Chapter 9 - Collisions Momentum and force Conservation of momentum Impulse Inelastic collisions Perfectly inelastic Elastic collisions in one dimension moving target stationary target Elastic collisions in two dimensions Center of mass

Momentum Linear momentum quantity of motion Product of mass times velocity The time rate of change of the momentum of an object is equal to the resulting net external force acting on the object.

Conservation of momentum If there are no external forces We say momentum is conserved For two particles we write:

Problem 1 Inelastic Collision Car 1 with a mass of 1000 kg and a velocity of 20 m/s runs into the rear end of a larger car with mass of 2000 kg initially at rest. The two cars stick together. Find the final velocity Find the energy lost in the collision

Applications of conservation of momentum

Impulse

Average force during a collision

Problem 2 A ball (mass = 0.1 kg) is released from 2 meters and rebounds to 1.5 meters. What is the Impulse of the floor on the ball

The ballistic pendulum If you can measure M, m, and h, how fast was the bullet traveling?

Elastic vs. inelastic Momentum is conserved in all collisions. Elastic collision – Kinetic energy is also conserved. Inelastic collision – Kinetic energy is not conserved. Perfectly Inelastic – Objects stick together after the collision.

Elastic collisions Momentum: Energy:

Elastic collisions

Elastic collisions – equal mass

Elastic collision – mass at rest v1 m1 m2

Elastic collision – general case v1 v2 m1 m2

Problem 3 Elastic Collision A 3 kg mass moving at 8 m/s in the x direction collides with a 5 kg mass initially at rest Find the final velocity of each mass. Find the final kinetic energy of each mass m1 m2

Elastic collision in two dimensions m2 is at rest

Problem 4 Two shuffleboard disks of equal mass are involved in a elastic glancing collision. One disk is initially at rest and is struck by the other which is moving with a speed of 4 m/s. After the collision, the incident disk moves along a direction that makes an angle of 30o with its initial direction of motion. The originally stationary disk moves in a direction perpendicular to the final direction of motion of the other disk. Find the final speeds. 30o 4 m/s 60o