Conceptual Physics Momentum Outline Hewitt: Chapter 7 Momentum Exercises: 4 Momentum Fill in the Charts completely Variables introduced or used in chapter: Quantity Symbol Units mass velocity momentum change in momentum change in velocity force time impulse Collision None Formula Chart* *In Class, we will use x for horizontal motion, and y for vertical motion instead of d Momentum Change in Momentum Impulse Impulse Momentum Law Conservation of Momentum: ELASTIC Collision Conservation of Momentum: INELASTIC Collision Impulse and Momentum page 1
Define the following terms using COMPLETE SENTENCES: Momentum Impulse Conserved Conservation of Momentum Elastic Collision Inelastic Collisions Answer the following questions in Complete Sentences: 1. Is momentum a vector or scalar? Why or why not? 2. Give examples of Increasing Momentum. 3. Give examples of Decreasing Momentum. 4. Draw a picture of an Elastic Collision 5. Draw a picture of Inelastic Collisions Impulse and Momentum page 2
Impulse and Momentum Homework Problems Impulse/Momentum: 1. A girl has a mass of 35.6 kg and her skateboard has a mass of 1.3 kg. What is the momentum of the girl on her skateboard together if they are traveling at 9.50 m/s?[350.55 kg m/s] 2. A hockey player makes a slap shot with a force of 30 N on the hockey puck for 0.16 seconds. a. What impulse is given to the hockey puck? [4.8 Ns] b. What is the change in velocity of the puck if it has a mass of 0.5 kg? [9.6 m/s] 3. A force of 6 N acts on a 3 kg object for 10 seconds a. What is the object's change in momentum? [60 kg m/s] b. What is its change in velocity? [20 m/s] 4. A baseball with a mass of 0.14 kg is thrown by a pitcher with a velocity of + 35 m/s a. What is the momentum of the baseball? [4.9 kg m/s] b. For a bowling ball with a mass of 7.26 kg to have the same momentum as the baseball, what would its velocity have to be? [0.675 m/s] 5. A baseball with a mass of 0.14 kg is thrown by a pitcher with a velocity of +38 m/s. It is hit back by the batter at a velocity of -38 m/s. a. What is the impulse (change in momentum)? [-10.64 Ns] b. If the bat stays in contact with the baseball for 0.1 second, calculate the force of the bat? [-106.4 N] c. What is the acceleration of the ball? [-760 m/s 2 ] 6. The brakes on a car exert a force of 640 N on a car. It was moving at 20 m/s and finally comes to a stop. The car weighs 15,680 N. a. What is the car's mass? [1600 kg] b. What was the car's original momentum? [32000 kg m/s] c. What was the change in momentum? [-32000 kg m/s] d. How much time did it take to bring the car to a stop? [50 s] Inelastic Collision 7. A railroad diesel engine has four times the mass of a flatcar. If a diesel coasts at 5 km/hr into a flatcar that is initially at rest, how fast do the two coast if they couple together? [4 km/hr] 8. A 0.105-kg hockey puck moving at 48 m/s is caught by a 75-kg goalie at rest. With what velocity does the goalie slide on the ice after catching the puck? [0.07 m/s] 9. A 0.35 kg bullet strikes a 5.0-kg stationary wooden block and embeds itself in the block (the bullet remains in the block). The block and bullet move together at 8.6 m/s. What was the original velocity of the bullet? [131.46 m/s] 10. A 3000-kg truck moving East with a speed of 5 km/hr collides head-on with a 1000-kg car moving West with a speed of 10 km/hr. The two vehicles stick together and move with the same velocity after the collision. Find the post-collision velocity of the car and truck. [1.25 km/hr, east] 11. During a goal-line stand, a 75-kg fullback moving eastward with a speed of 8 m/s collides head-on with a 100-kg lineman moving westward with a speed of 4 m/s. The two players collide and stick together, moving at the same velocity after the collision. Determine the post-collision velocity of the two players. [1.14 m/s east] Elastic Collision 12. A 0.35 kg bullet moving at 475 m/s strikes a 2.5-kg wooden block at rest. The bullet passes through the block, leaving at 275 m/s. How fast is the wooden block moving when the bullet leaves? Assume the mass of the wooden block does not change significantly. [28 m/s] 13. A 0.50-kg ball traveling East at 6.0 m/s collides head-on with a 1.00-kg ball moving in the opposite direction (West) at a velocity of 12.0 m/s. The 0.50-kg ball moves away (West) at 14 m/s after the collision. Find the velocity of the second ball. [2 m/s, left] Problems 14-23: For problems 14-18: A car with a mass of 1000 kg is at rest at a stoplight. When the light turns green, it is pushed by a net force of 2000 N for 10 s. 14. What is the value of the acceleration that the car experiences? [2m/s 2 ] 15. What is the value of the change in velocity that the car experiences? [20 m/s] 16. What is the value of the impulse on the car? [20000 Ns] 17. What is the value of the change in momentum? [20000kg m/s] 18. What is the final velocity of the car at the end of 10 seconds? [20 m/s] Impulse and Momentum page 3
