Collisions 碰撞

A collision is an interaction involving large forces acting for a short time.

During the short time of the collision, internal forces are much bigger than external forces. We can ignore the external forces during the collision.

Momentum principle:

Energy principle: (Careful – total energy is conserved, but the kinetic energy might not be conserved! Some might be converted to heat.)

We might still need to account for external forces during the time before and after the collision. Example: Gravity, acting on these two balls, is important before and after they collide. But during the collision, we can ignore it.

Elastic collisions 弹性碰撞 If the internal energy of the objects does not change: No change in temperature No change in shape No springs compressed No new rotations or vibrations Then:

Elastic collision of equal masses

Inelastic collisions 非弹性碰撞 If the internal energy of the objects does change: Change in temperature Change in shape Springs compressed, or New rotations or vibrations Then:

Maximally inelastic collision (“sticking collision”) of equal masses

How much kinetic energy was lost? Half of the kinetic energy was converted into heat.

Head-on collision of unequal masses System: Ping-pong ball + bowling ball Surroundings: Nothing significant. Initial state: Ping-pong ball moving, bowling ball at rest. Final state: Ping-pong ball bounces back with almost unchanged speed:

Head-on collision of unequal masses Momentum principle: The bowling ball ends up with about twice the momentum of the Ping-pong ball! How fast does it move?

Head-on collision of unequal masses Final speed of the bowling ball: Very small!

40 m/s EARTH

What is the recoil speed of the Earth? 后座 40 m/s v = ? EARTH

40 m/s v = ? At this speed, it would take over one million years to move the width of a single atom! EARTH

Collisions in 2-D and 3-D Momentum: x: Initial y: Final Energy (elastic collision): y x

Collisions in 2-D and 3-D Three equations… Four unknowns! p3 p4 θ φ These equations are only useful if we can somehow measure at least one of the unknowns.

In particle physics experiments, the momentum of a particle is measured by how much it curves in a magnetic field.

Special case: Identical particles, one at rest. Momentum: Initial Energy (elastic collision): (for v << c) Final

Special case: Identical particles, one at rest. Momentum: Initial Energy (elastic collision): Final

Special case: Identical particles, one at rest. Momentum: Initial Energy (elastic collision): Final

Special case: Identical particles, one at rest. Momentum: Initial Energy (elastic collision): Final Only possible if cos A = 0, so A = 90°.

How the nucleus was discovered by collisions Born in 1871, the son of a poor farmer in New Zealand. Won the Nobel prize (chemistry) in 1908. Died in 1937, in Cambridge, as “Lord Rutherford of Nelson”. Ernest Rutherford

Thompson’s “plum pudding” model for the atom In 1909, Rutherford decided to test this model by shooting alpha particles (helium nuclei) at a thin sheet of gold. At this stage, he had already won his Nobel prize for other work.

The experiment

What should have happened

What actually happened Rutherford thought he was shooting bowling balls at ping-pong balls. Actually, he was shooting bowling balls at even bigger bowling balls.

“It was the most incredible event that has ever happened to me in my life. It was almost as incredible as if you fired a 15 inch shell (炮弹) at a piece of tissue paper and it came back and hit you.”