# Collision Practice

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COLLISIONS & CM WORKSHEET Read each question carefully. Show all of your work and equations used. Don’t forget units on finals answers. 1.

A 9800 N car traveling at 22 m/s strikes a concrete bridge support and comes to a complete halt in 0.5 sec. a) Determine the magnitude of the force acting on the car. b) Suppose a barrier, which contained material that is gradually crushed during impact so that the stopping time was increased to 3 s, had surrounded the bridge support. What would be the magnitude of the new force?

2.

A 1 kg object traveling at 1 m/s collides head-on with a 2 kg object initially at rest. If the collision is completely inelastic, determine the velocity of the objects after impact and how much kinetic energy was lost during the collision.

3.

Max, who has a mass of 80 kg and his girlfriend, Allison, who has a mass of 50 kg are wearing skates and are standing together on a frozen lake. If they push apart and Max has a velocity of 0.72 m/s in the opposite direction of Allison, then what is the velocity of Allison? (Neglect friction)

4.

Stranded on a frozen and frictionless lake, David, who has a mass of 55 kg, takes off his new 0.15 kg Michael Jordan tennis shoes that he got from Santa Clause for Christmas. He throws the shoes horizontally directly away from the shore with a speed of 2 m/s. If David is 5 m away from shore, how long does it take before he reaches land?

5.

For a movie scene, a 60 kg, Jenna drops from a tree onto a 50 kg sled moving with a velocity of 6 m/s toward the shore of a frozen lake. a) What is the speed of the sled after Jenna is on board? b) If the sled hits the bank and stops but Jenna keeps going, then what speed does he leave the sled?

6.

Locate the center of mass of the two-particle system shown in the figure below from the reference of the 4 kg mass. 2m m2 = 1 kg m1 = 4 kg

7.

The mass of the Sun is 329,390 Earth masses, and the mean distance from the center of the Sun to the center of the Earth is 1.496 x 108 km. Treating the Earth and Sun as particles, with each mass concentrated at its respective geometric center; how far from the center of the Sun is the center of mass of the Earth-Sun system? Compare this distance with the mean radius of the Sun (6.96 x 105 km).

8.

Where is the center of mass of the three-particle system shown below using the origin as the reference point? y(m)

(-2,3) M1

M1 = 7 kg M2 = 5 kg M3 = 9 kg

(1,1) M2 x (m)

(-4,-3) M3

MOMENTUM & IMPULSE WORKSHEET 1. A compact car, mass of 725 kg, is moving at 100 km/hr. (a) Find its momentum. (b) At what velocity is the momentum of a larger car, mass of 2175 kg, equal to that of the smaller car? 2. A snowmobile has a mass of 250 kg. A constant force is exerted on it for 60 s. The snowmobile’s initial velocity is 6 m/s and it accelerates to 28 m/s (a) What is its change in momentum?

(b) What is the magnitude of the force exerted on it?

3. The brakes exert a 640 N force on a car weighing 15,680 N and moving at 20 m/s. The car finally stops. (a) What is the car’s mass? (b) What is its initial momentum? (c) What is the change in the car’s momentum?

(d) How long does the braking force act on the car to bring it to a halt?

4. A force of 6 N acts on a 3 kg object for 10 sec. (a) What is the object’s change in momentum? (b) What is its change in velocity? 5. The velocity of a 600 kg automobile is changed from 10 m/s to 44 m/s in 68 s by an applied constant force. (a) What is the change in momentum does the force produce? (b) What is the magnitude of the force?

Chapter 9: Momentum and Collisions Read each problem carefully. Be sure to use the correct equation(s). Show all of your work. Be sure to box and label final answers. 1.

A ball of mass 0.440 kg moving with a speed of 4.5 m/s collides head-on with a 0.220 kg ball at rest. If the collision is elastic, what will be the speed of each ball after the collision?

2.

A 4 kg ball with a velocity of 4 m/s in the positive x-direction has a head-on elastic collision with a stationary 2 Kg ball. What are the velocities of the balls after the collision?

3.

A ball with a mass of 100 g is traveling with a velocity of 50 cm/s in the positive x-direction and collides head-on with a 5 Kg ball that was at rest. Assuming that it is elastic, find the velocities (in m/s) of the balls after the collision.

4.

A 100 g bullet is fired horizontally into a 14.9 kg block of wood resting on a horizontal surface, and the bullet becomes embedded in the block. If the muzzle velocity of the bullet is 250 m/s, what is the velocity of the block containing the embedded bullet immediately after impact? (Neglect surface friction)

5.

A 90 kg astronaut Travis is stranded in space at a point 12 m from his spaceship. In order to get back to his ship, Travis throws a 0.50 kg piece of equipment so that it moves at a speed of 4 m/s directly away from the spaceship. How long will it take him to reach the ship?

