Linear Momentum & Impulse

Take out tables.

On a separate sheet:

Make a list of every equation we’ve already used in this class that has the velocity term in it.

Here is your choice:

a. I toss a bullet at you.

b. I shoot a bullet at you from a gun.

Which is more dangerous to you?

Why?

Linear Momentum&

Impulse

Linear Momentum = mass in motion

A measure of how hard it is to stop an object.

It is like a quantity of motion.

How is it different from inertia?

Momentum (p) depends on: mass & velocity of object.

p = mv m in kg

v in m/s

Units are … kg m no name.

s

Momentum is aVector Quantity

Same direction as velocity

All Energy KE too is a scalar

Ex 1. A 2250 kg pickup truck has v = 25 m/s east. What is the truck’s momentum?

p = mv = (2250 kg)(25 m/s)

= 5.6 x 104 kg m

s

Change in momentum - accl occurs any time an object changes

velocity (speed or direction).

Momentum Change &Newton’s 2nd Law

• F = ma

• F = m(v/t)

• Ft =mv m (vf - vi) for const mass.

• Ft = p Impulse.p = Change in momentum

Equations of Momentum Change

• J =Ft = p Impulse = change momentum.

• pf – pi.

p = mvf – mvi

• for velocity change with constant mass can factor out mass you can write,

• m (vf - vi) or mv.

Force is required to change velocity or momentum of a body in motion.Force must be in contact for some time.

Increased force & contact time on object give greatest impulse p = mv.

Hit a homerun needs large impulse. The more contact time, the less force needed to give same impulse p.

Impulse (J) is the momentum change. It has the same units.

kg m or Ns s

It is like force but includes a contact time component!

Ex 2. How long does it take an upward 100N force acting on a 50 kg rocket to increase its speed from 100 to 150 m/s?

F = 100 Nv = 50 m/sm = 50 kg

Ft = mv

t = mv F

50 kg(50 m/s) 100 kg m/s2 = 25 s.

 Concept: A pitcher throws a fastball to a catcher. Who exerts a larger force on the ball? Explain.

Concept: Explain, in terms of impulse and momentum, how airbags help avoid injury in a car crash.

Examples of Impulse/Change in Momentum

• Baseball batter swinging through ball.

• Applying brakes of car over time to stop.

Ex 3. How long does it take a 250 N force to increase to speed of a 100 kg rocket from 10 m/s to 200 m/s?

Ft = mv t = mv F

F = 250 Nm= 100 kgv =190 m/s

t = 100kg(190m/s) 250 kg m/s2. = 76 s.

Ex 4. The speed of a 1200 kg car increases from 5 to 29 m/s in 12 s. What force accelerated the car?

Ex 5: A 0.4 kg ball is thrown against a wall with a velocity of 15 m/s. If it rebounds with a velocity of 12 m/s:

a) what was its v?b) What was its p?

v = vf – vi.

-12 m/s – (15 m/s) = - 27 m/s.

p = mv

= 0.4kg(27m/s)

=10.8 kg m/s

• Running with momentum. 15 min.

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

• Relaxing with impulse.13 minutes.

• https://www.youtube.com/watch?v=0nOHLThv2mw

Understanding Car Crashes 22 minstart 8:53

• Hewitt Momentum 4:20

• https://www.youtube.com/watch?v=2FwhjUuzUDg

http://www.youtube.com/watch?v=yUpiV2I_IRI

Hwk read text 208 – 211

do pg 214 #1- 4 conceptsdo p 211 #1 - 4. Impulse prbs.

Also worksheet “Impulse Momentum”

Which are units of Impulse? 

NmN/sNsN/m

  A ball mass 0.10 kg is dropped from 12-m. Its momentum just as it strikes the ground is: 

1.5 kgm/s1.8 kgm/s2.4 kgm/s4.8 kgm/s

A 0.060-kg tennis ball, initially moving at 12 m/s, is struck by a racquet causing it to move in the opposite direction at a speed of 18 m/s. What is the impulse exerted by the racquet on the ball? 

0.36 kgm/s0.72 kgm/s1.1 kgm/s1.8 kgm/s

Graphs

Constant force f - t graph:p /Impulse is area under curve Ft.

For

ce N

Non-Constant ForceForce vs. time graph. The area under the curve =

impulse or p change in momentum.

What is the impulse during the 9 seconds of contact?

225 Ns

Consv Momentum Demos.

Conservation of Momentum

If no external force acts on a closed system, the total momentum remains unchanged even if objects interact.

What is a system?

Two or more objects that interact in motion. One may transfer part or all of its momentum to the other(s).

