Aim: How do we Analyze elastic collisions?

Conservation of Momentum If momentum is conserved in a collision, this means that the total momentum of the system before the collision is equal to the total momentum of the system after the collision. Pbefore = pafter

Elastic Collision A collision in which the total kinetic energy of the two particles before the collision is equal to the total kinetic energy of the two particles after the collision. (Kinetic Energy is conserved!)

Elastic Collision Elastic Collision m1v1i +m2v2i = m1v1f + m2v2f

Is the collision elastic? (Problem 1) Look at the given collision below between a 4 kg mass and a 6 kg mass. After the collision, the 4 kg mass moves to the left at 4 m/s. (Show all work including equation and substitution with units). Find the velocity of the 6 kg mass after the collision. Determine if the collision is an elastic collision.

COLLISION IS NOT ELASTIC

Elastic Collision Problem 2 A 3 kg mass moving at 3 m/s collides head on with a 5 kg mass moving at -2 m/s in a perfectly elastic collision. Find the velocities of each mass after colliding.

Elastic Collision Problem 3 A 4 kg bouncy ball moving at 2 m/s to the right collides with a 2 kg bouncy ball moving at 1 m/s to the left. This collision is elastic. What two quantities are conserved in this collision? Write down equations expressing the conservation of both quantities. Calculate the final velocities of each mass

Solving elastic collisions without calculations If two identical masses collide in an elastic collision, the masses will swap velocities. In other words, object A’s velocity before the collision will become object B’s velocity after the collision AND object B’s velocity before the collision will become object A’s velocity after the collision.

Elastic collision Problem 4 A neutron in a nuclear reactor makes an elastic head-on collision with the nucleus of a carbon atom initially at rest. What fraction of the neutron’s kinetic energy is transformed to the carbon nucleus? If the initial kinetic energy of the neutron is 1.60 x 10-13 J, find its final kinetic energy and the kinetic energy of the carbon nucleus after energy after the collision. (The mass of the carbon nucleus is nearly 12 times the mass of the neutron.) .284, 115fJ and 45.4fJ