For problems 19-20: The car continues at this speed for a while. 19. What is the value of the change in momentum the car experiences as it continues at this velocity? [0 kg m/s] 20. What is the value of the impulse on the car as it continues at this velocity? [0 Ns] The brakes are applied to the car, causing it to come to rest in 4 s. 21. What is the value of the change in momentum that the car experiences? [20000 kg m/s] 22. What is the value of the impulse on the car? [20000Ns] 23. What is the value of the force (average) that causes the car to stop? What is the acceleration? [5000N, 5 m/s 2 ] Conceptual: 24. Which has the greater mass, a heavy truck at rest or a rolling skateboard? Which has greater momentum? Why? 25. Distinguish between impact and impulse. Which designates a force and which is force X time? 26. When the force of impact on an object is extended in time, does the impulse increase or decrease? 27. For a constant force, suppose the impact time is doubled. a. How much is the impulse increased? b. How much is the resulting change in momentum increased? 28. In a car crash, why is it advantageous for an occupant to extend the time during which the collision takes place? 29. Explain the difference between an elastic and inelastic collision. 30. Complete the following verbal statements to illustrate your understanding of the effect of varying mass on the post-collision velocity. a. An object of mass m and velocity v collides inelastically with an object of mass 3m which is initially at rest, then the amount of total system mass in motion will increase by a factor of and the velocity of the system will decrease by a factor of. The new velocity (v') will be v. b. If an object of mass m collides and velocity v collides inelastically with an object of mass 4m which is initially at rest, then the amount of total system mass in motion will increase by a factor of and the velocity of the system will decrease by a factor of. The new velocity (v') will be v. c. If an object of mass 3m collides and velocity v collides inelastically with an object of mass 4m which is initially at rest, then the amount of total system mass in motion will increase by a factor of and the velocity of the system will decrease by a factor of. The new velocity (v') will be v. 31. Insert these words into the four blanks of the sentence: mass, momentum, acceleration, time, impact, weight, impulse, and force. (May have EXTRA words) In a collision, an object experiences a(n) acting for a certain amount of and which is known as a(n) ; it serves to change the of the object. Impulse and Momentum page 4
Conservation of Momentum Lab Purpose: To qualitatively explore conservation of momentum for elastic and inelastic collisions. Materials: Magnetic Cart Plunger Car 2 Cart Masses Cart Track Procedure: 1. Level the track by setting a cart on the track to see which way it rolls. Adjust the leveling feet to raise or lower the ends until a cart placed at rest on the track will not move. Create the following collision scenarios. 2. Part 1: Elastic Collisions - Orient the two carts so their magnetic bumpers are toward each other. Equal Masses: M 1 = M 2 1: V 2 = 0 m/s Place one cart at rest in the middle of the track. Give the other cart an initial velocity toward the cart at rest. 2: V 1 = V 2 : Start the carts with one at each end of the track. Give each cart approximately the same velocity toward each other. 3: V 1 < V 2 : Start both carts at one end of the track. Give the first cart a slow velocity and the second cart a faster velocity so that the second cart catches the first cart. Carts with unequal mass M 2 = 3M 1 : Put two mass bars in one of the carts so that the mass of one cart is approximately three times the mass (3M) of the other cart (M). 