Newton's cradle
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1. NEWTON’S CRADLE: KINETIC ENERGY AND MOMENTUM Mo Beaver P2

2. What is Newton’s Cradle? Newton’s Cradle is a device that has equally hung pendulums in a row. It was invented in 1967 by an English man named Simon Pebble. It is named after the famous scientist and mathematician of the 16- 1700s, Isaac Newton, because the cradle uses the Newton laws (Kurtus).

3. When a ball on one end is pulled back and then let go, it hits the rest of the balls and its energy is transferred How does it work? through them until the ball at the opposite end is driven upward with the same velocity as the initial ball. The process continues back and forth with the two balls on the ends until they lose momentum because of friction or the elasticity of the balls. Steel balls are commonly used because they are highly elastic, so they lose very little energy with collision. When the same process is conducted using two balls, two balls will also go off the other end. The number of balls swinging off the ends and the velocity will always be the same on both ends (Kurtus).

4. LAWS AND FORMULAS  Law of Conservation of Momentum:  The total linear momentum of a closed system is constant.  p=mv  p=p’  Law of Conservation of Energy:  The total kinetic energy of a system with no external forces acting on it remains constant.  KE= ½mv2  KE=KE’

5. NUMBER OF BALLS MOVED EQUAL ON BOTH ENDS  p=p’ p=mv=MV  Solve for v and square both sides of the equation:  v = MV/m  v2 = M2V2/m2  Substitute v2into the kinetic energy equation mv2/2:  mv2/2 = mM2V2/2m2 = M2V2/2m  Since:  mv2/2 = MV2/2 (Law of Conservation of Energy)  M2V2/2m = MV2/2  Then:  M/m = 1 or M = m  Also V=v (Kurtus)

6. CONCLUSION  The formula M=m means that the incoming and outgoing masses are equal to each other. The formula V=v means that the incoming and outgoing velocities are equal. You can’t release two balls on one end and have one ball from the other end have twice the velocity. These formulas prove that the number of balls on each end will be equal to each other because momentum and energy are conserved.