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Home , Impulse (physics), Momentum

Momentum and E xam Preparation Name ______P___

In this unit, we were introduced to the concept of m omentum. conceptually represents h ow difficult it is to stop a moving object – i t is mathematically equal to the of an object multiplied by the instantaneous of the object. The SI units for momentum are k g m/s. When comparing the momentum of two moving objects, a mo re massive object will have m ore momentum if the are the same. I mpulse is equal to the change in momentum. i s inversely proportional to the interval during which momentum is changed. If the change in momentum is fixed or constant (when an object is dropped, or a ), then we can apply the I mpulse-Momentum Theorem, and increase or decrease the amount of acceleration on the object through manipulation of the time variable. A small acceleration applied over a long time interval c an produce a large change in an object’s momentum, while a large acceleration d oes not always produce a large change in the object’s momentum – it depends on the time the acceleration is endured. For a constant acceleration, the longer the time applied, the greater the change in momentum. T he law of conservation of momentum states that the total momentum of all objects interacting with one another remains constant regardless of the nature of the between the objects – in other words, the t otal momentum before and after a collision is the same – that is, it is c onserved.

p = mv Impulse = J = mat = mΔv = Δp = c hange in momentum ∑p b efore = ∑p a fter

For the following questions, i dentify t he type of collision. (E lastic, Inelastic, )

1. A soccer ball collides with another soccer ball at rest.

2. Two objects stick together and move with a common velocity after colliding.

3. Two objects move separately after colliding, and the total momentum of the system remains constant.

4. A student is riding a skateboard and jumps off.

For the following questions, s how y our and make sure you do NOT have the same numbers as your neighbors.

5. What velocity must a ______kg car have in order to have the same momentum as a ______kg van traveling at a velocity of ______m/s to the west? (must be different than car)

6. Two skaters stand facing each other. One skater’s mass is _____ kg, and the other’s mass is ____ kg. If the skaters push away from each other, which skater will have a greater velocity? Explain.

7. A ball with a momentum of _____ kg∙ m /s hits a wall and bounces straight back. What is the change in the ball’s momentum?

8. What is the mass of an object that has a change in momentum of ______kg • m/s when its velocity changes from ______m/s to ______m/s?

9. A ______kilogram object starts out with a velocity of ______m/s and has momentum change of ______kg • m/s. Calculate the final velocity of the object.

10. Calculate the initial momentum of a ______kg mass that has a velocity change of ______m/s and has a final momentum of ______kg • m/s.

11. How much time does it take ______kg to change its velocity by ______m/s due to a mass of ______kg accelerated at a rate of ______m/s2 ?

12. Find the change in an object’s velocity if a mass of ______kg is accelerated at a ______m/s2 rate for a time of ______seconds.

13. Calculate the final velocity of an object with a mass of ______kg that starts out with an initial velocity of ______m/s and has an impulse of ______kg • m/s change its momentum.

14. A mass of ______kg has an initial velocity of ______m/s. It hits a mass of ______kg at rest in an . If the final velocity of the second is ______m/s then what is the final velocity of the first?

15. An object with an ______kg mass has an initial velocity of ______m/s. It hits a second mass of ______kg with an initial velocity of −______m/s in an elastic collision. If the velocity of the first mass is −______m/s after the collision then what is the final velocity of the second? (2 pts)

16. A mass of ______kg has an unknown initial velocity. It hits a second mass of ______kg with an initial velocity of −______m/s in an elastic collision. The final velocity of the second mass is ______m/s after the collision and the final velocity of the first is ______m/s. Calculate the initial velocity of the first. (2 pts)

17. A mass of ______kg has an initial velocity of ______m/s. It hits a second ______kg mass with an unknown initial velocity in an elastic collision. The velocity of the second object is − ______m/s after the collision and the final velocity of the first object is −______m/s. Calculate the initial velocity of the second mass.

18. A mass of ______kg has a velocity of ______m/s and strikes a mass of ______kg with a velocity of −______m/s in a perfectly . Find the final velocity of the two if after they are stuck together.

19. A ______kg mass has an unknown initial velocity and hits a mass of ______kg with a velocity of −______m/s in a perfectly inelastic collision so the two stick and move together with a final velocity of ______m/s. Find the initial velocity of the first object.

20. A mass of ______kg is at rest and spontaneously explodes into two pieces. ______kg of the mass flies off with a velocity of ______m/s and the remaining ______kg flies off with an unknown velocity. Calculate the unknown velocity for the remaining ______kg of mass. (2 pts)

21. Two snowballs are thrown towards each other and collide mid-air, exploding into the air in all directions. What can be said about the total momentum of the thousands of resulting ice crystal fragments?

22. A soccer ball collides with another soccer ball at rest. The total momentum of the balls a. is zero. c. remains constant. b. increases. d. decreases.

23. When comparing the momentum of two moving objects, which of the following is correct? a. The object with the higher velocity will have less momentum if the are equal. b. The more massive object will have less momentum if its velocity is greater. c. The less massive object will have less momentum if the velocities are the same. d. The more massive object will have less momentum if the velocities are the same.

24. A child with a mass of 23 kg rides a bike with a mass of 5.5 kg at a velocity of 4.5 m/s to the south. Compare the momentum of the child with the momentum of the bike.

25. A 75 kg person walking around a corner bumped into an 80 kg person who was running around the same corner. The momentum of the 80 kg person a. increased. c. remained the same. b. decreased. d. was conserved.

