Final(After Collision) MomentumKineticEnergyMomentumKineticEnergya.Object 1:Object 2:+6 kg·m/s0 kg·m/s15 J0 J+8 kg·m/s9 Jb.Object 1:Object 2:+8 kg·m/s-2 kg·m/s5 J7 J+6 kg·m/s12 Jc.Object 1:Object 2:-3 kg·m/s+4 kg·m/s1 J6 J+1 kg·m/s4 Jd.Object 1:Object 2: 0 kg·m/s-8 kg·m/s3 J8 J-8 kg·m/s11 J a b c d

C

A particle is moving along the +x axis, and the graph shows its momentum p as a function of time t. In each of the four regions a force, which may or may not be nearly zero, is applied to the particle. In which region is the magnitudeof the force largest and in which region is it smallest? C (largest), A (smallest) B (largest), D (smallest) C (largest), B (smallest) A (largest), D (smallest) A (largest), C (smallest)

C (largest), B (smallest)

As the ball swings down from its starting point, its acceleration along the direction of motion: Stays constant at about 10 m/s. Stays constant at some other value. Increases. Decreases

Decreases

During the collision between the ball and the sculpture, the mechanical energy of the whole system: Increases. Stays the same. Decreases. We cannot determine the answer from the given information.

Decreases.

During a maneuver in space, a space craft separates into two pieces, each of mass m. Before the separation, the spacecraft was moving with a speed v. If one of the pieces is at rest after the separation, which one of the following statements concerning this maneuver is true? The maneuver does not conserve total energy. This maneuver does not conserve momentum. This maneuver conserves kinetic energy. If one piece is at rest, the other is moving with a speed 2v. One piece cannot be at rest. The must both be moving with a speed v/2.

If one piece is at rest, the other is moving with a speed 2v.

A sled of mass m is coasting on the icy surface of a frozen river. While it is passing under a bridge, a package of equal mass m is dropped straight down and lands on the sled (without causing any damage). The sled plus the added load then continue along the original line of motion. How does the kinetic energy of the (sled + load) compare with the original kinetic energy of the sled? It is the same as the original kinetic energy of the sled. It is twice the original kinetic energy of the sled. It is 1/4 the original kinetic energy of the sled. It is 1/2 the original kinetic energy of the sled. It is 3/4 the original kinetic energy of the sled.

It is 1/2 the original kinetic energy of the sled.

Which one of the following is characteristic of an inelastic collision? Total energy is not conserved. Kinetic energy is not conserved. Linear momentum is not conserved. Total mass is not conserved. The change in momentum is less than the total impulse.

Kinetic energy is not conserved.

Which one of the following statements concerning momentum is true? The momentum of an object is always positive. Momentum is a scalar quantity. Momentum and impulse are measured in the same units. Momentum is a force. The SI unit of momentum is kg · m2/s.

Momentum and impulse are measured in the same units

Neglect air resistance. As the ball swings down from its starting point, but before it collides with the sculpture, the ball's: Momentum stays the same, and mechanical energy stays the same. Momentum stays the same, but mechanical energy changes. Momentum changes, but mechanical energy stays the same. Momentum changes, and mechanical energy changes.

Momentum changes, but mechanical energy stays the same.

Concept Simulation 7.1 reviews the concepts that are pertinent in this question. In movies, Superman hovers in midair, grabs a villain by the neck, and throws him forward. Superman however, remains stationary. This is not possible, because it violates which one or more of the following? The law of conservation of energy Newton's second law Newton's third law The principle of conservation of linear momentum

Newtons Second law Newtons third law The principle of conservation of linear momentum

As the text discusses, the conservation of linear momentum is applicable only when the system of objects is an isolated system. Which of the systems listed below are isolated systems? A ball is dropped from the top of a building. The system is the ball. A ball is dropped from the top of a building. The system is the ball and the earth. A moving billiard ball collides with a stationary billiard ball on a frictionless pool table. The system is the moving ball. A car slides to a halt in an emergency. The system is the car. A space probe is moving in deep space where gravitational and other forces are negligible. The system is the space probe. Only 2 and 5 are isolated systems. Only 4 and 5 are isolated systems. Only 1 and 3 are isolated systems. Only 5 is an isolated system. Only 3 and 5 are isolated systems.

