Momentum and Collisions

Coefficient of Elastic Restitution

"e" -Represents the bounciness of an object -The ratio of the velocities of an object after and before an impact -Vb= speed of object after impact -Vd=speed of object before impact -Hb=bounce height -Hd=drop height

Elastic Collision

A collision in which the total momentum and the total kinetic energy are conserved -the two objects collide and return to their original shapes with no loss of total kinetic energy. -after the collision, the objects move separately -the two objects bounce after the collision so that they move separately -conserved momentum and kinetic energy

Perfectly Inelastic Collision

A collision in which two objects stick together after colliding; the two objects essentially become one object after the collision -final mass is equal to the combined masses of the colliding objects -2 objects move (as one) with the same velocity after the collision -Kinetic energy is not conserved -the two objects stick together after the collision so that their final velocities are the same.

Moment of Inertia

A measure of a body's resistance to change in its angular motion -scalar quantity For a given body: -mass closer to axis of rotation = smaller 1 -mass further from axis of rotation = larger 1 r= distance from axis of rotation

Linear Momentum

A quantity defined as the product of the mass and velocity of an object. -quantity of motion with which a body proceeds in a certain direction -vector quantity; the direction of the momentum vector is the same as the direction of the velocity vector p= m*v

Newton's 1st Law: Principle of Conservation of Angular Momentum

A rotating body will continue to turn about its axis of rotation with constant angular momentum unless an external couple or eccentric force is exerted on it EX: Tucked Dive -At take off: L=I*W, I is large, W is small -Divers Tuck: I- decreases, W increases -Diver Extends: I increases, W decreases

22. Cars are equipped with padded dashboards. In collisions, the padded dashboards would be safer than non-padded ones because they ____. List all that apply. a. increase the impact time b. decrease an occupant's impulse c. decrease the impact force d. none of the above

A,C Padded dashboard serve to increase the time over which the momentum of a passenger is reduced to zero. With this increase in time, there is a decrease in force

6. Which of the following objects have momentum? Include all that apply. 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.

A,C,D An object has momentum if it has its mass in motion.

18. In a physics experiment, two equal-mass carts roll towards each other on a level, low-friction track. One cart rolls rightward at 2 m/s and the other cart rolls leftward at 1 m/s. After the carts collide, they couple (attach together) and roll together with a speed of _____________. Ignore resistive forces. a. 0.5 m/s b. 0.33 m/s c. 0.67 m/s d. 1.0 m/s e. none of these

A. (2 kg•m/s) - (1 kg•m/s) = (2 kg) v 1 kg•m/s = (2 kg)v (1 kg•m/s) / (2 kg) = v 0.5 m/s = v

23. A 4 kg object has a momentum of 12 kg•m/s. The object's speed is ___ m/s. a. 3 b. 4 c. 12 d. 48 e. none of these.

A. 3 This is a relatively simple plug-and-chug into the equation p=m*v with m=4 kg and p=12 kg•m/s.

1. Which of the following is true about Momentum?

Answers: a) Momentum is a vector quantity (the momentum of an object is not fully described until the direction of momentum is defined) d) an object which moving at a constant speed has momentum g) the momentum of an object varies directly with the speed of the object (as the speed of an object increases, so does the velocity p=m*v) h) Two objects of different mass are moving at the same speed; the more massive object will have the greatest momentum. (a more massive object has a greater product of mass and velocity) k) an object with changing speed will have a changing momentum (p=m*v)

2. Which of the following are true about the relationship between momentum and energy?

Answers: b) if an object has momentum, then it must also have mechanical energy (if an object is moving, it has kinetic energy and if an object has kinetic energy, then it has mechanical energy) e) Two objects of varying mass have the same momentum. The least massive of the two objects will have the greatest kinetic energy. (When comparing the kinetic energy of two objects, the velocity of an object is of double importance. So if two objects of different mass have the same momentum, then the object with the least mass has a greater velocity.)

24. A wad of chewed bubble gum is moving with 1 unit of momentum when it collides with a heavy box that is initially at rest. The gum sticks to the box and both are set in motion with a combined momentum that is ___. a. less than 1 unit b. 1 unit c. more than 1 unit d. not enough information

B. 1 Unit Before the collision, the total system momentum is 1 unit - all due to the motion of the wad of gum. Since momentum must be conserved, the total momentum of the box and gum after the collision must also be 1 unit.

