Chapter 7

Linear Momentum

Objectives• Define impulse, and relate to momentum.• Give examples of how both the size of the force and

length of time applied affect the change in momentum.• Solve momentum and impulse problems.

Warm-UpKnowing how to find momentum, how do youthink one can find the change in momentum?

Engagement / Exploration

• Demo – egg and sheet

• https://www.youtube.com/watch?v=7RSUjxiZnME

Exploration – Interpret the diagram

Impulse• When an object experiences a net force, its momentum

will change!

• Impulse is a change in momentum!J = Δ p

• Impulse = Force * Time J = F t

F t = Δ pF t = m Δv

F t = m (vf - vi)

Impulse changes Momentum

A greater impulse exerted on an object A greater change in momentum

OR

Impulse = Change in momentum

OR

Impulse = Δ(mv)Greek symbol “Delta”

Means “the change in…”

Impulse can be exerted on an object to either INCREASE or DECREASE its momentum.

Impulse-Momentum TheoremImpulse-Momentum Theorem

The theorem states that the impulse The theorem states that the impulse acting on the object is equal to the acting on the object is equal to the change in momentum of the objectchange in momentum of the object•

• Impulse=change in momentum (vector!)Impulse=change in momentum (vector!)• If the force is not constant, use the If the force is not constant, use the

average forceaverage force applied applied

1212 )( ppttF

Air BagsAir Bags

The air bag increases The air bag increases the time of the the time of the collisioncollision

It will also absorb It will also absorb some of the energy some of the energy from the bodyfrom the body

It will spread out the It will spread out the area of contactarea of contact• decreases the decreases the

pressurepressure• helps prevent helps prevent

penetration woundspenetration wounds

Case 1: Increasing MomentumExamples:

Hitting a golf ball:Apply the greatest force possible for the longest time possible.Accelerates the ball from 0 to high speed in a very short time.

Baseball and bat:The impulse of the bat decelerates the ball and accelerates it in the opposite direction very quickly.

Video: Changing Momentum – Follow Through

Case 2: Decreasing MomentumIt takes an impulse to change momentum, and

Remember … Impulse = F x t

If you want to stop something’s motion, you can apply a LOT of force over a short time,

Or, you can apply a little force over a longer time.

Remember, things BREAK if you apply a lot of force to them.

Case 3: Decreasing Momentum over a Short Time

If the boxer moves away from the punch, he extends the time and decreases the force while stopping the punch.

If he moves toward the punch, he decreases the time and increases the force

The airbag extends the time over which the impulse is exerted and decreases the force.

Hitting the bricks with a sharp karate blow very quickly maximizes the force exerted on the bricks and helps to break them.

7-3 Collisions and Impulse

During a collision, objects are deformed due to the large forces involved.

Since , we can

write

The definition of impulse:

(7-5)

Same Impulse

• If an object experiences a change in momentum, how can you minimize the force on the object?

• Extending the time, there by minimizing the force.

J= F t J= F t

7-3 Collisions and Impulse

Since the time of the collision is very short, we need not worry about the exact time dependence of the force, and can use the average force.

7-3 Collisions and ImpulseThe impulse tells us that we can get the same change in momentum with a large force acting for a short time, or a small force acting for a longer time.

This is why you should bend your knees when you land; why airbags work; and why landing on a pillow hurts less than landing on concrete.

Impulse examples

                      I small large

Follow through increases the time of collision and the impulse

Problem

• Bobo hits a 0.050 kg golf ball, giving it a speed of 75 m/s. What impulse did he impart on the ball? Assume the initial speed of a ball was 0 m/s.

• J = change in momentum (mv)

• J = 3.75 kg m/s

Questions• Pick one to run into, a brick wall or a

haystack.

• Catch a baseball, what do you do?

• Jump off a table, what do you do?

• On which surface is a dropped glass less likely to break: carpet or sidewalk?

• Why do boxers use short, fast jabs?

Conservation of MomentumIf no net external force (same as saying “no net impulse”) acts on a system, the system’s momentum cannot change.

Momentum = 0 before the shot

And after the shotCannon’s

momentumShell’s

momentum (equal and opposite)

Example 7-6• Advantage of bending knees when landing!

a) m =70 kg, h =3.0 m

Impulse: p = ?

