Chapter Elastic and inelastic collision

Objectives Identify different types of collisions. Determine the changes in kinetic energy during perfectly inelastic collisions. Compare conservation of momentum and conserva-tion of kinetic energy in perfectly inelastic and elastic collisions.

Collision What is a collision? A collision is an event where momentum or kinetic energy is transferred from one object to another. Momentum (p) is the product of mass and velocity (p = mv). A large truck massing 10,000 kg and moving at 2 meters/sec has the same momentum as a 1,000 kg compact car moving at 20 meters/sec; they both have p = 20,000 kg m/sec. The other quantity that can be transferred in a collision is kinetic energy. Kinetic energy is the energy of motion; it is defined as K = (1/2) m v^2. The relationship between kinetic energy and mass is linear, which means that a vehicle massing twice as much has twice as much kinetic energy. The relationship between kinetic energy and velocity is exponential, which means that as you increase your speed, kinetic energy increases dramatically.

Types of collision There are two general types of collisions in physics: elastic and inelastic. Inelastic collision: An inelastic collisions occurs when two objects collide and do not bounce away from each other.

Types of collision Momentum is conserved, because the total momentum of both objects before and after the collision is the same. However, kinetic energy is not conserved. Some of the kinetic energy is converted into sound, heat, and deformation of the objects. A high speed car collision is an inelastic collision. In the above example, if you calculated the momentum of the cars before the collision and added it together, it would be equal to the momentum after the collision when the two cars are stuck together. However, if you calculated the kinetic energy before and after the collision, you would find some of it had been converted to other forms of energy.

Types of collision Elastic collision An elastic collision occurs when the two objects "bounce" apart when they collide. Two rubber balls are a good example. In an elastic collision, both momentum and kinetic energy are conserved. Almost no energy is lost to sound, heat, or deformation. The first rubber ball deforms, but then quickly bounces back to its former shape, and transfers almost all the kinetic energy to the second ball.

Extreme types of collision Perfectly inelastic collision A collision in which two objects stick together after colliding and move together as one mass is called a perfectly inelastic collision. Conservation of momentum for a perfectly inelastic collision: m 1 v 1,i + m 2 v 2,i = (m 1 + m 2 )v f total initial momentum = total final momentum

Example #1 A 1850kg luxury sedan stopped at a traffic light is struck from the rear by a compact car with a mass of 975kg. The two cars become entangled as a result of the collision. If the compact car was moving at a velocity of 22m/s to the north. What is the velocity of the entangled mass after the collision?

Example#2 Do problem#1 in your book page 206

Student guided practice Do problems 2 and 3 in your book page 206

Example#3 Kinetic Energy in Perfectly Inelastic Collisions Two clay balls collide head-on in a perfectly inelastic collision. The first ball has a mass of kg and an initial velocity of 4.00 m/s to the right. The second ball has a mass of kg and an initial velocity of 3.00 m/s to the left. What is the decrease in kinetic energy during the collision?

Student guided practice Do problem 1 and 2 in your book 208

Example#4 A kg marble moving to the right at m/s makes an elastic head-on collision with a kg shooter marble moving to the left at m/s. After the collision, the smaller marble moves to the left at m/s. Assume that neither marble rotates before or after the collision and that both marbles are moving on a frictionless surface.What is the velocity of the kg marble after the collision?

Elastic collision For a head-on collision with a stationary object of equal mass, the projectile will come to rest and the target will move off with equal velocity, like a head- on shot with the cue ball on a pool table. This may be generalized to say that for a head-on elastic collision of equal masses, the velocities will always exchange.

Case 1 Click on any of the examples for further details.

Case 2 In a head-on elastic collision where the projectile is much more massive than the target, the velocity of the target particle after the collision will be about twice that of the projectile and the projectile velocity will be essentially unchanged.elastic collision

Case 3 a head-on elastic collision between a small projectile and a much more massive target, the projectile will bounce back with essentially the same speed and the massive target will be given a very small velocity. One example is a ball bouncing back from the Earth when we throw it down.

Video Lets watch a video about the difference between elastic and inelastic collision

Homework Do worksheet problems

Closure Today we learned about elastic and inelastic collisions Next class we are going to learn about circular motion