A ball at the end of a string has mass m 1 . It is displaced to a height h 1 and

Question

A ball at the end of a string has mass m1. It is displaced to a height h1 and released from rest. This ball collides elastically with another ball that has a mass m2 (see the diagram below).
a. Derive an expression for the maximum height h2 of the second ball (do not use any "magic" equations).
b. If m2 = 2.5m1 and h1 = 4.20 m, what is h2?

A ball at the end of a string has mass m1. It is displaced to a height h1 and released from rest. This ball collides elastically with another ball that has a mass m2 (see the diagram below). a. Derive an expression for the maximum height h2 of the second ball (do not use any ''magic'' equations). b. If m2 = 2.5m1 and h1 = 4.20 m, what is h2?

Explanation / Answer

When m1 hits m2 the kinetic energy of m1 transfers to m2 and will let to rise a height h2

Energy of m1 before hitting m2 = KE = mgh

KE = m1gh1

Since m1, m2 collides elastically, by energy conservation

m1gh1=m2gh2

Hence h2 = m1h1/m2

= (m1*4.2)/2.5m1

= 1.68 m

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