The Conservation of Momentum
The Conservation of Momentum
Recall: Newton’s Third Law of Motion
Action-ReactionF1 = - F2
The Law of Conservation of Momentum
§System: a set of objects that interact with each other§Isolated/closed system: system in
which the only forces present are those between the objects of the system
The total momentum of an isolated system remains constant if no external forces act on a system
Momentum before = Momentum afterpbefore = pafter
pAi + pBi = pAf + pBfmAvAi + mBvBi = mAvAf + mBvBf
§All conservation of momentum problems that we will deal with in this class will be with two objects either “colliding” or ”exploding”
§Since the closed system involves both objects, we must add the momentum of each object in order to describe the total momentum before and/or after the collision or explosion
Collisions
Elastic Collision§Momentum and total kinetic energy is
conserved§No deformation of the object(s) will
occur§Ex: billiard balls, marbles, particle
collisions
Inelastic Collision§ Total kinetic energy is not conserved§Only momentum is conserved§Some deformation of the object(s) will
occur§Perfectly inelastic collision = objects
actually “stick together” or combine to form one mass à both move with the same velocity
mAvAi + mBvBi = (mA + mB) vf§Ex: car crashes, catching a ball
Sample Problem
A 2275-kg car going 28 m/s rear-ends an 875-kg compact car going 16 m/s on ice in the same direction. The two cars stick together. How fast does the wreckage move immediately after the collision?
Given:§mA = 2275 kg§ vAi = 28 m/s§mB = 875 kg§ vBi = 16 m/sUnknown:§ vf = ? Equation:
§ mAvAi + mBvBi = mAvAf + mBvBf
§ vAf = vBf = vf
Substitute & Solve:§ mAvAi + mBvBi = (mA+ mB)vf
§ vf = mAvAi + mBvBimA+ mB
= (2275 kg)(28 m/s) + (875 kg)(16 m/s)2275 kg + 875 kg
= 25 m/s
Because the two cars stick together, their velocities after the collision (vf) are equal
You Try!
§Two grocery carts collide, a full one with a mass of 35 kg moving east at 2.0 m/s and an empty one with a mass of 10. kg moving west at 3.0 m/s. After the collision the full cart is moving east at 0.75 m/s. What is the velocity of the empty cart after the collision?§1.4 m/s
§Two football players have a head-on collision and grab onto each other’s uniforms. The 80 kg Ram was moving at 3 m/as, while the 70 kg Packer player was moving in the opposite direction at 2.5 m/as. What is their final velocity after impact?§ 0.43 m/s
Explosions
§Explosions = internal impulse that sends different parts of the system or object into different directions§Elastic collision in reverse
§ Initial momentum of system is zero § The “kickback” of a gun or cannon is due to the conservation of momentum
(recoil velocity)
You Try!
§Calculate the recoil velocity of a 5.0 kg rifle that shoots a 0.050 kg bullet at a speed of 120 m/s.§- 1.2 m/s