26. Two objects with different masses collide and bounce back after an elastic collision. Before the collision, the two were moving at velocities equal in magnitude but opposite in direction. After the collision, a. the less massive object had gained momentum. b. the more massive object had gained momentum. c. both objects had the same momentum. d. both objects lost momentum.

27. The law of conservation of momentum states that a. the total initial momentum of all objects interacting with one another usually equals the total final momentum. b. the total initial momentum of all objects interacting with one another does not equal the total final momentum. c. the total momentum of all objects interacting with one another is zero. d. the total momentum of all objects interacting with one another remains constant regardless

28. A student walks to class at a velocity of 3 m/s. To avoid walking into a door as it opens, the student slows to a velocity of 0.5 m/s. Now late for class, the student runs down the corridor at a velocity of 7 m/s. At what point in this scenario does the student have the least momentum?

29. An impulse is applied to stop a moving shopping cart. How would increasing the time interval change the impulse?

30. Is it possible for a spaceship traveling with constant velocity to experience a momentum change? Explain your answer.

31. On a pool table, a moving cue ball collides with the eight ball, which is at rest. Is it possible for both balls to be at rest immediately after the collision? Use the law of conservation of momentum to explain your reasoning.

32. A explodes into two fragments, one 25 heavier than the other. The magnitude of the momentum change of the lighter fragment is A) 25 times as great as the momentum change of the heavier fragment. B) The same as the momentum change of the heavier fragment. C) 1/25 as great as the momentum change of the heavier fragment. D) 5 times as great as the momentum change of the heavier fragment. E) 1/4 as great as the momentum change of the heavier fragment.

33. A rocket explodes into two fragments, one 25 times heavier than the other. The magnitude of the velocity change of the lighter fragment is A) 25 times as great as the velocity change of the heavier fragment. B) The same as the velocity change of the heavier fragment. C) 1/25 as great as the velocity change of the heavier fragment. D) 5 times as great as the velocity change of the heavier fragment. E) 1/4 as great as the velocity change of the heavier fragment.

34. In a collision between two unequal masses, which mass receives a greater impulse? Explain your answer.

35. Three objects are moving along a straight line as shown in the figure. Taking the positive direction to be to the right, what is the total momentum of this system?

A) +106 kg ∙ m/s B) -106 kg ∙ m/s C) +14.0 kg ∙ m/s D) -14.0 kg ∙ m/s E) 0.00 kg ∙ m/s

37. A ball is dropped from the same height upon various flat surfaces. For the same collision time, impulses are smaller when the most bouncing take place. (Justify your choice) a. True b. False

38. In order to catch a ball, a baseball player naturally moves his or her hand backward in the direction of the ball's once the ball contacts the hand. This habit causes the on the players hand to be reduced 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

A halfback (m = 60 kg), a tight end (m = 90 kg), and a lineman (m = 120 kg) are running down the football field. Consider their motion maps below.

39. Compare the velocities of these three players. How many times greater are the velocity of the halfback and the velocity of the tight end than the velocity of the lineman?

40. W hich p layer has the greatest momentum? Explain.

41. Construct a motion map to show three of the object’s movement along the horizontal dimension that is accelerating positively from rest. All dots should have labels of two vectors drawn at the appropriate lengths in the accurate direction. The spacing of the dots should show the change in this object’s velocity over this time period.

42. A student throws a rock with an initial h orizontal velocity of 2 m/s off the edge of a cliff. The rock leaves the student’s hand 45 meters above the ground at the bottom of the cliff. Find the time it takes for the object to land and use this to find the the of the rock’s landing spot from the base of the cliff.

43. The dots below represent a ball right after it was thrown, at its highest point and right before it lands. a. Assign initial values (at point P) for both horizontal and vertical components of the velocity, and determine the acceleration, then complete the table for the remaining b. O n each of the three dots draw three vectors representing the velocity components and acceleration. Your vectors should point in the accurate directions and be scaled to their proper lengths.

POINT vx vy a

P

Q

R

Analyze the /time graph to answer the questions below:

44. Describe the slope of the graph during the first half the graph.

a. Describe the slope of the graph at the halfway point.

b. Describe the slope of the graph during the second half the graph.

c. What does the slope represent?

d. Create a matching velocity/time and an e. acceleration/time graph on the axes provided:

45. Answer the questions using the velocity vs time graph: c. How much does it accelerate from point B to point C?

d. What is the object’s total from point C to point D?

e. How much does the object accelerate from point C to point D?

a. What is the object’s total displacement from point A f. What is the object’s total displacement from point D to to point B? point E?

b. How much does this object accelerate in g. What is the object’s total displacement from point A to from points A to B? point E?

46. A ball is kicked off a field at a 60∘ above the field with an initial velocity of 15.0 m/s.

a. Calculate the the ball’s initial vertical velocity and its initial horizontal velocity.

b. State the ball’s vertical and horizontal velocity at its greatest height above the field.

c. Find the amount of time it took for this ball to reach the high point in its motion.

d. Calculate the height of the ball when it reached its highest point above the field.

e. Calculate the distance from the ball’s landing point from where it was first kicked.

47. An object’s velocity is pointing in the negative direction and it has a constant acceleration in the negative direction.

b. Does the of this object increase or decrease? Justify your response.

c. Does the velocity of this object increase or decrease? Justify your response.

48. Write a reflection below about how your performance on the acceleration assessment could have been better. You may discuss the issues there were with the test design or the lack of time you had to finish but the reflection should focus on things you have control over. This may be about how you study, the way you take notes or how often you ask for help. The goal of this reflection is to get you to think about how to improve your performance on future assessments.