Aim: What is the law of conservation of momentum?

Do Now:

A 20 kg object traveling at 20 m/s stops in 6 s. What is the change in momentum?

Δp = mΔv

Δp = m(vf – vi)

Δp = (20 kg)(0 m/s – 20 m/s)

Δp = -400 kg·m/s

Newton’s cradle demo

How can we explain what is going on?

The momentum of: one goes in, one goes out

two goes in, two goes out

etc.

The Law of The Law of Conservation of Conservation of

MomentumMomentumThe momentum of any The momentum of any closed, isolated system closed, isolated system

does not change. does not change.

A 2,000 kg car traveling north at 3 m/s strikes a 3,000 kg car traveling south at 2 m/s. What is the final momentum after the cars collide? pi = pf

p1i + p2i = pf

mv1i + mv2i = pf

(2,000 kg)(3 m/s) + (3,000 kg)(-2 m/s) = pf

6,000 kg·m/s – 6,000 kg·m/s = pf

pf = 0 kg·m/s

When firing a gun, there will always When firing a gun, there will always be a recoil due to momentum being be a recoil due to momentum being conservedconserved

http://www.youtube.com/watch?v=sTHPfz0bVychttp://www.youtube.com/watch?v=sTHPfz0bVyc

A 5 kg gun fires a 0.02 kg bullet. If the A 5 kg gun fires a 0.02 kg bullet. If the bullet exits the gun at 800 m/s East, bullet exits the gun at 800 m/s East, calculate the recoil velocity of the calculate the recoil velocity of the gun.gun.

Spring or Gun

Rifle Recoil Video

Inelastic Collision

A collision where the objects stick together after the collision

•Masses combine

•Velocity decreases after the collision

A 1 kg cart traveling at 1 m/s to the right strikes a 0.7 kg cart initially at rest. After the collision, the two stick together. Calculate the final velocity of the two cart system.

pi = pf

p1i + p2i = p(1+2)f

mv1i + mv2i = (m1 + m2)vf

(1 kg)(1 m/s) + (0.7 kg)(0 m/s) = (1 kg + 0.7 kg)vf

1 + 0 = 1.7vf

1 = 1.7vf

vf = 0.59 m/s right

Elastic Collision

Collision where the objects bounce off

each other

Mass 1 (1 kg) is traveling at 1 m/s to the right and strikes mass 2 (1 kg) that is at rest. After the collision, mass 1 is at rest. What is the velocity of the mass 2?

pi = pf

p1i + p2i = p1f + p2f

m1v1i + m2v2i = m1v1f + m2v2f

(1 kg)(1 m/s) + (1 kg)(0 m/s) = (1 kg)(0 m/s) +(1 kg)v2f

1 + 0 = 0 + 1v2f

v2f = 1 m/s right

What if a heavier objects strikes a lighter object?

•Both will continue to move in the same direction

•The heavier object will slow down

Mass 1 (1 kg) is traveling at 1 m/s to the right and strikes mass 2 (0.7 kg) that is at rest. After the collision, mass 1 is traveling at 0.18 m/s to the right. What is the velocity of the mass 2?

pi = pf

p1i + p2i = p1f + p2f

m1v1i + m2v2i = m1v1f + m2v2f

(1 kg)(1 m/s) + (0.7 kg)(0 m/s) = (1 kg)(0.18 m/s) +(0.7 kg)v2f

1 + 0 = 0.18 + 0.7v2f

0.82 = 0.7v2f

v2f = 1.17 m/s right

What if a lighter object strikes a heavier object?

•The lighter object will bounce off in the opposite direction

Mass 1 (1 kg) is traveling at 1 m/s to the right and strikes mass 2 (1.4 kg) that is at rest. After the collision, mass 2 is traveling at 0.83 m/s to the right. What is the velocity of the mass 1?

pi = pf

p1i + p2i = p1f + p2f

m1v1i + m2v2i = m1v1f + m2v2f

(1 kg)(1 m/s) + (1.4 kg)(0 m/s) = (1 kg)v1f +(1.4 kg)(0.83 m/s)

1 + 0 = v1f + 1.2

v1f = -0.2 m/s or 0.2 m/s left