AP Physics 1 Assignment – Momentum

Reading   Chapter 8, Open Stax College Physics; Chapter 7, Giancoli

 

Objectives/HW

 

The student will be able to:

HW:

1

Define and calculate momentum using appropriate SI units.

1

2

Define and calculate impulse and solve problems relating impulse, momentum, and force.

2 – 6

3

State and apply the law of conservation of momentum with proper consideration to internal and external forces.  Define and analyze center of mass in qualitative terms.

7 – 9

4

Use conservation of momentum to solve related problems.

10 – 19

5

Define elastic and inelastic collisions and use the definitions to solve related problems.

20 – 26

 

Homework Problems

 

1.     Can a bullet have the same momentum as a truck?  Explain.

2.     An object with initial momentum 5.00 kg m/s, 0.0¡ experiences a net force of 20.0 N, 180¡ for a duration of 1.50 seconds.  (a) Determine the net impulse.  (b) Determine the objectÕs momentum at the end of the 1.50 seconds.

3.     A rubber ball of mass 50.0 grams bounces off the floor.  Its velocity just before the bounce is 5.00 m/s, 270¡ and just after the bounce 4.50 m/s, 90¡.  (a) Determine the change in momentum of the ball.  (b) Determine the net impulse acting on the ball.  (c) Determine the average force of the ball acting on the floor if the bounce lasts just 0.010 seconds.

4.     The momentum of a certain car changes by 500 kg m/s in 2.00 seconds.  (a) Determine the amount of net force on the car.  (b) If the car has mass 1500 kg, by how much does its velocity change?

5.     The main engines of the space shuttle each burn fuel at a rate of 492 kg/s.  The exhaust gases have a velocity of 3390 m/s, 270.0¡.  (a) What is the thrust developed by each of the main engines?  (b) The solid boosters produce a thrust of 11.8 MN.  Assuming the exhaust velocity is the same as the main engines what is the mass burn rate?

6.     An old house has a chimney in which the old mortar between the bricks has dried out.  The homeowner worries that the wind could blow it over.  Suppose the wind reaches 33.5 m/s (75 mph) and blows directly against the side of the chimney, which has dimensions 3.0 m × 0.90 m.  The density of air is 1.2 kg/m3.  (a) Find the amount of force on the chimney due to the wind, assuming the air is brought to a stop by the impact.  (b) Determine the wind speed that would double the force found in part (a).

7.     If only an external force can change the momentum of a system or object, how can the internal force of a carÕs brake pads and rotors bring the car to a stop?   

8.     A kid sitting in a wagon tries to make the wagon move by rocking forward and back.  (a) Assuming there is no net external force on the kid and wagon explain why this action should not move the wagon.  Explain what happens to the center of mass of the system as the kid moves forward in the wagon.  (b) In reality an action like this might propel the kid and wagon forward (albeit slowly) – explain how this happens using physics concepts.

9.     A hockey puck slides over a smooth icy surface and collides with a box of greater mass that is initially at rest.  Ignore friction.  (a) Explain why the center of mass of the puck/box system moves with constant velocity before, during, and after the collision.  (b) Which type of collision would make the box move fastest – if the puck sticks in the box or if the puck bounces back off the box?  Explain by referring to the center of mass of the system.

10.  A 95 kg fullback, running at 8.2 m/s, 0.0¡, collides in midair with a 128 kg defensive tackle moving in the opposite direction.  Both players end up with zero speed.  (a) What was the fullbackÕs momentum before the collision?  (b) What was the change in the fullbackÕs momentum?  (c) What was the change in the tackleÕs momentum?  (d) What was the tackleÕs original momentum?  (e) What was the tackleÕs speed originally?

11.  Ball A, mass 5.0 g, moves at a velocity of 20.0 cm/s, 180.0¡.  It collides with Ball B, mass 10.0 g, moving with velocity 10.0 cm/s, 180.0¡.  After the collision, ball A is still moving but with a velocity of 8.0 cm/s, 180.0¡.  (a) Find the momentum of ball B after the collision.  (b) Find the resulting velocity of ball B.  (c) By how much did each ballÕs momentum change?   

12.  A 2575 kg van runs into the back of an 925 kg compact car at rest.  Immediately afterward the two vehicles move off together at 3.5 m/s.  (a) Find the initial speed of the van.  (b) Supposing the duration of the impact is between 0.10 and 0.50 seconds, calculate a range of values for the force of impact acting on the car.

13.  A bullet of mass m is shot into a wooden block of mass M initially at rest on a frictionless surface.  The block, with the bullet in it, acquires a speed of v.  Supposing that M is a multiple of m such that M = nm, derive in simplest terms a formula that gives the initial speed v0 of the bullet as a function of v, the speed after the collision.   

14.  A hockey puck, mass 0.115 kg, moving at 35.0 m/s, strikes an octopus thrown on the ice by a fan.  The octopus has a mass of 265 g.  The puck and octopus slide off together.  Find the speed.  (Yes, there truly are hockey fans that throw octopuses on the ice.  IsnÕt life strange?)

15.  A 50 kg woman, riding on a 10 kg cart, is moving east at 5.0 m/s.  The woman jumps off the cart and hits the ground running at 7.0 m/s, eastward, relative to the ground.  Calculate the velocity of the cart after she jumps off.

