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Momentum and Impulse

What is Momentum?

- Momentum The product of the mass and velocity

of an object. Has magnitude and direction. - Momentum p mv
- P momentum
- M mass
- V velocity
- Units kgm/s

Inertia?

- Remember Newtons 1st Law?
- An object at rest will stay at rest
- and
- An object in motion will stay in motion in the

same speed and direction unless acted on by an

outside force.

Whats Inertia Got to Do with It?

- Momentum is directly related to the second part

of Newtons 1st Law - An object in motion stays in motion (same speed

and direction) unless acted on by a force

Lets practice

- A 1200 kg car drives west at 25 m/s for 3 hours.

What is the cars momentum? - Identify the variables
- 1200 kg mass
- 25m/s, west velocity
- 3 hours time
- P mv 1200 x 25 30000 kg m/s, west

How hard is it to stop a moving object?

- Impulse Product of force and time interval

during which the force acts. Impulse equals

momentum change. - Impulse F?t
- F force (N)
- ?t time elapsed (s)
- Units Ns

How hard is it to stop a moving object?

- Using Newtons 2nd Law we get
- Impulse change in momentum
- F?t m?v

Why does an egg break or not break?

- An egg dropped on a tile floor breaks, but an egg

dropped on a pillow does not. Why? - F?t m?v
- In both cases, m and ?v are the same.
- If ?t goes up, what happens to F, the force?
- Right! Force goes down. When dropped on a

pillow, the egg starts to slow down as soon as it

touches it. A pillow increases the time the egg

takes to stops.

Practice Problem

- A 57 gram tennis ball falls on a tile floor. The

ball changes velocity from -1.2 m/s to 1.2 m/s

in 0.02 s. What is the average force on the

ball? - Identify the variables
- Mass 57 g 0.057 kg
- ?velocity 1.2 (-1.2) 2.4 m/s
- Time 0.02 s
- using F?t m?v
- F x (0.02 s) (0.057

kg)(2.4 m/s) - F 6.8 N

Car Crash

- Would you rather be in a head on collision

with an identical car, traveling at the same

speed as you, or a brick wall? - Assume in both situations you come to a

complete stop. - Take a guess

http//techdigestuk.typepad.com/photos/uncategoriz

ed/car_crash.JPG

Car Crash (cont.)

- The answer is
- It Does Not Matter!
- Look at F?t m?v
- In both situations, ?t, m, and ?v are the same!

The time it takes you to stop depends on your

car, m is the mass of your car, and ?v depends

on how fast you were initially traveling.

Conservation of Momentum

Conservation of Momentum

- Just like energy, momentum is conserved.
- The total momentum at the start will equal the

total momentum at the end

Vectors!

- Remember that momentum is a vector value, so if

two momentums are in opposite directions, they

are opposite signs and end up cancelling (at

least in part)

Two Flavors!!

- Collisions may be
- Elastic the objects completely bounce off each

other - Billiards (pool) ball have elastic

collisions - Inelastic the objects stick together at the

collision and travel together thereafter - Car Crashes have become inelastic with

better engineering

Momentum Formulas

- The standard formula for momentum is
- Pmv
- What happens if we have two objects that collide

and bounce off each other..elastic?? - We can make a formula for this due to the

conservation of momentum! - M1V1i M2V2i M1V1f M2V2f

Practice Elastic

- A 50 kg skater traveling at 10 m/s hits a 40 kg

skater sitting still, imparting all his momentum

into the 2nd skater. What is the velocity of the

2nd skater? - M1V1i M2V2i M1V1f M2V2f
- (50 kg)(10 m/s) (40 kg)(0 m/s) (50 kg)(0 m/s)

(40 kg)V2f - (500 kgm/s) (0 kgm/s) (0 kgm/s) (40

kg)V2f - 12.5 m/s V2f

Practice Problem

- A 50 kg skater traveling at 10 m/s hits a 40 kg

skater sitting still. The 1st skater ends up at 2

m/s. What is the velocity of the 2nd skater? - M1V1i M2V2i M1V1f M2V2f
- (50 kg)(10 m/s) (40 kg)(0 m/s) (50 kg)(2 m/s)

(40 kg)V2f - (500 kgm/s) (0 kgm/s) (100 kgm/s) (40

kg)V2f - 10 m/s V2f

Practice Problem

- A 50 kg skater traveling at 20 m/s hits a 40 kg

skater moving in the same direction at 3 m/s. The

1st skater ends up at 5 m/s. What is the velocity

of the 2nd skater? - M1V1i M2V2i M1V1f M2V2f
- (50 kg)(20 m/s) (40 kg)(3 m/s) (50 kg)(5 m/s)

(40 kg)V2f - (1000 kgm/s) (120 kgm/s) (125 kgm/s) (40

kg)V2f - 24.875 m/s V2f

Inelastic Collision Formula

- Since the objects travel together after the

collision, we have a slightly different formula

for inelastic collisions - M1V1i M2V2i (M1 M2)Vf
- This shows the final momentum is created by the

total mass of the two objects together

Practice Inelastic

- A 50 kg skater traveling at 20 m/s picks up a 40

kg passenger skating sitting still, what is the

velocity of the two skaters? - M1V1i M2V2i (M1 M2)Vf
- (50 kg)(20 m/s) (40 kg)(0 m/s) (90 kg)Vf
- (1000 kgm/s) (0 kgm/s) (90 kg)Vf
- 11.1 m/s Vf

Practice Problem

- A 50 kg skater traveling at 20 m/s picks up a 40

kg passenger skating in the same direction at 5

m/s, what is the velocity of the two skaters? - M1V1i M2V2i (M1 M2)Vf
- (50 kg)(20 m/s) (40 kg)(5 m/s) (90 kg)Vf
- (1000 kgm/s) (200 kgm/s) (90 kg)Vf
- 13.3 m/s Vf

Practice Problem

- A 50 kg skater traveling at 20 m/s picks up a 40

kg passenger skating in the opposite direction at

5 m/s, what is the velocity of the two skaters? - M1V1i M2V2i (M1 M2)Vf
- (50 kg)(20 m/s) (40 kg)(-5 m/s) (90 kg)Vf
- (1000 kgm/s) - (200 kgm/s) (90 kg)Vf
- 8.89 m/s Vf