Impulse & Momentum

2 of 42 Have you ever wondered… Why golfers and bowlers “follow through”? Why skydivers bend their knees upon impact? Why falling on a wood floor (or into a swimming pool) hurts less than falling on a cement one?

3 of 42 Have you ever wondered… What’s the best strategy to win a “water balloon toss” or an “egg toss”? Why we make auto air bags and padded dash boards? How the police can figure out how fast you were going BEFORE an accident by measuring your skid marks?

4 of 42 Impulse and Momentum ImpulseMomentum To answer all of these questions--you need to understand: Impulse and Momentum Recall, Newton’s first law…The Law of Inertia The study of inertia for moving objects is the study of “momentum”

5 of 42 Consider the following: When a baseball bat hits a baseball, a force is applied OVER A SHORT PERIOD OF TIME.

6 of 42 Impulse Defn: A force applied over a period of time is called an IMPULSE. What are the SI units of Impulse?

7 of 42 Example - Impulse A batter hits a 0.5 kg ball with a force of 200N. If the time of contact was seconds, find the impulse of the ball.

8 of 42 Example #2 A batter hits a 0.5 kg ball with a force of 500N. If the time of contact was seconds, find the impulse of the ball. a) 0 N·s b) N·s c) N·s d) N·s e) I have no clue…

9 of 42 Example #3 A batter hits a 0.5 kg ball with a force of 500N. If the impulse is 75 N·s, then what is the contact time between the ball & bat? a) 0 sec b) sec c) 75 sec d) sec e) I have no clue…

10 of 42 Answer: (b) A batter hits a 0.5 kg ball with a force of 500N. If the impulse is 75 N·s, then what is the contact time between the ball & bat?

11 of 42 Example #4 A batter hits a 0.5 kg ball and the impulse given to the ball is 125 N·s. If the ball & bat are in contact for 200 milli-seconds, then what is the force of the bat? a) 0 N b) N c) 2.5 N d) 625 N e) I have no clue…

12 of 42 Back to baseball...Which will have the greater speed afterward? A large or a small ball? A fast or a slow ball? A large or a small bat? A fast or a slow swing?

13 of 42 Momentum Defn: The MOMENTUM of a body is equal to the product of its mass and its velocity. Is momentum a vector or a scalar? What are the SI units of momentum?

14 of 42 Example #5 A boy standing at one end of a floating raft that is stationary relative to the shore walks to the opposite end of the raft, away from the shore. As a consequence, the raft. (a) remains stationary, (b) moves away from the shore, (c) moves toward the shore (d) Not enough information given

15 of 42 Answer: (c) A boy standing at one end of a floating raft that is stationary relative to the shore walks to the opposite end of the raft, away from the shore. As a consequence, the raft. Answer: (c) moves toward the shore - Newton’s 3 law

16 of 42 Example #6 Which has a greater momentum, a heavy truck at rest or a moving skateboard? (a) Heavy truck, (b) Skateboard, (c) Neither (same momentum) (d) Not enough information given

17 of 42 Answer: (b) Which has a greater momentum, a heavy truck at rest or a moving skateboard? Answer: (b) The truck at rest has no speed, hence no momentum. So the moving skateboard has greater momentum.

18 of 42 Making the Connection: Look at the units of Impulse and Momentum…Do you notice anything? Recall, F = m·a…can you rearrange the equation to say something about Impulse or Momentum?

19 of 42 Making the Connection: F = m a A = v/t F = m (v/t) Ft = mv Impulse = Momentum!

20 of 42 The Impulse-Momentum Theorem When a net force acts upon a body for a period of time, the Impulse applied by the force is equal to the body’s change in Momentum!

21 of 42 Impulse-Momentum Theorem #1: If your Force is limited, how can you MAXIMIZE the impulse you apply? By increasing the time of contact! Golfing…Baseball…

22 of 42 Impulse-Momentum Theorem #2 If your change in momentum is constant, how can you MINIMIZE the force applied to you? By increasing the time of contact! Bending knees upon impact, rolling with the punches, crumple zones, running shoes, air bags…

23 of 42 Momentum Changes and Bouncing Is it more dangerous when a flower pot falls on your head and breaks or stays in one piece and bounces back up? When an object bounces, what happens to it’s velocity? How does that effect it’s change of momentum? Since ∆p is greater in bouncing situations, the Impulse applied will be greater!

