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Work Energy Theorem

A small block...

Question

A small block is released from rest inside a cylinderical [fixed] pipe of radius R = 3m as shown in the figure. Speed of the block when it reaches B from A is (coefficient of friction between block & cylinder is $μ = 0.7$ and $g = 10 m / s^{2}$ ). Write the answer until two digits after the decimal point.

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Solution

By work energy theorem $/ m g R - μ / m g R = \frac{1}{2} / m v^{2}$
$g R (1 - μ) = \frac{v^{2}}{2}$
$v = \sqrt{2 g R (1 - μ)} = \sqrt{2 \times 10 \times 3 (1 - 0.7)}$
$v = 3 \sqrt{2} = 4.242 m / s$

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