Instructor: Dr. Tatiana Erukhimova Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lectures 23, 24

Center of Mass

Find the position of the center of mass of the system of the sun and Jupiter. (Since Jupiter is more massive than the rest of the planets put together, this is essentially the position of the center of mass of the solar system.) Does the center of mass lie inside or outside the sun?

Motion of the Center of Mass

The center of mass of a system moves as if all of the mass of the system were concentrated at that point and as if all of the forces were acting at that point There is only the external forces that affect the motion of the center of mass ( ) Only external forces affect the motion of the center of mass

Momentum is a vector! Vector equation!

If

Conservation of Momentum If there is no external force on a system, then the total momentum of the system is a constant

True in X and Y directions separately!

BEFORE and AFTER Do X and Y Separately Problem Solving For Conservation of Momentum problems: BEFORE and AFTER Do X and Y Separately

Before Y X

After Y X

Inelastic collision A collision in which the total kinetic energy after the collision is not equal to the kinetic energy before the collision is called an inelastic collision. BEFORE B A AFTER Vafter? B A

Perfectly elastic collision A collision in which the total kinetic energy after the collision is the same than that before the collision is called an elastic collision. B A

A block of mass m is moving along x axis with a velocity of V0 A block of mass m is moving along x axis with a velocity of V0. It collides with a block of mass M, initially at rest. 1) What is the change in kinetic energy of the system of two balls: a) if the collision is perfectly elastic; b) if the collision is perfectly inelastic (balls stick together after collision). 2) For m = M = m0, find the velocity of each ball after a perfectly elastic collision.