6.

A 0.300 kg ball, moving with a speed of 2.5 m/s, has a head-on collision with at 0.600 kg ball initially at rest. Assuming a perfectly elastic collision, what will be the velocity of each ball after the collision?

7.

Two billiard balls of equal mass undergo a perfectly elastic head-on collision. If the speed of one ball was initially 2 m/s, and the other was 3 m/s in the opposite direction, what will be their speeds after the collision?

8.

A 2.5 kg block sliding on a frictionless horizontal surface with a constant velocity of 6 m/s approaches a stationary 6.5 kg block. If the blocks have a completely inelastic collision, what is their velocity after the collision?

9.

A 100 g bullet is fired horizontally into a 14.9 kg block of wood resting on a horizontal surface, and the bullet becomes embedded in the block. If the muzzle velocity of the bullet is 250 m/s, what is the velocity of the block containing the embedded bullet immediately after impact? (Neglect surface friction)

10.

Block A with mass 12 kg moving 2.4 m/s makes an elastic head-on collision with block B, mass 36 kg, which is at rest. Find the velocities of the two blocks after the collision.

11.

Darcy who has a mass of 65 kg is ice skating and traveling at 4 m/s to the north. Traveling in the opposite direction of Adele, Darcy suddenly grabs the hand of Adele, who has a mass of 56 kg and is traveling at 12 m/s. While holding hands, the two girls continue skating together with joined hands. What is the final velocity of the two skaters?

12.

Brett, who has a mass of 76 kg and is initially at rest in a stationary 45 kg boat, steps out of the boat and onto a dock. If the boater, Brett, moves out of the boat with a velocity of 2.5 m/s to the right, what is the velocity of the boat?

13.

A 2,250 kg car is slowed down uniformly from 20 m/s to 5 m/s in 4 seconds. What is the constant force acting on the car during this time?

14.

You are sitting at a LCHS baseball game when Brent hits a foul ball that comes your way. Not having a glove, you prepare to catch Brent’s foul ball barehanded. In order to catch it safely, should you move your hands toward the ball, hold them still, or move them in the same direction as the moving ball? Explain using the concept of change of momentum and impulse. Be sure to use complete sentences.

15. Block A with mass 12 kg moving 2.4 m/s makes an elastic collision with block B, mass 36 kg, which is at rest. Find the velocities of the two blocks after the collision.

16. Jayme, who has a mass of 40 kg, is ice-skating and traveling at 4 m/s to the north towards Anthony, who has a mass of 65 kg and is traveling South at 12 m/s towards Jayme. As the two approach each other, Jayme suddenly grabs the arm of Anthony. While holding his arm, the two continue skating together. What is the final velocity of Jayme and Anthony skating together?

17. Ashleigh and August dock a paddle boat. Ashleigh, who has a mass of 50 kg, moves forward at 3.8 m/s as she leaves the boat. At what speed and in what direction do the paddle boat and August move if their combined mass is 105 kg?

18. A 23 g bullet traveling 230 m/s penetrates a 2.0 kg block of wood and emerges cleanly at 170 m/s. If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?

19. A 50 g tennis ball travels at a velocity of 15 m/s, hits a basketball with a mass of 600 g that is stationary on a frictionless surface and then rebounds back in the opposite direction with a velocity of -6 m/s . How fast will the basketball be moving after the collision?

PART II: Fill In Write the answer that best completes each statement in the space to the left. 20. _______________________________ Momentum is the product of an object’s ___ and velocity. 21. _______________________________The quantity Ft is called ____. 22. _______________________________ The change of momentum for an object is equal to and caused by the ___ given to the object. 23. _______________________________ If the momentum of a cannon is considered positive after it fires a shell, the momentum of the shell is considered ___. 24. _______________________________ A moving object containing a bomb explodes. If the object had a total of 20 units of momentum just before the explosion, its pieces would have a total of ___ units of momentum just after the explosion. 25. _______________________________ A(n) ____ force cannot change the momentum of a system. 26. _______________________________ In a system consisting of objects upon which no external force is acting, the momentum of the system is ___. 27. _______________________________ The unit of momentum in the SI system is ____. Define each of the following 28. Impulse – 29. Linear Momentum – 30. Impulse-momentum theorem – 31. Closed system – 32. Isolated system – 33. Law of conservation of momentum – 34. Elastic Collision – 35. Completely Inelastic Collision – 36. Inelastic Collision – Answer the following questions. 37. Write the equation for momentum and its units. 38. Can a bullet and a truck have the same momentum? Explain. 39. Considering impulse, why are cars made with bumpers that can be pushed during a crash?