4: V 2 = 0 m/s Place the 3M cart at rest in the middle of the track. Give the other cart an initial velocity toward the cart at rest. 5: V 1 = V 2 : Start the carts with one at each end of the track. Give each cart approximately the same velocity toward each other. 6: V 1 < V 2 : Start both carts at one end of the track. Give the 1M cart a slow velocity and the 3M cart a faster velocity so that the 3M cart catches the 1M cart. 3. Part 2: Inelastic Collisions - Orient the two carts so their Velcro pieces will stick together. Make sure the plunger is pushed completely in so it won t interfere with the collision. Equal Masses: M 1 = M 2 7: V 2 = 0 m/s Place one cart at rest in the middle of the track. Give the other cart an initial velocity toward the cart at rest. 8: V 1 = V 2 : Start the carts with one at each end of the track. Give each cart approximately the same velocity toward each other. Carts with unequal mass M 2 = 3M 1 : Put two mass bars in one of the carts so that the mass of one cart is approximately three times the mass (3M) of the other cart (M). 9: V 2 = 0 m/s Place the 3M cart at rest in the middle of the track. Give the other cart an initial velocity toward the cart at rest. Write Up for Conservation of Momentum 1. On your own paper, draw the diagrams, label the mass of the car inside of the box. Use: 1M for a car with no additional masses and 3 M for a car with 2 additional masses. 2. Label the velocity underneath the box using an arrow to represent the velocity vector. Use: a short arrow for slow velocity, a longer arrow for faster velocity and put a zero if the car is at rest. Make sure the differences in arrow lengths is clear. 3. Write a brief description about the total momentum before the collision and the total momentum after the collision. Include information about conservation of momentum. 4. The first one for each case is done for you. Impulse and Momentum page 5
Elastic 1 Equal Mass: M 1 =M 2 M 1 M 2 M 1 M 2 V 1 V 2 =0 m/s V 1 = 0 m/s V 2 InElastic 7 Equal Mass: M 1 =M 2 Drawing with arrows M 1 M 2 M 1 M 2 V 1 V 2 =0 m/s V 1 2 3 4 5 6 M 1 P 1 = MV M 2 P 2 = 0 kg m/s Total Mom M 1 Final P = MV P 1 = 0 kg m/s M 2 Final Total Final P 2 = MV P = MV Equal How does P compare to P Inelastic M 1 M 2 Total 7 P 1 = MV P 2 = 0 kgm/s P = MV Final Mass M = 2M Final Velocity Total Final V = ½ V P = (2M)(1/2V) = MV Relationship between P and P Equal 8 9 Analysis Overall: 1. What is the conservation of momentum? 2. Do you think that the law of conservation of momentum was followed in each case? Explain Rubric: -1 for Sentence fragments, It, contractions, slang Title (1 pts) Diagrams (9x5=45) Data Tables (49 pts) Analysis Questions (2 x 2.5 each = 5 pts) Impulse and Momentum page 6
A1 Conceptual Physics Impulse and Momentum Spring 2011 Chapter 7 Impulse and Momentum REVIEW: Due BEFORE Test Conceptual: 1. How do you determine the momentum of an object? 2. Momentum has a and a which make it a vector quantity. 3. If a is applied to an object it will change the object s, which causes a change in momentum. 4. The net force on an object multiplied by the time the net force is exerted is the and it is equal to the change in. 5. In what units is momentum measured? 6. What is the momentum of a parked car? Why? Does it have inertia? Why? 7. Name two ways a hockey player could increase the momentum (particularly the velocity) of a hockey puck? 8. Why would it be better to hit an air bag as opposed to a dashboard? 9. What is the Law of Conservation of Momentum? 10. What is an elastic collision? 11. What is the equation for an elastic collision? 12. What is an inelastic collision? 13. If two objects of equal and opposite momentums collide elastically what are their momentums afterwards? a. What is the momentum of the system before and after? [0 kg m/s] b. What happens to the final velocity if the aforementioned objects collide inelastically? [0m/s] 14. Which of the following statements are true about momentum?