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Distance

A ball moves ...

Question

A ball moves over a fixed track as shown in the figure. From A to B the ball rolls without slipping. If surface BC is frictionless and $K_{A}, K_{B}$ and $K_{C}$ are kinetic energies of the ball at A, B and C respectively, then

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Solution

$E_{a} = m g h_{A} + K_{a}$
$E_{B} = K_{B}$
$E_{c} = m g h_{C} + K_{C}$
Using conservation of energy-
$E_{A} = E_{B} = E_{C}$
$K_{b} >= K_{c}$
$M (h_{A} - h_{C}) + (K_{A} - K_{C})$
$h_{A} - h_{C} = \frac{K_{C} - K_{A}}{M g}$

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