Impulse & Momentum

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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?

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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?

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Impulse and Momentum

To answer all of these questions--you need to understand: ImpulseImpulse and MomentumMomentum

Recall, Newton’s first law…The Law of Inertia The study of inertia for moving objects is the

study of “momentum”

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Consider the following:

When a baseball bat hits a baseball, a force is applied OVER A SHORT PERIOD OF TIME.

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Impulse

Defn: A force applied over a period of time is called an IMPULSE.

What are the SI units of Impulse?

I F t

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Example - Impulse

A batter hits a 500g ball with a force of 200N. If the time of contact was 0.205 seconds, find the impulse of the ball.

I F t

I 200N 0.205sec

I 41N sec

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Example #2

A batter hits a 500g ball with a force of 500N. If the time of contact was 0.205 seconds, find the impulse of the ball.

I F ta) 0 N·sb) 102.5 N·s c) 51250 N·sd) 250000 N·se) I have no clue…

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Example #3

A batter hits a 500g 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 secb) 0.150 sec c) 75 secd) 37500 sece) I have no clue…

I F t

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Answer: (b)

A batter hits a 500g ball with a force of 500N. If the impulse is 75 N·s, then what is the contact time between the ball & bat?

I Ft

t =I

F

t =75 N sec

500 Nt = 0.150 sec

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Example #4

A batter hits a 500g 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 Nb) 0.625 N c) 2.5 Nd) 625 Ne) I have no clue…

I F t

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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?

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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?

p m

v

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Determine the following momentums…

Ex #1 - A 1200lb car moving at 60mph Ex #2 - A 5.0g bullet moving at 900m/s Ex #3 - A 3 ton elephant sitting still Ex #4 - A 150g hummingbird flying at 40mph

– ALL answers need to be in kg m/s

1 lb = 0.454 kg; 1 mph = 0.447 m/s

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Determine the following momentums…Solution

Ex #1 - A 1200lb car moving at 60mph = 14599.7 kg m /s

Ex #2 - A 5.0g bullet moving at 900m/s = 4.5 kg m/s

Ex #3 - A 3 ton elephant sitting still = 0 kg m/s

Ex #4 - A 150g hummingbird flying at 40mph = 2.68 kg m/s

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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

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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

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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

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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.

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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?

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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!

F t m

v m(

v f

v 0)

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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…

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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…

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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!

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The Law of Conservation of Momentum

Internal forces are forces that act within a system, external forces are forces that act on a system from outside…

If a system is not affected by any net external force, it is said to be “ISOLATED”.

In an isolated system, the total linear momentum is always conserved!

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Example - Recoil

A hunter shoots a 0.22 rifle and the 3.0 kg gun recoils with a speed of 0.042 m/s. If the bullet has a mass of 0.5 g, find the muzzle speed of the gun.

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Example - Recoil ~ Answer

(P)before (P)after

Prifle Pbullet before Prifle Pbullet after

mV rifle mV bullet

before mV rifle

mV bullet after

3000g0ms 0.5g0m

s 3000g 0.042ms 0.5gV m

s 0 126

gmsec

0.5V

126gmsec

0.5V

V 252m

s564mph

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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 10km/h. How fast do Jocko and the ball move across the ice?

(a) 0 km/hr (b) 2.5 km/hr (c) 200 km/hr (d) no way to determine

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Answer: (b)

(b): The momentum before the catch is all in the ball, 20kg x 10km/h = 200kg·km/h. 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 = 200kg·km/h v = 200kg·km/h/80kg = 2.5km/h

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Answer: (b)

(P)before (P)after

Pball PJocko before Pball PJocko after

mV ball mV Jocko

before mV ball

mV Jocko after

20kg10kmhr 60kg0km

hr 80kgV kmhr

200kgkm

hr80kgV km

hr

V 200kgkm

hr

1

80kg

V 2.5kmhr

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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

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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.

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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.)

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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.

The End...