Elastic and Inelastic Collisions

Chapter 6 Section 3

Collisions

• There are many different collisions in which two objects collide.– Sports– Vehicles– Arrow and target

Kinetic Energy and Collisions

• Momentum is always conserved in a collision, but the total kinetic energy is generally not conserved.

• Some of the energy is converted to thermal energy (heat) and internal elastic potential energy when the objects deform.

Perfectly Inelastic Collisions

• Perfectly Inelastic collisions – A collision in which two objects stick together and move with a common velocity after colliding.

• Examples:– Arrow hitting a target– Bullet lodging into a wood block– Meteorite colliding with Earth

and becomes buried

Perfectly Inelastic Collisions

m1v1i + m2v2i = (m1+m2)vf

• Since the objects stick together after the collision, the masses must be added together for the final velocity.

Distinctions Between Collisions

• Elastic Collision – Objects maintain their original shape and are not deformed after colliding.

• Inelastic Collision – Objects are deformed during the collision and lose kinetic energy.

• Perfectly Inelastic Collision – Objects join together after a collision to form one mass.

Kinetic Energy Lost

• Energy is lost during an inelastic collision and not a elastic collision.

• In most cases energy is lost during a perfectly inelastic collision, but not always.– How much deformation and how the objects

stick together play a factor.

Kinetic Energy Equations

KElost = KEi – KEf

Kinetic Energy Lost = Initial Kinetic Energy – Final Kinetic Energy

Example Problem

• A clay ball with a mass of 0.35 kg hits another 0.35 kg ball at rest, and the two stick together. The first ball has an initial speed of 4.2m/s

1. What is the final speed of the balls?2. Calculate the decrease in kinetic energy that

occurs during the collision.3. What percentage of the kinetic energy is

converted to other forms of energy?

Example Problem Answers

1. 2.1m/s2. 1.6J3. 52%

Elastic Collisions

• Elastic Collisions – A collision in which the total momentum and the total kinetic energy remains constant.

• The objects remain separate after the collision.

• Examples:– Kicking a soccer ball with your foot– Hitting a baseball with a bat– Billiards

Everyday Collisions

• Most collisions are neither elastic or perfectly inelastic in everyday activities.

• In most collisions, kinetic energy is lost.– This places them into the category of inelastic

collisions.

Kinetic Energy and Elastic Collisions

• Kinetic energy is conserved in elastic collisions.

• The total momentum and the total kinetic energy remain constant through out the collision.

Momentum and Kinetic Energy Equations

m1v1i + m2v2i = m1v1f + m2v2f

• Momentum equation can be used for all collisions.

½m1v1i²+ ½m2v2i²= ½m1v1f²+ ½m2v2f²• Kinetic Energy equation can only be used

for elastic collisions.

Making Sure Collisions Are Elastic

• To check and see if a collision is an elastic collision:– Solve the problem using the conservation of

momentum equation.– Plug the velocities into the conservation of

kinetic velocity equation and see if the total initial velocity and the total final velocity are equal.

– If they are, then it is a true elastic collision.