An object with a mass of $4 k g$ $4 kg$ is on a plane with an incline of $- \frac{π}{4}$ $- pi/4$ . If it takes $7 N$ $7 N$ to start pushing the object down the plane and $5 N$ $5 N$ to keep pushing it, what are the coefficients of static and kinetic friction?

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An object with a mass of $4 k g$ $4 kg$ is on a plane with an incline of $- \frac{π}{4}$ $- pi/4$ . If it takes $7 N$ $7 N$ to start pushing the object down the plane and $5 N$ $5 N$ to keep pushing it, what are the coefficients of static and kinetic friction?

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Answer 1 · 2018-07-04T10:40:40

$μ_{s} = 1.252$ $\mu_s=1.252$ & $μ_{k} = 1.18$ $\mu_k=1.18$

Explanation:

The force $F$ $F$ required to push an object of mass $m = 4$ $m=4$ kg downward on an inclined plane at an angle $θ = - \frac{π}{4} = - 45^{\circ}$ $theta=-{\pi}/4=-45^\circ$ & coefficient of static friction $μ_{s}$ $\mu_s$

$F = μ_{s} m g cos θ - m g sin θ$ $F=\mu_s mg\cos\theta-mg\sin\theta$

$μ_{s} = \frac{F + m g sin θ}{m g cos θ}$ $\mu_s=\frac{F+mg\sin\theta}{mg\cos\theta}$

$μ_{s} = \frac{7 + 4 \times 9.81 {sin 45}^{\circ}}{4 \times 9.81 {cos 45}^{\circ}}$ $\mu_s=\frac{7+4\times9.81\sin45^\circ}{4\times9.81\cos45^\circ}$
$= 1.252$ $=1.252$

Similarly, when the motion starts, then the force (F) required to keep the object moving

$F = μ_{k} m g cos θ - m g sin θ$ $F=\mu_k mg\cos\theta-mg\sin\theta$

$μ_{k} = \frac{F + m g sin θ}{m g cos θ}$ $\mu_k=\frac{F+mg\sin\theta}{mg\cos\theta}$

$μ_{k} = \frac{7 + 4 \times 9.81 {sin 45}^{\circ}}{4 \times 9.81 {cos 45}^{\circ}}$ $\mu_k=\frac{7+4\times9.81\sin45^\circ}{4\times9.81\cos45^\circ}$
$= 1.18$ $=1.18$

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An object with a mass of $4 k g$ $4 kg$ is on a plane with an incline of $- \frac{π}{4}$ $- pi/4$ . If it takes $7 N$ $7 N$ to start pushing the object down the plane and $5 N$ $5 N$ to keep pushing it, what are the coefficients of static and kinetic friction?

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Explanation:

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An object with a mass of 4kg4 kg is on a plane with an incline of −π4 - pi/4 . If it takes 7N7 N to start pushing the object down the plane and 5N5 N to keep pushing it, what are the coefficients of static and kinetic friction?

1 Answer

Explanation:

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An object with a mass of $4 k g$ $4 kg$ is on a plane with an incline of $- \frac{π}{4}$ $- pi/4$ . If it takes $7 N$ $7 N$ to start pushing the object down the plane and $5 N$ $5 N$ to keep pushing it, what are the coefficients of static and kinetic friction?