Chapter 6 - Momentum

for all collisions in the absence of external forces, net momentum before collision equals net momentum after collision

(net mv)before = (net mv)after

41) marshall pushes crates starting from rest across the floor of his classroom for 3 s with a net force as shown. for each crate, rank the following from greatest to least a) impulses delivered b) changes in momentum c) final speeds d) momenta in 3 s

a) a, b, c b) a, b, c c) c, b, a d) a, b, c

65) explain how a swarm of flying insects can have a net momentum of zero

the swarm can have a net momentum of zero if its stays in the same location; then the momenta of the many insects cancel and there is no net momentum in any given direction

47) in terms of impulse and moment, why do mountain climbers favor nylon ropes, which stretch considerably under tension?

when the climber pulls the rope downward, the rope simultaneously pulls the climber upward--the direction desired by the climber

13) is it correct to say that, if no net impulse is exerted on a system, then no change in the momentum of the system will occur?

yes; the statement is correct

inelastic collision

a collision in which objects become distorted, generate heat, and possibly stick together

elastic collision

a collision in which objects rebound without lasting deformation or the generation of heat

51) when you catch a fast-moving baseball with your bare hand, why is it important to extend your hand forward for the catch?

an extended hand allows more time for reducing the momentum of the ball to zero, resulting in a smaller force of impact on your hand

49) when you jump from a significant height, why is it advantageous to land with your knees slightly bent?

bent knees allow more time for momentum to decrease, therefore reducing the force of landing

69) here are the familiar pair of carts connected by a spring. what are the relative speeds of the carts when the spring is released?

both recoiling carts have the same amount of momentum. so the cart with twice the mass has half the speed of the less massive cart; that is 2m(v/2) = mv

17) railroad car a rolls at a certain speed and makes a perfectly elastic collision with car b of the same mass. after the collision, car a is observed to be at rest. how does the speed of car b compare with the initial speed of car a?

car b has the speed of car a before the collision

Ft =

change in (mass x velocity)

53) many years ago automobiles were manufactured to be as rigid as possible, whereas today's autos are designed to crumple upon impact. why?

crumpling allows more time for reducing the momentum of the car, resulting in a smaller force of impact on the occupants

73) if you toss a ball upward, is the momentum of the moving ball conserved? is the momentum of the system consisting of ball + earth conserved? explain

for the system of only the ball, momentum changes and is therefore not conserved. but for the larger system of ball + earth, momentum is conserved because the impulses acting are internal impulses. the change of momentum of the ball is equal and opposite to the change of momentum of the recoiling earth

impulse =

force x time

31) a car carrying a 75 kg test dummy crashes into a wall at 25 m/s and is brought to rest in 0.1 s. show that the average force exerted by the seat belt on the dummy is 18.750 N.

from Ft = change in mv, F = change in mv/t = (75 kg)(25 m/s)/0.1 s = 18,750 N

25) what impulse occurs when the same force of 10 N acts on the cart for twice the time? impulse = Ft

i = (10 N)(5 s) = 50 N*s

27) how much impulse stops a 50 kg carton that is sliding at 4 m/s when it meets a rough surface? impulse = change in momentum: Ft = mv

i = change in mv = (50 kg)( 4 m/s) = 200 N*s

75) drop a stone from the top of a high cliff. identify the system in which the net momentum is zero as the stone falls

if the system is the stone only, its momentum certainly changes as it falls. if the system is enlarged to include the stone + earth, the the downward momentum of the stone is canceled by the equal but opposite momentum of the earth "racing" up to meet the stone

9) why is it advantageous to roll with the punch in boxing?

if you roll with the punch, the impact occurs over a long time, which means a less forceful punch

3) what are the two ways to increase pulse?

impulse can be increased by increasing the force or increasing the time of application

impulse-momentum relationship

impulse is equal to the change in the momentum of the object that the impulse acts upon Ft = m*v

59) why are the impulses that colliding objects exert on each other equal and opposite?

impulse is force x time. the forces are equal and opposite, by newton's third law, and the times are the same, so the impulses are equal and opposite

law of conservation of momentum

in the absence of an external force, the momentum of a system remains unchanged. hence, the momentum before an event involving only internal forces is equal to the momentum after the event mv(before event) = mv(after event)

55) a lunar vehicle is tested on earth at a speed of 10 km/h. when it travels as fast on the moon, is its momentum more, less, or the same?

its momentum is the same (its weight might change, but not its mass)

7) when you are struck by a moving object, is it favorable that the object makes contact with you over a short time or over a long time? explain.

less force occurs if momentum is decreased over a long time

momentum =

mass x velocity

37) two automobiles, each of mass 1000 kg, are moving at the same speed, 20 m/s, when they collide and stick together. in what direction and at what speed does the wreckage move (a) if one car was driving north and one south and (b) if one car was driving north and one east?

momentum conservation can be applied in both cases a) for head-on motion the total momentum is zero, so the wreckage after the collision is motionless b) the total momentum is directed to the northeast--the resultant of two perpendicular vectors, each of magnitude 20,000 kg*m/s. it has magnitude 28,200 kg*m/s. the speed of the wreckage is the momentum divided by the total mass v = (28,300 kg*m/s / 2000 kg) = 14 m/s

71) your friend says that the law of momentum conservation is violated when a ball rolls down a hill and gains momentum? what do you say?

momentum is not conserved for the ball itself because an impulse is exerted on it (gravitational force x time), so the ball gains momentum. only in the absence of an external force does momentum not change.

