Momentum and Impulse HMH Physics Chapter 6 pages 190-223 Section 3 pages 206-214

Learning Objectives Identify different types of collisions. Determine change in Kinetic Energy during perfectly inelastic collisions. Compare conservation of momentum and conservation of kinetic energy in collisions. 4. Find the final velocity of an object after a collision.

Collisions When two moving objects make contact with each other, they undergo a collision. Conservation of momentum is used to analyze all collisions. Newton’s Third Law is also useful. It tells us that the force exerted by body A on body B in a collision is equal and opposite to the force exerted on body B by body A.

Collisions During a collision, external forces are ignored. The time frame of the collision is very short. The forces are impulsive forces (high force, short duration).

Collisions Three types Elastic Inelastic Perfectly inelastic

Collision Types Elastic collisions Inelastic collisions Also called “hard” collisions No deformation occurs, no kinetic energy lost Inelastic collisions Deformation occurs, kinetic energy is lost Perfectly Inelastic (stick together) Objects stick together and become one object

Elastic Collision In elastic collisions, there is no deformation of colliding objects, and no change in kinetic energy of the system. Therefore, two basic equations must hold for all elastic collisions Spb = Spa (momentum conservation) SKb = SKa (kinetic energy conservation)

Elastic Collisions m1v1i + m2v2i = m1v1f + m2v2f Two objects collide and move separately m1v1i + m2v2i = m1v1f + m2v2f 1st object 2nd object 1st object 2nd object initial initial final final momentum momentum momentum momentum

(Perfectly) Inelastic Collisions Simplest type of collisions. After the collision, there is only one velocity, since there is only one object. Kinetic energy is lost. Explosions are the reverse of perfectly inelastic collisions in which kinetic energy is gained!

Inelastic Collision m1v1i + m2v2i = (m1 + m2)vf Two objects collide and stick together m1v1i + m2v2i = (m1 + m2)vf 1st object 2nd object (1st object + 2nd object) initial initial final momentum momentum momentum

A 0. 215 kg golf club is swung with a speed of 55 A 0.215 kg golf club is swung with a speed of 55.0 m/s and strikes a 0.046 kg golf ball at rest. After the collision, the club travels at a speed of 43.0 m/s. What is the speed of the golf ball just after the impact?

Sample Problem An 80-kg roller skating grandma collides inelastically with a 40-kg kid. What is their velocity after the collision? How much kinetic energy is lost?

Sample Problem A fish moving at 2 m/s swallows a stationary fish which is 1/3 its mass. What is the velocity of the big fish after dinner?

A 0.25 kg arrow with a velocity of 12 m/s to the west strikes the center of a 6.9 kg target. What is the final velocity of the combined mass?

A 90. 0 kg fullback moving south with a speed of 5 A 90.0 kg fullback moving south with a speed of 5.0 m/s has an inelastic collision with a 95.0 kg opponent running north at 3.0 m/s. What is the velocity of the players just after impact?

2D-Collisions Momentum in the x-direction is conserved. SPx (before) = SPx (after) Momentum in the y-direction is conserved. SPy (before) = SPy (after) Treat x and y coordinates independently. Ignore x when calculating y Ignore y when calculating x Let’s look at a simulation: http://surendranath.tripod.com/Applets.html

Sample problem Calculate velocity of 8-kg ball after the collision. 3 m/s 2 kg 8 kg 0 m/s Before 2 m/s v After 50o x y