16.  A 92 kg fullback, running at 5.0 m/s, attempts to dive across the goal line for a touchdown.  Just as he reaches the goal line, he is met head-on in midair by two 75 kg linebackers, one moving at 2.0 m/s and the other at 4.0 m/s.  If they all become entangled as one mass, with what velocity do they travel?  Does the fullback score?

17.  A 10.0 g bullet leaves a rifle with a speed of 800.0 m/s.  (a) What should be the minimum mass of the rifle in order that its recoil speed cannot possibly exceed 2.50 m/s?  (b) Make any convenient estimate of the length of the barrel and then calculate the following values for the bullet:  time, net force, and net impulse.  Compare to the change in momentum.  (c) Consider the person firing the rifle – would the impulse of the rifle acting on the person depend on the mass of the rifle?  Explain.

18.  A robotic space probe of mass 7600 kg is traveling through space at 120 m/s.  Mission control determines that a change in course of 30.0¡ is necessary and instructs the probe to fire rockets perpendicular to its direction of motion.  If the escaping gas leaves the craftÕs rockets at an average speed of 3200 m/s, what mass of gas should be expelled?

19.  You are investigating a car wreck.  Mr. Q was traveling east in an 1800 lb car and collided with Ms. X who was traveling south in a 2200 lb car.  The cars stuck together and the skid marks indicate that they moved in a direction of 325¡ after the collision.  Both drivers claim to have been driving the speed limit of 45 mph.  (a) Show mathematically that one of them has to be lying.  (b) Assuming Ms. X is telling the truth, how fast was Mr. Q driving? 
(c) Assuming Mr. Q is telling the truth, how fast was Ms. X driving?  (Now, who do you think was really lying?)

20.  When two automobiles collide it will always be an inelastic collision.  And if there is friction the total momentum of the two cars will be reduced in the collision.  (a) Is this type of collision a violation of the law of conservation of energy?  Explain.  (b) Is this type of collision a violation of the law of conservation of momentum?  Explain.

21.  A railroad car with mass of 5.0 × 105 kg collides with a stationary railroad car of equal mass.  After the collision, the two cars lock together and move off at 4.0 m/s.  (a) Determine the initial speed of the first car.  (b) Determine the amount of momentum before and after the collision.  (c) Determine the total amount of kinetic energy before and after the collision.  (d) Explain what becomes of the ÒmissingÓ kinetic energy.

22.  A golf ball, mass 0.046 kg, rests on a tee.  It is struck by a golf club with an effective mass of 0.220 kg and velocity 44 m/s, 0.0¡.  (a) Assuming the collision is perfectly elastic, find the speed of the ball when it leaves the tee.  (b) Determine the net impulse on the club.

23.  A steel glider with a mass of 1.50 kg moves along an air track at 2.00 m/s, 0¡.  It collides with a second glider of mass 0.500 kg moving in the opposite direction at 0.400 m/s.  After the collision the smaller glider has velocity 3.20 m/s, 0¡.  Ignore friction.  (a) With what velocity did the larger glider leave the collision? (b) Was the collision elastic? (prove your answer numerically)  (c) During the collision there is an instant when the two gliders have the same speed, which is the speed of the center of mass – find this value.  (d) If the gliders bounce apart because of a spring between them with constant k = 750 N/m, how much is the spring compressed during the collision?

24.  A proton (mass = 1.67 × 10-27 kg) moves with a speed of 6.00 Mm/s.  Upon colliding elastically with a stationary particle of unknown mass, the proton rebounds on its own path with a speed of 3.60 Mm/s.  Find the mass of the unknown particle.  Note:  this problem has an interesting symbolic solutionÉ

25.  Ball A of mass 5.00 kg moves at a velocity of 4.00 m/s, 0¡ to collide with a stationary, identical ball, B.  After the collision ball A moves in a direction of 30.0¡; ball B moves toward 300.0¡.  (a) Determine the momentum of ball A and of ball B after the collision. 
(b) Find the velocity of each ball after the collision.  (c) Show numerically that the collision is elastic.

26.  Choose and solve one of these problems from either text:
Open Stax College Physics Problems & Exercises found at end of sections 8.2 – 8.6
Giancoli, pp. 202 – 208, Chapter 7:  12, 61, 68, 69, 71, 76, 77

Selected Answers

6.67 × 10-27 kg

3.20 kg

160 kg

3480 kg/s

angle would be 309¡, not 325¡

5.4 cm

0.041 m/s forward,TD!

16 cm/s, 180¡

0.333 m/s

0.800 m/s, 0.0¡

1.40 m/s

3.46 m/s, 30.0¡; 2.00 m/s, 300.0¡

4.8 m/s

5.0 m/s, west

6.1 m/s

8.0 m/s

10.6 m/s

26 mph

79 mph

47 m/s

73 m/s

410 m/s

48.0 N, 270.0¡

250 N

3600 N

6.5 to 32 kN

1.67 MN

40.0 J before and after

3.04 J before and after

16 MJ; 8.0 MJ

 

 

 

 

 

 

 

 

 

 

 

 

 

 

60 g cm/s

160 g cm/s, 180¡

0.475 kg m/s, 90.0¡

17.3 kg m/s, 30.0¡; 10.0 kg m/s, 300.0¡

25.0 kg m/s, 180¡

40.0 kg m/s, 180¡

40.0 kg m/s, 0¡

780 kg m/s, 0¡

780 kg m/s, 180¡

780 kg m/s, 0¡

780 kg m/s, 180¡

4.0 × 106 kg m/s

0.475 N s, 90.0¡

3.3 N s, 180¡

30.0 N s, 180¡