15) when a cannonball is fired, momentum is conserved for the system cannon + cannonball. would momentum be conserved for the system if momentum were not a vector quantity? explain.

momentum would not be conserved if force, and therefore impulse, was not a vector quantity

35) a 5 kg fish swimming at 1 m/s swallows a 1 kg fish swimming toward it at a speed that brings both fish to a halt immediately after lunch. show that the speed of the approaching smaller fish before lunch must have been 5 m/s

momentum(before) = momentum(after) (5 kg)(1 m/s) + (1 kg)v = 0 5 m/s + v = 0 v = -5 m/s so if the little fish approaches the big fish at 5 m/s, the momentum after lunch is zero

67) if you throw a ball horizontally while standing on roller skates, you roll backward with a momentum that matches that of the ball. will you roll backward if you go through the motions of throwing the ball but don't let go of it? explain

no, if no momentum is imparted to the ball, no oppositely directed momentum will be imparted to the thrower. going through the motions of throwing has no net effect. no momentum given to the ball means no recoil momentum gained by you

23) what is the momentum of a 50 kg carton that slides at 4 m/s across an icy surface? momentum = mv

p = mv = (50 kg)(4 m/s) = 200 kg*m/s

19) suppose a ball of putty moving horizontally with 1kg*m/s of momentum collides with and sticks to an identical ball of putty moving vertically with 1 kg*m/s of momentum. what is the magnitude of their combined momentum?

since they are same magnitude vectors at right angles to each other, the combined momentum is square root of 2 kg*m/s

29) bowling barry asks how much impulse is needed to stop a 10 kg bowling ball moving at 6 m/s? what is your answer?

the bowling ball has a momentum of (10 kg)(6 m/s) = 60 kg*m/s, which has the magnitude of the impulse to stop it. that's 60 N*s (note the units N*s = kg*m/s)

45) in terms of impulse and momentum, why do air bags in cars reduce the risk of injury in accidents?

the forces must be equal and opposite because they are the only forces acting on the person, who obviously is not accelerating. note that the pair of forces do not make an action-reaction pair, however, because they act on the same body. the downward force, the man's weight, earth pulls down on man, has the reaction man pulls up on earth , not the floor pushing up on him. and the upward force of the floor on the man has the reaction of man against the floor, not the interaction between the man and earth

5) how is the impulse-momentum relationship related to newton's second law?

the impulse-momentum relationship is derived from newton's second law

57) why is it difficult for a firefighter to hold a hose that ejects large amounts of water at a high speed?

the large momentum of the spurting water is met by a recoil that makes the hose difficult to hold, just as a shotgun is difficult to hold when it fires birdshot

63) why do 8-ounce boxing gloves hit harder than 16-ounce gloves?

the lighter gloves have less padding and less ability to extend the time of impact. therefore they result in greater forces of impact for a given punch

33) a 2 kg ball of putty moving to the right has a head-on inelastic collision with a 1 kg putty ball moving to the left. if the combined blob doesn't move just after the collision, what can you conclude about the relative speeds of the balls before the collision?

the momentum after the collision is zero, which means the net momentum before the collision must have been zero. the 1 kg ball must be moving twice as fast as the 2 kg ball so that the magnitudes of their momenta are equal

43) when a supertanker is brought to a stop, its engines are typically cut off about 25 km from port. why is it so difficult to stop or turn a supertanker?

the momentum of a supertanker is enormous, which means enormous impulses are needed to change its motion--which are produced by applying modest forces over long periods of time. due to the force of water resistance, the supertanker must coast 25 km to sufficiently reduce the momentum

61) when an apple falls from a tree and strikes the ground without bouncing, what becomes of its momentum?

the momentum of the falling apple is transferred to the earth. interestingly, when the apple is released, the earth and the apple move toward each other with equal and oppositely directed momenta. because of earth's enormous mass, its motion is imperceptible. when the apple and earth hit each other, their momenta are brought to a halt--zero, the same value as before

1) which has a greater momentum: a heavy truck at rest or a moving skateboard?

the moving skateboard has a greater momentum because only it is moving

impulse

the product of the force acting on an object and the time during which it acts

momentum

the product of the mass of an object and its velocity