Description:

Perhaps not the greatest triumph of applied physics, Newton's pendulum is still, arguably, the best coffee table ornament... here's a description of how it works in terms of the law of conservation of momentum and the law of conservation of energy.

Watch Video:

Possible Incorporated Topics:

• Conservation of Momentum
• Conservation of Energy
• Elastic Collision

 Theory:In an elastic collision, both momentum (p) and kinetic energy (T) are conserved. That ispf = pi and Tf = TiNewton's pendulum is five metal spheres suspended so they all touch one another in line. One or more spheres can be drawn back and released. The released spheres swing down and collide with the remaining spheres.Each sphere has mass m, and the spheres collide essentially elastically. Of course, the fact that the spheres click when they connect means that some kinetic energy is being converted into sound energy and lost, but these losses are negligible in a single collision.When one or more spheres are drawn back and released, it/they have mass Mi = m, 2m, 3m, 4m,depending on if one, two, three, or four spheres are drawn back.At the instant just before these spheres collide with the other hanging spheres, they have a velocity (in the horizontal direction) of vi. The momentum and kinetic energy are thus pi = Mivi , and Ti =(1/2)Mivi2.An instant after the spheres collide, some mass of spheres (Mf) must keep moving with velocity (in the horizontal direction) vf. Applying the conservation of momentum to this collision gives the following equation:pf = piMfvf = MiviMf = Mi(vi/vf) Conserving kinetic energy gives....Tf = Ti(1/2)Mfvf2 = (1/2)Mivi2Mf = Mi(vi/vf)2The red and green equations above can be combined to eliminate Mf.Mi(vi/vf)2 = Mi(vi/vf)vi = vfSo the velocity of any moving spheres after the collision is the same as the velocity of the moving spheres before the collision. Substituting this into the red equation gives...Mf = Mi(vi/vf)Mf = Mi (vi/vi)Mf = MiThe number of spheres moving after the collision is the same as the number moving before the collsion.

Apparatus:

• A Newton's Pendulum

Procedure:

1. Pull back one of the spheres in the pendulum, then release.
2. You can do this with two, three or four spheres.
3. The demonstration works most smoothly if the sphere(s) is/are released from a small angle.