Only 2 and 5 are isolated systems.

A high-jumper, having just cleared the bar, lands on an air mattress and comes to rest. Had she landed directly on the hard ground, her stopping time would have been much shorter. Using the impulse-momentum theorem as your guide, determine which one of the following statements is correct. The air mattress exerts a greater impulse, and a greater net average force, on the high-jumper than does the hard ground. The air mattress exerts the same impulse, but a greater net average force, on the high-jumper than does the hard ground. The air mattress exerts the same impulse, but a smaller net average force, on the high-jumper than does the hard ground. The air mattress exerts a greater impulse, but a smaller net average force, on the high-jumper than does the hard ground. The air mattress exerts a smaller impulse, and a smaller net average force, on the high-jumper than does the hard ground.

The air mattress exerts the same impulse, but a smaller net average force, on the high-jumper than does the hard ground.

A stunt person jumps from the roof of a tall building, but no injury occurs because the person lands on a large, air-filled bag. Which one of the following best describes why no injury occurs? The bag provides the necessary force to stop the person. The bag reduces the impulse to the person. The bag decreases the amount of time during which the momentum is changing and reduces the average force on the person. The bag increases the amount of time the force acts on the person and reduces the change in momentum. The bag increases the amount of time during which the momentum is changing and reduces the average force on the person.

The bag increases the amount of time during which the momentum is changing and reduces the average force on the person.

Two objects are involved in an elastic collision. Which one of the following statements concerning this situation is false? The total kinetic energy before the collision is equal to the total kinetic energy after the collision. The kinetic energy of each object is the same before and after the collision. The total kinetic energy is conserved. The total momentum is conserved. The magnitude of the force exerted by each object on the other object is equal.

The kinetic energy of each object is the same before and after the collision.

Two objects constitute an isolated system. In an elastic collision between the two objects, which one of the following statements is a false statement? The magnitudes of the forces exerted by each object on the other object are equal. The total kinetic energy is conserved. The total kinetic energy before the collision is equal to the total kinetic energy after the collision. The kinetic energy of each object is the same before and after the collision. The total momentum is conserved.

The kinetic energy of each object is the same before and after the collision.

A tennis ball has a velocity of 12 m/s downward just before it strikes the ground and bounces up with a velocity of 12 m/s upward. Which statement is true concerning this situation? The momentum of the ball and the momentum of the earth both change. Both the momentum and the kinetic energy of the ball change because of the collision. Neither the momentum of the ball nor the momentum of the earth changes. The momentum of the ball is changed; and the momentum of the earth is not changed. The momentum of the ball is unchanged; and the momentum of the earth is changed.

The momentum of the ball and the momentum of the earth both change.

Which one of the following statements concerning the momentum of a system when the net force acting on the system is equal to zero newtons is true? The momentum of the system is equal to zero kg·m/s. The momentum of the system has a constant value. The momentum of the system is increasing. The momentum of the system has a negative value. The momentum of the system is decreasing.

The momentum of the system has a constant value.

Which one of the following statements concerning the momentum of a system when the net force acting on the system has a positive value is true? The momentum of the system has a negative value. The momentum of the system is increasing. The momentum of the system is decreasing. The momentum of the system is equal to zero kg · m/s. The momentum of the system has a constant value.

The momentum of the system is increasing.

A space vehicle of mass m has a speed v. At some instant, it separates into two pieces, each of mass 0.5m. One of the pieces is at rest just after the separation. Which one of the following statements concerning this situation is true? This process does not conserve momentum. The moving piece has speed 2v. The process does not conserve total energy. This process conserves kinetic energy. The piece at rest possesses kinetic energy.

The moving piece has speed 2v.

