An object with a mass of $12 k g$ $12 kg$ is on a plane with an incline of $- \frac{π}{6}$ $- pi/6$ . If it takes $6 N$ $6 N$ to start pushing the object down the plane and $4 N$ $4 N$ to keep pushing it, what are the coefficients of static and kinetic friction?

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An object with a mass of $12 k g$ $12 kg$ is on a plane with an incline of $- \frac{π}{6}$ $- pi/6$ . If it takes $6 N$ $6 N$ to start pushing the object down the plane and $4 N$ $4 N$ to keep pushing it, what are the coefficients of static and kinetic friction?

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Answer 1 · 2018-05-14T17:44:36

coefficient of static friction $μ s = 0.366 . \sqrt{3}$ $mu s = 0.366 .sqrt(3)$
coefficient of kinetic friction $μ k = 0.355 . \sqrt{3}$ $mu k = 0.355 .sqrt(3)$

Explanation:

the incline is making an angle of $- \frac{π}{6}$ $-pi/6$ = -30 degrees from the horizontal.

the forces operating on the body is the weight m.g vertically

down = $12 k g . 10 \frac{m}{s^{2}}$ $12 kg . 10 m/s^2$ = 120 N

the normal reaction of the plane acting perpendicular to the plane. say R

breaking the weight in components along the plane and

perpendicular to the plane inclined at 30 degree to horizontal

$m g . cos 30$ $mg.cos 30$ = $120 . \frac{\sqrt{3}}{2}$ $120 . sqrt(3) /2$ = R and

mg. sin30 will act along the plane .

as a force of 6 N is needed to start the motion

so frictional force f s = 6 N + mg sin 30 = 6 N + 120/2 = 66 N

$f s = μ s . R$ $fs = mu s . R$ = 66N so, $μ s = {\frac{66}{60 . \sqrt{3}}}$ $mus = {66 / (60. sqrt (3))}$

$μ s$ $mu s$ = $0.366 \sqrt{3}$ $0.366 sqrt(3)$

however ,when the body starts moving a force of 4 N is sufficient to maintain the motion , therefore

$f k = μ k . R$ $f k = mu k .R$ = 64N so, $μ k = {\frac{64}{60 . \sqrt{3}}}$ $mu k = {64 / (60. sqrt (3))}$

$μ k = 0.355 . \sqrt{3}$ $mu k = 0.355. sqrt(3)$

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An object with a mass of $12 k g$ $12 kg$ is on a plane with an incline of $- \frac{π}{6}$ $- pi/6$ . If it takes $6 N$ $6 N$ to start pushing the object down the plane and $4 N$ $4 N$ 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 12kg12 kg is on a plane with an incline of −π6 - pi/6 . If it takes 6N6 N to start pushing the object down the plane and 4N4 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 $12 k g$ $12 kg$ is on a plane with an incline of $- \frac{π}{6}$ $- pi/6$ . If it takes $6 N$ $6 N$ to start pushing the object down the plane and $4 N$ $4 N$ to keep pushing it, what are the coefficients of static and kinetic friction?