30. When a mass M experiences a velocity change of v in a time of t, it experiences a force of F. Assuming the same velocity change of v, the force experienced by a mass of 2M in a time of (1/2)t is ____. a. 2F b. 4F c. (1/2)*F d. (1/4)*F e. none of these

B. 4F F = m*(Delta vel.)/t

31. When a mass M experiences a velocity change of v in a time of t, it experiences a force of F. Assuming the same velocity change of v, the force experienced by a mass of 2M in a time of (1/4)t is ____. a. 2F b. 8F c. (1/2)*F d. (1/8)*F e. none of these

B. 8F F = m*(Delta vel.)/t

25. A relatively large force acting for a relatively long amount of time on a relatively small mass will produce a relatively ______. List all that apply. a. small velocity change b. large velocity change c. small momentum change d. small acceleration

B. Large velocity change A large force and for a long time will result in a large impulse and therefore a large momentum change.

28. A 5-N force is applied to a 3-kg ball to change its velocity from +9 m/s to +3 m/s. The impulse experienced by the ball is ____ N•s. a. -2.5 b. -10 c. -18 d. -45 e. none of these

C. -18 The impulse equals the momentum change. The momentum change in this problem is -18 kg•m/s. Thus, the impulse is -18 N•s

27. A 5-N force is applied to a 3-kg ball to change its velocity from +9 m/s to +3 m/s. This impulse causes the momentum change of the ball to be ____ kg•m/s. a. -2.5 b. -10 c. -18 d. -45 e. none of these

C. -18 the momentum change of an object can be found if the mass and the velocity change are known. In this equation, m=3 kg and the velocity change is -6 m/s. When finding the velocity change, always subtract the initial velocity from the final velocity (vf - vi).

14. 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

C. Both the same Each object experiences the same force (Newton's third law) for the same amount of time, leading to the same impulse, and subsequently the same momentum change.

13. 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

C. Both the same The object with the least mass always receives the greatest velocity change and acceleration.

7. 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 ________________. a. zero b. quadrupled c. doubled d. unchanged

C. Doubled Momentum is directly related to the mass of an object.

26. Consider the concepts of work and energy (presuming you have already studied it) and those of impuse and momentum. Force and time is related to momentum change in the same manner as force and displacement pertains to ___________. a. impulse b. work c. energy change d. velocity e. none of these.

C. Energy change A force multiplied by a time gives an impulse which will cause (and be equal to) a momentum change.

21. Two objects, A and B, have the same size and shape. Object A is twice as massive as B. The objects are simultaneously dropped from a high window on a tall building. (Neglect the effect air resistance.) The objects will reach the ground at the same time but object A will have a greater ___. Choose all that apply. a. speed b. acceleration c. momentum d. none of the above quantities will be greater

C. Momentum the heavier object however has more momentum since momentum takes into account both the speed and the mass of the object (p=m*v)

20. The firing of a bullet by a rifle causes the rifle to recoil backwards. The speed of the rifle's recoil is smaller than the bullet's forward speed because the ___. a. force against the rifle is relatively small b. speed is mainly concentrated in the bullet c. rifle has lots of mass d. momentum of the rifle is unchanged e. none of these

C. Rifle has lots of mass Because of the large mass of the rifle, the acceleration and the recoil speed of the rifle is small.

11. 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

C. The time of impact is increased Imparting such an impulse over a long time results in a small force.

19. A physics cart rolls along a low-friction track with considerable momentum. If it rolls at the same speed but has twice as much mass, its momentum is ____. a. zero b. four times as large c. twice as large d. unchanged

C. Twice as large If the mass of an object is somehow doubled, the momentum is doubled as well.

36. Consider the head-on collision between a lady bug and the windshield of a high speed bus. Which of the following statements are true? List all that apply. a. The magnitude of the force encountered by the bug is greater than that of the bus. b. The magnitude of the impulse encountered by the bug is greater than that of the bus. c. The magnitude of the momentum change encountered by the bug is greater than that of the bus. d. The magnitude of the velocity change encountered by the bug is greater than that of the bus. e. The magnitude of the acceleration encountered by the bug is greater than that of the bus.

D and E In any collision between two objects, the force, impulse, and momentum change are the same for each object. However, the smaller mass object encounters a greater acceleration and velocity change.

9. 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.

D. All of the above The lower mass object always receives the greater velocity change and acceleration.

12. Suppose that Paul D. Trigger fires a bullet from a gun. The speed of the bullet leaving the muzzle will be the same as the speed of the recoiling gun ____. a.because momentum is conserved b.because velocity is conserved c. because both velocity and momentum are conserved d. only if the mass of the bullet equals the mass of the gun e. none of these

D. Only if the mass of the bullet equals the mass of the gun The velocity change would only be the same if their masses were the same. Otherwise, the smaller-mass object receives a greater velocity change.

10. It is NOT possible for a rocket to accelerate in outer space because ____. List all that apply. a.there is no air in space b.there is no friction in space c.there is no gravity in outer spaced. d.... nonsense! Rockets do accelerate in outer space.