Ft= p = m(0-v)

First, find v (just before

hitting): KE + PE = 0

m(v2 -0) + mg(0 - h) = 0

v = 7.7 m/s

Impulse: p = mv

p = -540 N s

Just before he hits the ground

Just after he hits the ground

Opposite the person’s momentum

• Advantage of bending knees when landing!

Impulse: p = -540 N s

m =70 kg, h =3.0 m, F = ?

b) Stiff legged: v = 7.7 m/s to

v = 0 in d = 1 cm (0.01m)!

vavg = (½ )(7.7 +0) = 3.9 m/s

Time t = d/v = 2.6 10-3 s

F = p/t = 540 Ns/2.6 10-3 s

= 2.1 105 N (Net force upward on person)From free body diagram,

F = Fgrd - mg 2.1 105 N

Fgrd =F + mg = 2.1 105 N + (70kg x 9.80 m/s/s) 2.1 105 N Enough to fracture leg bone!!!

• Advantage of bending knees when landing!

Impulse: p = -540 N s

m =70 kg, h =3.0 m, F = ?

c) Knees bent: v = 7.7 m/s to

v = 0 in d = 50 cm (0.5m)

vavg = (½ )(7.7 +0) = 3.8 m/s

Time t = d/v = 0.13 s

F = p/t = 4.2 103 N

(Net force upward on person)

From free body diagram,

F = Fgrd - mg 4.9 103 N

Leg bone does not break!!!

Practice ProblemPractice Problem

A 57 gram tennis ball falls on a tile floor. The A 57 gram tennis ball falls on a tile floor. The ball changes velocity from -1.2 m/s to +1.2 ball changes velocity from -1.2 m/s to +1.2 m/s in 0.02 s. What is the average force on m/s in 0.02 s. What is the average force on the ball?the ball?

Identify the variables:Identify the variables:Mass = 57 g = 0.057 kgMass = 57 g = 0.057 kgΔΔvelocity = +1.2 – (-1.2) = 2.4 m/svelocity = +1.2 – (-1.2) = 2.4 m/sTime = 0.02 sTime = 0.02 s

using Fusing FΔΔt= mt= mΔΔv v F x (0.02 s) = (0.057 kg)(2.4 m/s)F x (0.02 s) = (0.057 kg)(2.4 m/s)

F= 6.8 NF= 6.8 N

Example: Crash Test• Crash test: Car, m = 1500 kg, hits

wall. 1 dimensional collision. +x is to the right. Before crash, v = -15 m/s. After crash, v = 2.6 m/s. Collision lasts Δt = 0.15 s. Find: Impulse car receives & average force on car. Assume: Force exerted by wall is large

compared to other forces

Gravity & normal forces are perpendicular & don’t effect the horizontal momentum

Use impulse approximation

p1 = mv1 = -22500 kg m/s, p2 = mv2 = 3900 kg m/s J = Δp = p2 – p1 = 2.64 104 kg m/s

(∑F)avg = (Δp/Δt) = 1.76 105 N

Closure - Car CrashClosure - Car Crash Would you rather be in a Would you rather be in a

head on collision with an head on collision with an identical car, traveling identical car, traveling at the same speed as at the same speed as you, or a brick wall? you, or a brick wall?

Assume in both situations Assume in both situations you come to a complete you come to a complete stop. stop.

Take a guessTake a guess

http://techdigestuk.typepad.com/photos/uncategorized/car_crash.JPG

Car Crash (cont.)Car Crash (cont.)

Everyone should vote Everyone should vote nownow

Raise Raise oneone finger if you finger if you think it is better to hit think it is better to hit another car, another car, twotwo if it if it’’s s better to hit a wall and better to hit a wall and threethree if it doesn if it doesn’’t t matter.matter.

And the answer is…..And the answer is…..

Car Crash (cont.)Car Crash (cont.)The answer is…The answer is…

It Does Not Matter!It Does Not Matter!

Look atLook at FFΔΔt= mt= mΔΔvvIn both situations,In both situations, ΔΔt, m, t, m, andand

ΔΔv v are the same! The are the same! The time it takes you to stop time it takes you to stop depends on your car, m is depends on your car, m is the mass of your car, and the mass of your car, and ΔΔv depends on how fast v depends on how fast you were initially traveling.you were initially traveling.

HomeworkHomework

Chapter 7 Chapter 7 problemsproblems

15, 16, 17, 19, 15, 16, 17, 19, 2020

Kahoot 7-3Kahoot 7-3