An object with a mass of $2 k g$ $2 kg$ is on a ramp at an incline of $\frac{π}{12}$ $pi/12$ . If the object is being pushed up the ramp with a force of $8 N$ $8 N$ , what is the minimum coefficient of static friction needed for the object to remain put?

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An object with a mass of $2 k g$ $2 kg$ is on a ramp at an incline of $\frac{π}{12}$ $pi/12$ . If the object is being pushed up the ramp with a force of $8 N$ $8 N$ , what is the minimum coefficient of static friction needed for the object to remain put?

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Answer 1 · 2018-06-03T03:03:45

$μ = 0.155$ $mu = 0.155$

Explanation:

we can write $\frac{π}{12}$ $pi/12$ as 15° in degree.
enter image source here
Now please consider the image and look at the free body diagram and the forces acting on it.

$8 N$ $8N$ force acting upwards and $m g sin θ$ $mgsintheta$ , $μ m g cos θ$ $mu mg costheta$ downwards. where the $μ$ $mu$ is coefficient of static friction, $m$ $m$ is mass and $g$ $g$ is accelaration due to gravity.

Thus for the object to be put,
$\Rightarrow 8 N = m g sin θ + μ m g cos θ$ $rArr 8N = mgsintheta + mu mgcostheta$

$rArr (8 - 2*9.8*sin15°)/(2*9.8*cos15°) = mu$

as $sin15°=0.256 and cos15°=0.998$

after calculation $mu= 0.155$

Hence coefficient of static friction is $mu = 0.155$

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An object with a mass of $2 k g$ $2 kg$ is on a ramp at an incline of $\frac{π}{12}$ $pi/12$ . If the object is being pushed up the ramp with a force of $8 N$ $8 N$ , what is the minimum coefficient of static friction needed for the object to remain put?

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An object with a mass of 2 kg2kg2 kg is on a ramp at an incline of pi/12 π12pi/12 . If the object is being pushed up the ramp with a force of 8 N8N 8 N, what is the minimum coefficient of static friction needed for the object to remain put?

1 Answer

Explanation:

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An object with a mass of $2 k g$ $2 kg$ is on a ramp at an incline of $\frac{π}{12}$ $pi/12$ . If the object is being pushed up the ramp with a force of $8 N$ $8 N$ , what is the minimum coefficient of static friction needed for the object to remain put?