Collisions and Experiment 4 Momentum and Collisions 8

Collisions and Experiment 4: Momentum and Collisions 8. 01 W 07 D 2 Associated Reading Assignment: Young and Freedman: 8. 3 -8. 4

Announcements No Math Review Night Next Week Test Two Next Week Thursday Oct 27 7: 30 -9: 30 Rooms TBA Pset 7 Due Tuesday Oct 25 at 9 pm Next Reading Assignment W 07 D 3: Young and Freedman: 8. 1 -8. 5

Demo: Momentum and Impulse: Cart Colliding with Spring

Table Problem: Experiment 4 Totally Inelastic Collision A car of mass m 1 moving with speed v 1, i collides with another car that has mass m 2 and is initially at rest. After the collision the cars stick together and move with speed vf. What is the speed of the cars immediately after the collision?

One Dimensional Elastic Collision: Relative Velocity

Elastic Collision: Conservation of Momentum Two particles interact elastically with no external forces along direction of motion: momentum equation

Elastic Collision: Conservation of Energy Two particles interact elastically with no external forces along direction of motion: energy equation

Elastic Collision: Conservation of Momentum and Energy Summary: Divide bottom by top: Rewrite:

Relative Velocity Summary of conservation equations: Define relative velocities: Conclusion: x-component of initial relative velocity is equal to the negative of the x-component of the final relative velocity

Table Problem: One Dimensional Elastic Collision: Relative Velocity Consider the elastic collision of two carts; the incident cart 1 has mass m 1 and moves with initial speed v 1, i. The target cart 2 has mass m 2 = 2 m 1 and is initially at rest. Immediately after the collision, the incident cart has final speed v 1, f and the target cart has final speed v 2, f. Find the final velocities of the carts as a function of the initial speed v 1, i.

Solution: One Dim. Elastic Collision Relative velocities: Use relative velocity law: which becomes: Momentum Equation: using m 2 = 2 m 1 becomes: Eliminate v 1, x, f from momentum equation: Solve for v 2, x, f : Solve for v 1, x, f :

Table Problem: Relative Velocity Two Ball Bounce Two superballs are dropped from a height h above the ground. The ball on top has a mass m 1. The ball on the bottom has a mass m 2, such that m 2 >> m 1. Assume that the lower ball collides elastically with the ground. Then as the lower ball starts to move upward, it collides elastically with the upper ball that is still moving downwards. Use the concept of relative velocity to determine the velocity of the lighter ball immediately after the collision. m 2>>m 1

Experiment 4: One Dimensional Collisions

Next Reading Assignment: W 07 D 3 Young and Freedman: 8. 1 -8. 5