
NEWTON, Ask A Scientist!
Name: Michael T.
Status: educator
Age: 50s
Location: N/A
Country: N/A
Date: 12/12/2004

I know how Newton's cradle demonstrates the laws of conservation of momentum and energy, but is it really a good demonstration of Newton's 3rd law? If so, how?

No, it is not a "good" (direct and clear) demonstration of Newton's 3rd law. However, it is a good example of the conservation of momentum and energy, which can be derived directly and quickly from Newton's 2nd and 3rd laws.

If a force F acts on a mass m for a time t, then Ft = mat = mv (since v = at, assuming the mass m starts from rest). When two bodies collide the forces the two bodies feel are equal and opposite by Newton's 3rd law, so the mv of the two bodies is equal in magnitude and opposite in direction. This is conservation of energy. Further, as the bodies move in contact, Fx = max = mv^2/2. So the kinetic energy of the two bodies will be equal (I am ignoring some fine points about the force varying in order to make the main point clear.)

With Newton's cradle, if one ball swings down and strikes four other balls, the only way momentum and energy can be conserved is for one ball to come off the other end of the cradle with the same speed as the incoming ball struck the first ball. Try it!

Best, Dick Plano...

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