A rock is dropped from a high tower and falls freely under the influence of gravity. Which one of the following statements concerning the rock as it falls is true? Neglect the effects of air resistance. The amount of momentum the rock gains will be proportional to the amount of potential energy that it loses. The rock will gain an equal amount of momentum during each second. The rock will gain an equal amount of kinetic energy during each second. The rock will gain an equal amount of speed for each meter through which it falls. The rock will gain an equal amount of momentum for each meter through which it falls.

The rock will gain an equal amount of momentum during each second.

A rocket is propelled forward as very high speed gases are ejected out of its back. Which one of the following is the best explanation as to why the rocket is propelled forward? The rocket is propelled forward due to the conservation of momentum. Because the gases are pushing against the air, the air propels the rocket forward. The rocket is propelled forward because both energy and momentum must be conserved. The high speed gases push backward on the rocket as they are ejected and propel it forward. The rocket is propelled forward due to the conservation of energy.

The rocket is propelled forward due to the conservation of momentum.

An object of mass 3m, initially at rest, explodes breaking into two fragments of mass m and 2m, respectively. Which one of the following statements concerning the fragments after the explosion is true? They will fly off at right angles. The smaller fragment will have twice the speed of the larger fragment. The larger fragment will have twice the speed of the smaller fragment. The smaller fragment will have four times the speed of the larger fragment. They will fly off in the same direction.

The smaller fragment will have twice the speed of the larger fragment.

A stationary bomb explodes in space breaking into a number of small fragments. At the location of the explosion, the net force due to gravity is zero newtons. Which one of the following statements concerning this event is true? All of the fragments must have equal kinetic energies. The vector sum of the linear momenta of the fragments must be zero. The mass of any one fragment must be equal to the mass of any other fragment. Kinetic energy is conserved in this process. The sum of the kinetic energies of the fragments must be zero.

The vector sum of the linear momenta of the fragments must be zero.

Which one of the following statements concerning center of mass is true? The velocity of the center of mass of a system of objects is greatly affected by a collision of objects within the system. The velocity of the center of mass of a system of objects is constant when the sum of the external forces acting on the system is zero. The center of mass of a system of objects cannot change even if there are forces acting on the objects. All of an object's mass is located at its center of mass. The center of mass of an object must be located within the object.

The velocity of the center of mass of a system of objects is constant when the sum of the external forces acting on the system is zero.

Two identical cars are traveling at the same speed. One is heading due east and the other due north, as the drawing shows. Which statement is true regarding the kinetic energies and momenta of the cars? They have the same kinetic energies and the same momenta. They have the same kinetic energies, but different momenta. They have different kinetic energies, but the same momenta. They have different kinetic energies and different momenta.

They have the same kinetic energies, but different momenta.

Two objects have the same momentum. How do their velocities compare? They must have same directions and the same magnitudes. They must have the same magnitudes but they could have different directions. They must have the same directions but they could have different magnitudes. Their directions and the magnitudes could both be different.

They must have the same directions but they could have different magnitudes.

In Times Square in New York City, people celebrate on New Year's Eve. Some just stand around, but many move about randomly. Consider a group consisting of all of these people. Approximately, what is the total linear momentum of this group at any given instant? zero their average speed multiplied by their total mass their total impulse

Zero

A canoe with two people aboard is coasting with an initial momentum of +110 kg m/s. Then, one of the people (person 1) dives off the back of the canoe. During this time, the net average external force acting on the system (the canoe and the two people) is zero. The table lists four possibilities for the final momentum of person 1 and the final momentum of person 2 plus the canoe, immediately after person 1 dives off. Only one possibility could be correct. Which one is it? Person 1Person 2 and Canoe(a)-60 kg·m/s+170 kg·m/s(b)-30 kg·m/s+110 kg·m/s(c)-40 kg·m/s-70 kg·m/s(d)+80 kg·m/s-30 kg·m/s (a) (b) (c) (d

a

The momentum of an object is not dependent on which one of the following quantities? velocity acceleration inertia speed mass

