An object with a mass of $14 k g$ $14 kg$ is on a plane with an incline of $- \frac{5 π}{12}$ $-(5 pi)/12$ . If it takes $12 N$ $12 N$ to start pushing the object down the plane and $7 N$ $7 N$ to keep pushing it, what are the coefficients of static and kinetic friction?

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An object with a mass of $14 k g$ $14 kg$ is on a plane with an incline of $- \frac{5 π}{12}$ $-(5 pi)/12$ . If it takes $12 N$ $12 N$ to start pushing the object down the plane and $7 N$ $7 N$ to keep pushing it, what are the coefficients of static and kinetic friction?

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Answer 1 · 2018-06-28T23:33:52

$4.07, 3.93$ $4.07, 3.93$

Explanation:

The force $F$ $F$ required to push an object of mass $m = 9$ $m=9$ kg downward on an inclined plane at an angle $θ = - \frac{5 π}{12} = - 75^{\circ}$ $theta=-{5\pi}/12=-75^\circ$ & coefficient of static friction $μ_{s}$ $\mu_s$ is given as

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

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

$μ_{s} = \frac{12 + 14 \times 9.81 {sin 75}^{\circ}}{15 \times 9.81 {cos 75}^{\circ}}$ $\mu_s=\frac{12+14\times9.81\sin75^\circ}{15\times9.81\cos75^\circ}$
$= 4.07$ $=4.07$

Similarly, when the motion starts, then the force (F) required to keep the object moving on the plane is given as

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

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

$μ_{k} = \frac{7 + 14 \times 9.81 {sin 75}^{\circ}}{15 \times 9.81 {cos 75}^{\circ}}$ $\mu_k=\frac{7+14\times9.81\sin75^\circ}{15\times9.81\cos75^\circ}$
$= 3.93$ $=3.93$

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An object with a mass of $14 k g$ $14 kg$ is on a plane with an incline of $- \frac{5 π}{12}$ $-(5 pi)/12$ . If it takes $12 N$ $12 N$ to start pushing the object down the plane and $7 N$ $7 N$ 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 14kg14 kg is on a plane with an incline of −5π12 -(5 pi)/12 . If it takes 12N12 N to start pushing the object down the plane and 7N7 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 $14 k g$ $14 kg$ is on a plane with an incline of $- \frac{5 π}{12}$ $-(5 pi)/12$ . If it takes $12 N$ $12 N$ to start pushing the object down the plane and $7 N$ $7 N$ to keep pushing it, what are the coefficients of static and kinetic friction?