D. Rockets do accelerate in outer space Newton's third law of motion; It does not matter that there is no air outside of the rocket.

32. When a mass M experiences a velocity change of v in a time of t, it experiences a force of F. Assuming the same velocity change of v, the force experienced by a mass of (1/2)M in a time of (1/2)t is ____. a. 2F b. 4F c. (1/2)*F d. (1/4)*F e. none of these

E. None of these

17. Three boxes, X, Y, and Z, are at rest on a table as shown in the diagram at the right. The weight of each box is indicated in the diagram. The net or unbalanced force acting on box Y is _____. a. 4 N down b. 5 N down c. 5 N up d. 10 N up e. zero

E. Zero

Newton's 3rd Law:

For every torque that is exerted by one body on another, there is an equal and opposite torque exerted by the second body on the first. Ex: Stop yourself from falling forward -Start to fall forward -Swing your arms in direction of fall -Torso rotates in opposite direction Body exerts a torque on the earth, but the I of the earth is so large, the acceleration it experiences as a result is imperceptible.

Inelastic Collision

Most collision are neither elastic nor perfectly inelastic, they are inelastic -the two objects bounce and move separately after the collision -the total kinetic energy decreases in the collision -the two objects deform during the collision so that the total kinetic energy decreases, but the objects move separately after the collision -conserves momentum

Transfer of Angular Momentum

Process of redistributing the angular momentum within the body during flight phase; Can alter angular momentum of individual body segments - Ex: Pike Dive -Angular momentum initially in upper body during ascending phase -Angular momentum transferred to legs during descending phase -Go into pike; L of legs close to 0; L of arms and trunk is large -Extend out of pike: L of arms and trunk close to 0; L of legs is large Can alter axis of rotation.

35. If mass and collision time are equal, then impulses are greater on objects which rebound (or bounce). a. TRUE b. FALSE

TRUE More velocity change means more momentum change and thus more impulse.

Impulse-Momentum Theorem

The impulse exerted by a force is equal to the change in momentum caused by that force. -Extending the time interval over which a constant force is applied allows a smaller force to cause a greater change in momentum

Impulse

The product of force and the time over which the force acts on an object -Vector quantity: has magnitude and direction -J=F*t -Changes in momentum are caused by forces

Angular Momentum (L)

The quantity of a body's angular motion -L=I*w -vector quantity -A body w/ L during flight is rotating -Need more L to complete more turns -L generated at takeoff by torque or eccentric force W= angular velocity; radians

Newton's 2nd Law

The rate of change of angular momentum of a body is proportional to the torque causing it and the change takes place in the direction in which the torque acts [T=I*a]

Conservation of Linear Momentum

You can never create or destroy momentum; all we can do is transfer momentum from one object to another -a total momentum of a system of masses isolated from external forces is constant in time

5. Which of the following statements are true about elastic and inelastic collisions?

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. e) Elastic collisions occur when the collision force is a non-contact force. (kinetic energy is transformed into different energy such as sound and heat). f) Most collisions are not inelastic because the collision forces cause energy of motion to be transformed into sound, light and thermal energy (to name a few). g) 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. (If large amounts of kinetic energy are conserved when a ball collides with the ground, then the post-collision velocity is high compared to the pre-collision velocity) i) 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.

4. Which of the following are true about collisions?

a) two colliding forces will exert equal forces upon each other even if their masses are significantly different. (Newton's law of action-reaction) b) During a collision, an object always encounters an impulse and a change in momentum (collision force has some time to cause an impulse, and this impulse acts on the momentum) f) in a collision, two colliding objects can have different acceleration values (if different masses, there will be equal forces that produce different acceleration)

3. Which of the following statements are true about impulse?

b) Impulse is a vector quantity (not fully described unless it has direction) d) objects involved in collisions experience impulse (in a collision, there is a collision force which endures for the some amount of time.) f) kg*m/s is the units for impulse (N*s into kg*m/s^2-> kg*m/s g) An object which experiences a net impulse will definitely experience a momentum change. (impulse acts upon object to change velocity and momentum) h) In a collision, the net impulse experienced by an object is equal to its momentum change.

8. TRUE or FALSE: 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. a. True b. False

b. False For the same collision time, bouncing involves a greater velocity change, a greater momentum change, and therefore a greater impulse.

29. A 5-N force is applied to a 3-kg ball to change its velocity from +9 m/s to +3 m/s. The impulse is encountered by the ball for a time of ____ seconds. a. 1.8 b. 2.5 c. 3.6 d. 10 e. none of these

c. 3.6 t = m*(delta v)/F = (3 kg)*(-6 m/s) / (5 N) t = 3.6 s