An object, previously at rest, slides $6 m$ $6 m$ down a ramp, with an incline of $\frac{3 π}{8}$ $(3pi)/8$ , and then slides horizontally on the floor for another $8 m$ $8 m$ . If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?

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Answer 1 · 2016-06-06T10:44:05

$μ = 0.409301$ $mu = 0.409301$

Here $d_{1} = 6$ $d_1 = 6$ [m], $d_{2} = 8$ $d_2 = 8$ [m] and $α = 3 \frac{π}{8}$ $alpha = 3 pi/8$ and $μ$ $mu$ is the kinetic friction coefficient.

The initial potential energy is

$m g d_{1} sin (α)$ $m g d_1 sin(alpha)$

The total dissiped work is given by

$τ_{1} + τ_{2}$ $tau_1+tau_2$

where $τ_{1} = m g sin (α) μ d_{1}$ $tau_1 = m g sin (alpha) mu d_1$ and $τ_{2} = m g μ d_{2}$ $tau_2=m g mu d_2$

so equating

$m g d_{1} sin (α) = m g sin (α) μ d_{1} + m g μ d_{2}$ $m g d_1 sin(alpha) = m g sin (alpha) mu d_1 + m g mu d_2$

Solving for $μ$ $mu$ gives

$μ = \frac{d_{1} sin (α)}{d_{1} sin (α) + d_{2}} = 0.409301$ $mu = (d_1 sin(alpha))/(d_1 sin(alpha) + d_2) = 0.409301$

An object, previously at rest, slides 6m6 m down a ramp, with an incline of 3π8(3pi)/8 , and then slides horizontally on the floor for another 8m8 m. If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?