An object, previously at rest, slides $9 m$ $9 m$ down a ramp, with an incline of $\frac{π}{6}$ $(pi)/6$ , and then slides horizontally on the floor for another $24 m$ $24 m$ . If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?

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An object, previously at rest, slides $9 m$ $9 m$ down a ramp, with an incline of $\frac{π}{6}$ $(pi)/6$ , and then slides horizontally on the floor for another $24 m$ $24 m$ . 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 · 2016-02-20T21:57:41

$k ≅ 0, 142$ $k~=0,142$

Explanation:

$\frac{π}{6} = 30^{o}$ $pi/6=30^o$
$E_{p} = m \cdot g \cdot h Potential Energy of Object$ $E_p=m*g*h " Potential Energy of Object"$
$W_{1} = k \cdot m \cdot g \cdot cos 30 \cdot 9$ $W_1=k*m*g*cos 30*9$
$Lost energy because friction on inclined plane$ $"Lost energy because friction on inclined plane"$
$E_{p} - W_{1} : energy when object on ground$ $E_p-W_1": energy when object on ground"$
$E_{p}_W_{1} = m \cdot g \cdot h - k \cdot m \cdot g \cdot {cos 30}^{o} \cdot 9$ $E_p_W_1=m*g*h-k*m*g*cos 30^o*9$
$W_{2} = k \cdot m \cdot g \cdot 24 lost energy on the floor$ $W_2=k*m*g*24 " lost energy on the floor"$
$k*cancel(m*g)*24=cancel(m*g)*h-k*cancel(m*g)*cos 30^o*9$
$24*k=h-9*k*cos 30^o$
$"using "cos 30^o=0,866 ;h=9*sin30=4,5 m$
$24*k=4,5-9*k*0,866$
$24*k+7,794*k=4,5$
$31,794*k=4,5$
$k=(4,5)/(31,794)$
$k~=0,142$

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An object, previously at rest, slides $9 m$ $9 m$ down a ramp, with an incline of $\frac{π}{6}$ $(pi)/6$ , and then slides horizontally on the floor for another $24 m$ $24 m$ . If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?

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1 Answer

Explanation:

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An object, previously at rest, slides $9 m$ $9 m$ down a ramp, with an incline of $\frac{π}{6}$ $(pi)/6$ , and then slides horizontally on the floor for another $24 m$ $24 m$ . If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?