40. When you ride a bicycle at full speed and the bike stops suddenly, why do you have to push hard on the handlebars to keep from flying off?

41. Why do you tend to lean backward when carrying a heavy load in your arms?

Two dimensional momentum problems 1. A car of 2500kg heading west at 6m/s collides with a 3500kg car heading north at 12m/s. What is the final speed and angle the mangled mess is traveling at?

2. A jogger jogging at 3m/s south hits a walker traveling at 1.5m/s east. If the jogger continues south at 1.5m/s, what is the final speed and angle of the walker?

3. A car of 2000kg heading west collides with a 3000kg car heading north at 14m/s. If the final speed is 25m/s at 230 north of west. What is the initial speed of the westbound car?

4. A 75kg jogger jogging at 6m/s north hits a 150kg walker traveling 3m/s west. If the jogger continues north at 1.5m/s, what is the final speed and angle of the walker?

5. In the game of curling the red team’s stone is traveling at 8m/s and hits the blue team’s stone (at rest) and leaves at a 300 angle while the blue team’s stone leaves at 30o below the horizontal what is the final speed of each stone?

6. A car of unknown mass heading west at 6m/s collides with a 3500kg car heading north at 12m/s. What is the mass of the car if the final speed is 10m/s and the angle is 25 degrees?

7. A 2600kg car heading west at 15m/s collides with a 3500kg car heading north. What is the initial speed of the car if the final speed is 18m/s and the angle is 25o?

Angular Momentum and Torque Worksheet Angular momentum and the Principle of Conservation of Angular Momentum 1. What is the angular momentum of a 0.25 kg mass rotating on the end of a piece of rope in a circle of radius 0.75m at an angular speed of 12.5 m/s?

2. A figure skater rotates on ice at a rate of 3.5 rad/s with her arms extended horizontally. When she lowers her arms to her side, she speeds up to 7.5 rad/s. Find the ratio of her moment of inertia in the first case to that in the second case.

3. A 5kg tetherball at rest (rope is 2m long) is hit with a 15N force for 1milisecond so that the angle between the rope and pole is 25 degrees. A. What is the torque on the ball? B. What is the change in angular momentum of the ball? (Hint: In this part theta is 90 degrees) C. What is the final speed of the ball? D. What is the final rotational speed of the ball? E. What is the moment of inertia of the ball? F. What is the angular acceleration of the ball? G. What is the linear acceleration of the ball?

4. A bowling ball has a mass of 5.5 kg and a radius of 12.0 cm. It is released so that it rolls down the alley at a rate of 12 rev/s. Find the magnitude of its angular momentum.

5. A 14kg tetherball at rest (rope is 5m long) is hit with a 150N force for 0.01miliseconds so that the angle between the rope and pole is 25 degrees. A. What is the torque on the ball? B. What is the change in angular momentum of the ball? (Hint: theta is 90 degrees) C. What is the final speed of the ball? D. What is the final rotational speed of the ball? E. What is the moment of inertia of the ball? F. What is the angular acceleration of the ball? G. What is the linear acceleration of the ball?

6. If a 20kg basketball (diameter 75cm) is shot with a velocity of 4m/s. What is the angular momentum of the ball?

Conservation of Momentum – The total momentum of any closed, isolated system does not change. This law allows you to make connections between objects before and after they collide. po = p m1v1o + m2v2o = m1v1 + m2v2 Isolated system – A closed system that is free from the influence of a net external force that can change the momentum of the system; a closed system does not gain or lose mass (objects neither enter nor leave it).

Types of collisions – (1)

Inelastic collision – Momentum is conserved but not kinetic energy. The kinetic energy, which is lost, is turned into heat, sound, etc. Use the conservation equation to solve these collision problems… m1v1o + m2v2o = m1v1 + m2v2

(2)

Elastic collision – Both momentum and kinetic energy are conserved; takes place at the subatomic level. The objects have a “head-on” collision and bounce off each other. Use the following equations to solve these collision problems… �m - m �

� 2m

� 2m

�m - m �

v1 = � 1 2 �v1o + � 2 �v2o �m1 + m2 � �m1 + m2 � �

v2 = � 1 �v1o + � 2 1 �v2o �m1 + m2 � �m1 + m2 � (3)

Perfectly (Completely) Inelastic collision – Two objects collide and stick together so that their final velocities are the same; only momentum is conserved. Use the following equation to solve these collision problems… m1v1o + m2v2o = (m1+ m2) v

(4)

Explosion – The two objects are together and then separate; recoil. It is like a backwards perfectly (completely) inelastic collision. The collision starts from rest (vo = 0). Use the following equation to solve these types of collision problems… vo(m1+ m2) = m1v1 + m2v2
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