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(v f – v i ) 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 Conservation of Momentum The momentum of any closed, isolated system 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? p i = p f p 1i + p 2i = p f mv 1i + mv 2i = p f (2,000 kg)(3 m/s) + (3,000 kg)(-2 m/s) = p f 6,000 kg·m/s – 6,000 kg·m/s = p f p f = 0 kg·m/s

When firing a gun, there will always be a recoil due to momentum being conserved A 5 kg gun fires a 0.02 kg bullet. If the bullet exits the gun at 800 m/s East, calculate the recoil velocity of the 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. p i = p f p 1i + p 2i = p (1+2)f mv 1i + mv 2i = (m 1 + m 2 )v f (1 kg)(1 m/s) + (0.7 kg)(0 m/s) = (1 kg kg)v f = 1.7v f 1 = 1.7v f v f = 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? p i = p f p 1i + p 2i = p 1f + p 2f m 1 v 1i + m 2 v 2i = m 1 v 1f + m 2 v 2f (1 kg)(1 m/s) + (1 kg)(0 m/s) = (1 kg)(0 m/s) +(1 kg)v 2f = 0 + 1v 2f v 2f = 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? p i = p f p 1i + p 2i = p 1f + p 2f m 1 v 1i + m 2 v 2i = m 1 v 1f + m 2 v 2f (1 kg)(1 m/s) + (0.7 kg)(0 m/s) = (1 kg)(0.18 m/s) +(0.7 kg)v 2f = v 2f 0.82 = 0.7v 2f v 2f = 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? p i = p f p 1i + p 2i = p 1f + p 2f m 1 v 1i + m 2 v 2i = m 1 v 1f + m 2 v 2f (1 kg)(1 m/s) + (1.4 kg)(0 m/s) = (1 kg)v 1f +(1.4 kg)(0.83 m/s) = v 1f v 1f = -0.2 m/s or 0.2 m/s left