acceleration

A multiple-stage rocket is moving in outer space with a momentum of +150 000 kg·m/s. There are no external forces acting on the rocket. The rocket then separates into two stages, each of which moves along the same direction (either forward or backward) as the initial rocket. The table lists five possibilities for the momenta of the two stages. There is only one possibility that can be correct. Which is it? Stage 1Stage 2a.+200 000 kg·m/s+50 000 kg·m/sb.+75 000 kg·m/s-75 000 kg·m/sc.+30 000 kg·m/s+90 000 kg·m/sd.+250 000 kg·m/s-100 000 kg·m/se.+250 000 kg·m/s-150 000 kg·m/s e b d a c

d

Two balls collide in a one-dimensional elastic collision. The two balls constitute a system, and the net external force acting on them is zero. The table shows four possible sets of values for the initial and final momenta of the two balls, as well as their initial and final kinetic energies. Only one set of values could be correct. Which is it? Initial (Before Collision)Initial (Before Collision)Final (After Collision)Final (After Collision)MomentumKinetic EnergyMomentumKinetic Energy(a)Ball 1:Ball 2:+4 kg·m/s-3 kg·m/s12 J5 J-5 kg·m/s-1 kg·m/s10 J7 J(b)Ball 1:Ball 2:+7 kg·m/s+2 kg·m/s22 J8 J+5 kg·m/s+4 kg·m/s18 J15 J(c)Ball 1:Ball 2:-5 kg·m/s-8 kg·m/s12 J31 J-6 kg·m/s-9 kg·m/s15 J25 J(d)Ball 1:Ball 2:+9 kg·m/s+4 kg·m/s25 J15 J+6 kg·m/s+7 kg·m/s18 J22 J (a) (b) (c) (d)

d

A satellite explodes in outer space, far from any other body, sending thousands of pieces in all directions. Is the linear momentum of the satellite before the explosion less than, equal to, or greater than the total linear momentum of all the pieces after the explosion? less than equal to greater than

equal to

The ball weighs W= 2000 N. Immediately before the ball collided with the sculpture, the tension in the chain was: zero. positive, but less than 2000 N. 2000 N. greater than 2000 N.

greater than 2000 N.

Which one of the following quantities is equal to the change in momentum of an object during a collision? net force impulse work change in kinetic energy maximum force

impulse

Complete the following statement: Different types of collisions between interacting bodies are categorized on the basis of the temporal duration of the collision. kinetic energy conservation. the magnitude of the forces involved. mechanical energy conservation. linear momentum conservation.

kinetic energy conservation.

A boy of mass m runs with a speed v and jumps onto a sled on an icy pond. The sled was at rest before the boy jumped onto it. After the jump, the sled and boy move at a speed v/2. What is the mass of the sled? 2m m 4m m/2 3m

m

A rifle of mass M is initially at rest. A bullet of mass m is fired from the rifle with a velocity v relative to the ground. Which one of the following expressions gives the velocity of the rifle relative to the ground after the bullet is fired. Mv/m mv/M -mv -mv/M mv

mv/M

Where would you expect the center of mass of a baseball bat to be located? halfway between the ends of the bat nearer the lighter end nearer the heavier end

nearer the heavier end

Complete the following statement: the center of mass of a system of particles has a constant velocity if the forces exerted by the particles on each other sum to zero the external forces acting on particles of the system sum to zero the velocity of the center of mass is initially zero the particles are distributed symmetrically around the center of mass the center of mass is at the geometric center of the system

the external forces acting on particles of the system sum to zero

Complete the following statement: Momentum will be conserved in a two-body collision only if the internal forces of the two body system cancel in action-reaction pairs. the collision is perfectly elastic. the net external force acting on the two-body system is zero. both bodies come to rest. the kinetic energy of the system is conserved.

the net external force acting on the two-body system is zero.

Complete the following statement: The center of mass is the region of an object where most of the mass is located. the point within an object that moves as if all of the object's mass were located there. the point at the geometrical center of an object. the only point on an object at which the gravitational force acts. the region of an object where the density has the largest value.

the point within an object that moves as if all of the object's mass were located there.

Complete the following statement: A collision is elastic if the objects stick together. the final kinetic energy is zero. the final momentum is zero. the total kinetic energy is conserved. the final velocities are zero.

the total kinetic energy is conserved.