[a, c, d, g, h, k] a. Momentum is a vector quantity. b. The standard unit on momentum is the Joule. c. An object with mass will have momentum. d. An object which is moving at a constant speed has momentum. e. An object can be traveling eastward and slowing down; its momentum is westward. f. Momentum is a conserved quantity; the momentum of an object is never changed. g. The momentum of an object varies directly with the speed of the object. h. Two objects of different mass are moving at the same speed; the more massive object will have the greatest momentum. i. A less massive object can never have more momentum than a more massive object. j. Two identical objects are moving in opposite directions at the same speed. The forward moving object will have the greatest momentum. k. An object with a changing speed will have a changing momentum. 15. Which of the following statements are true about impulse? [b, c, d, f g, h, i] a. Impulse is a force. b. Impulse is a vector quantity. c. An object which is traveling east would experience a westward directed impulse in a collision. d. Objects involved in collisions encounter impulses. e. The Newton is the unit for impulse. f. The kg m/s is equivalent to the units on impulse. g. An object which experiences a net impulse will definitely experience a momentum change. h. In a collision, the net impulse experienced by an object is equal to its momentum change. i. A force of 100 N acting for 0.1 seconds would provide an equivalent impulse as a force of 5 N acting for 2.0 seconds. j. The units for impulse are kg m/s 16. Which of the following statements are true about collisions? [a, b, e, g, j] a. Two colliding objects will exert equal forces upon each other even if their mass is significantly different. b. During a collision, an object always encounters an impulse and a change in momentum. Momentum p 7
A1 Conceptual Physics Impulse and Momentum Spring 2011 Chapter 7 c. During a collision, the impulse which an object experiences is equal to its velocity change. d. The velocity change of two respective objects involved in a collision will always be equal. e. In a collision, the two colliding objects could have different acceleration values. f. In a collision between two objects of identical mass, the acceleration values could be different. g. Total momentum is always conserved between any two objects involved in a collision. h. When a moving object collides with a stationary object of identical mass, the stationary object encounters the greater collision force. i. When a moving object collides with a stationary object of identical mass, the stationary object encounters the greater momentum change. j. A moving object collides with a stationary object; the stationary object has significantly less mass. The stationary object encounters the greater momentum change. 17. Which of the following statements are true about elastic and inelastic collisions? [a,b, e, f,g] a. Perfectly elastic and perfectly inelastic collisions are the two opposite extremes along a continuum; where a particular collision lies along the continuum is dependent upon the amount kinetic energy which is conserved by the two objects. b. Most collisions tend to be partially to completely elastic. c. Momentum is conserved in an elastic collision but not in an inelastic collision. d. Elastic collisions occur when the collision force is a non-contact force. e. A ball is dropped from rest and collides with the ground. The higher that the ball rises upon collision with the ground, the more elastic that the collision is. f. A moving air track glider collides with a second stationary glider of identical mass. The first glider loses all of its kinetic energy during the collision as the second glider is set in motion with the same original speed as the first glider. This is a perfectly inelastic collision. g. The collision between a tennis ball and a tennis racket tends to be more elastic in nature than a collision between a halfback and linebacker in football. 18. Which of the following objects have non-zero momentum? Include all that apply. [a, c,d] a. An electron is orbiting the nucleus of an atom. b. A UPS truck is stopped in front of the school building. c. A Yugo (a compact car) is moving with a constant speed. d. A small flea walking with constant speed across Fido's back. e. The high school building rests in the middle of town. 19. A truck driving along a highway road has a large quantity of momentum. If it moves at the same speed but has twice as much mass, its momentum is. 20. Consider a karate expert. During a talent show, she executes a swift blow to a cement block and breaks it with her bare hand. During the collision between her hand and the block, the. a. time of impact on both the block and the expert's hand is the same b. force on both the block and the expert's hand have the same magnitude c. impulse on both the block and the expert's hand have the same magnitude d. all of the above. e. none of the above. 