Common examples: collisions, explosions.

One Ball transfers all its momentum.

The astronaut transfers part of his momentum to the second astronaut.

Conservation of Momentum Calc’s

• Total momentum before = total after interactions.

• Collisions.

• Explosions

• Pushing apart.

Pbefore = pafter

m1v1 + m2v2 = m1fv1f + m2fv2f

v1 and v2 velocities for objects one and two.

m1 and m2 masses of objects

To Calculate:

Recoil From Explosions

Recoil illustrates conservation of momentum where initial and

final momentum = 0.0 = p1 + p2.

1. The cannon is 100kg and the cannonball is 5 kg. If the ball leaves the cannon with a speed of 100 m/s, find the recoil velocity of the cannon.

Before Firing After Firingm1v1 + m2v2 = m1fv1f + m2fv2f

0 = (100kg)vcf + (5kg)(100m/s) -500 kgm/s = (100 kg) vcf

- 5 m/s = vcf recoil velocity of cannon

Extra Example – not on sheet

• A 63-kg astronaut is in spacewalk when the tether breaks. The astronaut throws a 10-kg oxygen tank directly away from the spaceship at 12 m/s. Assuming the astronaut was initially at rest, what is his final speed after throwing the tank?

• 1.9 m/s

• Hwk. Read text p 215-218. Do pg 221 #2, and pg 233 #17, 19, 20, 24, 25.

Recoil Hewitt 6:25

https://www.youtube.com/watch?v=1-s8NZ8xKW0

Let’s say a 4 kg fish swimming at 5 m/s, eats a 1 kg fish. What is their final

velocity?

Stick em together problems

Bg fish sm.fish Bg fish sm.fishm1v1 + m2v2 = m1fv1f + m2fv2f

(4kg)(5m/s)+(1 kg)0 =(4kg)v1+(1kg)v2

But the final velocities are equal so factor out the vf:

20 kg m/s = vf (4+1kg)

vf = (20 kg m/s) / (5kg) = 4m/s

Fish lunch Hewitt 4:00

https://www.youtube.com/watch?v=MK0B5hEU7OI

Find the final velocity of the cart and brick together

2. A 2 kg brick is dropped on a 3 kg cart moving at 5.0 m/s.

cart brick cart brickm1v1 + m2v2 = m1fv1f + m2fv2f

(3kg)(5.0m/s) + 0 = (3kg)v1 + (2kg)v2

150 kg m/s = v (3kg + 2 kg)

(150 kg m/s )/5 kg = 3.0 m/s

Elastic & Inelastic Collisions

Totally Elastic: no KE lost at all(to heat, light, sound etc.) Usu. Involves objects that don’t make contact or bounce off.

Totally Inelastic: involves greatest loss of KE. Usu damage done. Most extreme case – objects stick together.

Which is totally elastic? Inelastic?

Inelastic Collisionmc = 1000 kg mt = 3000 kgvc = 20 m/s vt = 0pc = pt =

m1v1 + m2v2 = m1fv1f + m2fv2f (1000kg)(20m/s) + 0 = (1000)v + (3000)v

(20000 kg m/s) = (1000kg + 3000kg)v

(20000 kg m/s) = (4000 kg)v

(20000 kg m/s) = v4000 kg

v = 5 m/s

Elastic Collision mc = 1000 kg mt = 3000 kg

vc = 20 m/s vt = 0

Find final velocity of the car if truck has final velocity of 10 m/s.

m1v1 + m2v2 = m1fv1f + m2fv2f

(1000kg)(20m/s) + 0 =(1000kg)vc+(3000kg)(10m/s)

20,000 kg m/s = (1000kg)vc+30000 kg m/s

20,000 kg m/s – 30,000 kg m/s = vc

(1000kg)

- 10 m/s = vc

Do Now: On July 4th my family likes to shoot off fireworks. One rocket was shot straight up, climbed to a height 18-m and exploded into hundreds of pieces in all directions at its highest point.

Thinking about conservation laws, think about the rocket at its highest point just before & just after it explodes:

How does the rocket’s momentum compare before & after the explosion?

How does its KE compare compare before & after the explosion?

Inelastic CollisionsStick em together

KE “lost” converted

Elastic Collisions – no KE lost.Bounce off each other.

• Pg 233 #17, 19, 20, recoil prbs24, 25.

• Sentences, equations, show work w/units.

In classpg 221 #1 write out and hand in to

be graded.

and do pg 219 #1 – 4 calcs

Film Car Crashes or Running with momentum.

http://www.youtube.com/watch?v=yUpiV2I_IRI