The Law of Action-Reaction A collision is an interaction between two objects which have made contact (usually) with each other. A collision results in a force being applied to the two colliding objects. Such collisions are governed by Newton's laws of motion.

Newton's third law of motion applied to collisions between two objects. In a collision between two objects, both objects experience forces which are equal in magnitude and opposite in direction. Such forces cause one object to speed up (gain momentum) and the other object to slow down (lose momentum). According to Newton's third law, the forces on the two objects are equal in magnitude.

Effect of collisions on acceleration While the forces are equal in magnitude and opposite in direction, the acceleration of the objects are not necessarily equal in magnitude.

And so, in comes Newton ’ s Second Law of Motion The acceleration of an object is dependent upon both force and mass. Thus, if the colliding objects have unequal mass, they will have unequal accelerations as a result of the contact force which results during the collision.

Example: A collision occurs between the moving club head and the stationary golf ball.

You can observe unequal accelerations. Although there is a high speed given to the ball as the result of the collision, you are not observing unequal forces upon the ball and club head.

F = m * a Since club head and ball experience equal forces, but the mass of the ball is much smaller than that of the club, acceleration will be bigger. The least massive object receives the greatest acceleration.

the law of conservation of momentum For a collision occurring between object 1 and object 2 in an isolated system, the total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision.

the law of conservation of momentum the momentum lost by object 1 is equal to the momentum gained by object 2 total momentum of a collection of objects (a system) is conserved the total amount of momentum is a constant or unchanging value.

The Equation p A1 + p B1 = p A2 + p B2

Inelastic Collisions Post-collision: The objects stick together. Ex: Catching a ball Treat the mass post-collision as one unit (add together). (m A x v 1A ) + (m B x v 1B ) = (m A + m B ) x v 2

35 of 42 Example #7 Jocko, who has a mass of 60kg and stands at rest on ice, catches a 20kg ball that is thrown to him at 3m/s. How fast do Jocko and the ball move across the ice? (a)0 m/s (b).75 m/s (c) 200 m/s (d) no way to determine

36 of 42 Answer: (b) (b): The momentum before the catch is all in the ball, 20kg x 3m/s = 60kg·m/s. This is also the momentum after the catch, where the moving mass is 80kg (60kg for Jocko and 20kg for the caught ball.) 80kg x v = 60kg·m/s v = 60kg·m/s/80kg =.75m/s

Elastic Collisions Each object remains independent after the collision. Ex: playing billiards (pool) (m A x v 1A ) + (m B x v 1B ) = (m A x v 2A ) + (m B x v 2B )

38 of 42 Example #8 Which would be more damaging: (a)Driving into a massive concrete wall (b)Driving at the same speed into a head-on collision with an identical car traveling toward you at the same speed (c)Neither - the same amount of damage (d)Not enough information given

39 of 42 Answer: (c) (c): Both cases are equivalent, because either way, your car rapidly decelerates to a dead stop. The dead stop is easy to see when hitting the wall, and identical cars at equal speeds means equal momenta—zero before, zero after collision.

Recoil When a gun is fired, remember Newton’s Third Law (action-reaction.) The energy of the explosion sends the bullet forward, but also sends the gun backwards. The backwards motion of the gun is called Recoil.

41 of 42 Example #9 Strictly speaking, when a gun is fired, compared with the momentum of the recoiling gun, the opposite momentum of the bullet is (a) less (b) more (c) the same (d) no way to determine (Neglect the effect of the hand.)

42 of 42 Answer: (a) (a) Why? Because more than just a bullet comes out of the barrel when a gun is fired. The gas, formed when the powder in the cartridge burns, pushes the bullet along the barrel and this gas too has appreciable mass and exits at high speed. So, Momentum of recoiling gun = momentum of bullet + momentum of gases.

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