21. In order to catch a ball, a baseball player naturally moves his or her hand backward in the direction of the ball's motion once the ball contacts the hand. This habit causes the force of impact on the players hand to be reduced in size principally because _. a. the resulting impact velocity is lessened b. the momentum change is decreased c. the time of impact is increased d. the time of impact is decreased e. none of these Momentum p 8
A1 Conceptual Physics Impulse and Momentum Spring 2011 Chapter 7 22. Suppose that you're driving down the highway and a moth crashes into the windshield of your car. Which undergoes the greater change is momentum? a. the moth b. your car c. both the same 23. Suppose that you're driving down the highway and a moth crashes into the windshield of your car. Which undergoes the greater force? a. the moth b. your car c. both the same 24. Suppose that you're driving down the highway and a moth crashes into the windshield of your car. Which undergoes the greater impulse? a. the moth b. your car c. both the same 25. Suppose that you're driving down the highway and a moth crashes into the windshield of your car. Which undergoes the greater acceleration? a. the moth b. your car c. both the same Problems: 26. What is the momentum of a 1000 kg car traveling at 20 m/s? [20,000 kg m/s] 27. A 40 kilogram bowling ball goes down the lane at a velocity of 7 m/s and comes to a complete stop when it hits a bumper in the middle of the bowling lane. a. What was the change in momentum for the bowling ball? [-280 kg m/s] b. If the force of impact was -25 N, what time did it take for the bowling ball to stop upon impact with the bumper? [11.2 s] 28. A 2,000 kg car traveling at 25 m/s comes to a complete stop in 3 seconds. What was the force needed to stop the car? [-16,666.67 N] 29. A 1 kg soccer ball traveling at 3 m/s collides with another ball traveling at - 5m/s. The other ball comes to rest and the soccer ball travels back the way it came at - 7 m/s. What kind of collision is this? What is the mass of the second ball? (2 kg) 30. A 500 kg wagon is rolling at 2 m/s collides with a 1000 kg wagon rolling at - 2 m/s. If the wagons stick together, what is their final velocity? What kind of collision is this? (- 0.67 m/s) 31. A 95 kg fullback running at 8.2 m/s collides in mid-air with a 128 kg defensive tackle moving in the opposite direction. Both players end up with zero speed. a. What was the fullback's momentum before the collision? [779 kg m/s] b. What was the change in the fullback's momentum? [-779 kg m/s] c. What was the change in the tackle's momentum? [779 kg m/s] d. What was the tackle's original momentum? [-779 kg m/s] e. How fast was the tackle moving originally? (original velocity) [-6.09 m/s] 32. A 2,575 kg van runs into the back of a 825 kg compact car at rest. They move off together at 8.5 m/s. Assuming no friction with the ground, find the initial velocity of the van. [11.22 m/s] 33. A car with a mass of 1245 kg is moving at a velocity of 29 m/s. It hits a 2175 kg car traveling at 15 m/s in the same direction as the first car. The bumpers lock and the cars move together in the same direction. At what velocity will they move if there is no friction? [20.10 m/s] 34. An SUV with a mass of 4000 kg traveling at 30 m/s hits a small car that is traveling in the same direction at 15 m/s. Their bumpers lock and they move together at 28 m/s. What was the mass of the small car? [615.38 kg] 35. A car has a mass of 2,000 kg and is traveling at 15 m/s. It comes to a stop with a force of - 5,000 Newtons. a. What is the car s impulse? [-30,000 Ns] b. How much time does it take to stop the car? [6 s] 36. A ball is given a force of 40 Newtons over 2 seconds of time. What is its impulse? [80 Ns] 37. A 2000 kg car (Car A) traveling at 2 m/s is rear-ended by a 3000 kg car (Car B) going at 6 m/s. After the collision, the Car A travels at 3 m/s. What is the velocity of Car B after the collision? [5.33 m/s] Momentum p 9