A small steel ball of mass slides without friction along a straight track and…

PHYSICS · Multi-part · CBSE · Physics · Work, Energy and Power · Work, Energy and Power

Problem

A small steel ball of mass

m

slides without friction along a straight track and collides head-on with a much larger block of mass

M

that is initially at rest on the same track. The interaction between the ball and the block conserves the total kinetic energy of the two-object system. (a) Derive an expression for the speed

v_{m,\,\text{f}}

of the ball immediately after the collision in terms of

m

M

, and the ball’s initial speed

v_{m,\,\text{i}}

. (b) Derive a corresponding expression for the speed

v_{M,\,\text{f}}

of the block immediately after the collision. (c) Evaluate the expression from part (a) in the limiting case

M\gg m

and interpret the physical meaning of your result. (d) For

M=3m

and

v_{m,\,\text{i}}=4.0\,\text{m}\!\cdot\!\text{s}^{-1}

, calculate the numerical values of

v_{m,\,\text{f}}

and

v_{M,\,\text{f}}

, including appropriate signs to indicate direction.

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