Question

A block with initial velocity of 3 m/s slides 9 m across a rough horizontal surface before coming to rest. What is the coefficient of kinetic
friction?

Answer 1

The coefficient of kinetic friction between the block and the horizontal surface is 0.051.

The given parameters;

• initial velocity, u = 3 m/s
• distance traveled by the block, s = 9 m

The acceleration of the block is calculated as follows;

$v^2 = u^2 + 2(-a)s\\\\v^2 = u^2 - 2as\\\\a = \frac{u^2 - v^2}{2s} \\\\a = \frac{3^2 - 0^2}{2\times 9} \\\\a =0.5 \ m/s^2$

The coefficient of kinetic friction between the block and the horizontal surface is calculated as follows;

$\mu_k mg = ma\\\\\mu_k = \frac{a}{g} \\\\\mu_k = \frac{0.5}{9.8} \\\\\mu_k = 0.051$

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