Chapter 7 - Impulse and Momentum CYU

[7.2] 7. 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) No. (b) No.

[7.2] 12. 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

[7.1] 3. Two objects have the same momentum. Do the velocities of these objects necessarily have (a) the same directions and (b) the same magnitudes?

(a) Yes. (b) No.

[7.5] 19. A sunbather is lying on a floating raft that is stationary. 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) zero (b) Yes, opposite to the motion of the sunbather.

[7.1] 6. 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 6(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) The impulse of the thrust is equal to the magnitude and opposite in direction to the impulse of the force due to air resistance.

[7.1] 4. (a) Can a single object have a kinetic energy but 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). No (b). Yes

[7.1] 1. Two identical automobiles have the same speed, one traveling east and one traveling west. Do these cars have the same momentum?

No.

[7.3] 16. In an elastic collision, is the kinetic energy of each object the same before and after the collision?

No. It is the total kinetic energy of the system that is the same before and after the collision.

[7.1] 2. 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?

The total linear momentum is zero because of the random directions and random speeds of the moving people.

[7.2] 9. On a distant asteroid, a large catapult is used to throw chunks of stone into space. Could such a device be used as a propulsion system to move the asteroid closer to the earth?

Yes.

[7.2] 10. 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? Final Momenta Person 1 ... Person 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

[7.5] 20. Water, dripping at a constant rate from a faucet, falls to the ground. At any instant there are many drops in the air between the faucet and the ground. Where does the center of mass of the drops lie relative to the halfway point between the faucet and the ground? (a) Above it (b) Below it (c) Exactly at the halfway point

a

[7.1] 5. Suppose you are standing on the edge of a dock and jump straight down. If you land on sand your stopping time is much shorter than if you land on water. Using the impulse-momentum theorem as a guide, determine which one of the following statements is correct. (a) In bringing you to a halt, the sand exerts a greater impulse on you than does the water. (b) In bringing you to a halt, the sand and the water exert the same impulse on you, but the sand exerts a greater average force. (c) In bringing you to a halt, the sand and the water exert the same impulse on you, but the sand exerts a smaller average force.

b) In bringing you to a halt, the sand and the water exert the same impulse on you, but the sand exerts a greater average force.

[7.2] 13. Concept Simulation 7.1 at www.wiley.com/college/cutnell 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: (a) The law of conservation of energy (b) Newton's second law (c) Newton's third law (d) The principle of conservation of linear momentum

b,c,d

[7.3] 17. Concept Simulation 7.2 at www.wiley.com/college/cutnell illustrates the concepts that are involved in this question. Also review Multiple-Concept Example 7. Suppose two objects collide head on, as in Example 7, where initially object 1 (mass = m1) is moving and object 2 (mass = m2) is stationary. Now assume that they have the same mass, so m1 = m2. Which one of the following statements is true? (a) Both objects have the same velocity (magnitude and direction) after the collision. (b) Object 1 rebounds with one-half its initial speed, while object 2 moves to the right, as in Figure 7.10, with one-half the speed that object 1 had before the collision. (c) Object 1 stops completely, while object 2 acquires the same velocity (magnitude and direction) that object 1 had before the collision.

c

[7.3] 15. 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 set is it? Initial (Before Collision) Final (After Collision) Momentum Kinetic Energy Momentum Kinetic Energy (a)Ball 1:+4 kg · m/s12 J−5 kg · m/s10 J Ball 2:−3 kg · m/s 5 J−1 kg · m/s 7 J (b)Ball 1:+7 kg · m/s22 J+5 kg · m/s18 J Ball 2:+2 kg · m/s 8 J+4 kg · m/s15 J (c)Ball 1:−5 kg · m/s12 J−6 kg · m/s15 J Ball 2:−8 kg · m/s31 J−9 kg · m/s25 J (d)Ball 1:+9 kg · m/s25 J+6 kg · m/s18 J Ball 2:+4 kg · m/s15 J+7 kg · m/s22 J

d

[7.2] 11. You are a passenger on a jetliner that is flying at a constant velocity. You get up from your seat and walk toward the front of the plane. Because of this action, your forward momentum increases. Does the forward momentum of the plane itself decrease, remain the same, or increase?

decrease

[7.2] 8. 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?

equal to

[7.5] 18. 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, or nearer the heavier end?

nearer the heavier end

[7.2] 14. The energy released by the exploding gunpowder in a cannon propels the cannonball forward. Simultaneously, the cannon recoils. The mass of the cannonball is less than that of the cannon. Which has the greater kinetic energy, the launched cannonball or the recoiling cannon? Assume that momentum conservation applies.

the cannonball