An object with a mass of $5 k g$ $5 kg$ is on a ramp at an incline of $\frac{π}{8}$ $pi/8$ . If the object is being pushed up the ramp with a force of $2 N$ $2 N$ , what is the minimum coefficient of static friction needed for the object to remain put?

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Answer 1 · 2018-04-30T10:58:17

$0.37 8888$ $color(blue)(0.37)color(white)(8888)$ 2 d.p.

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Since the $2 N$ $bb(2 N)$ force is acting upwards the frictional force $F r$ $bb(Fr)$ is acting in the opposite direction.

For the body to remain static, we have:

$F r = μ R$ $Fr=muR$

Where $μ$ $mu$ is the coefficient of friction.

Resolving forces perpendicular to the plane:

$R = 5 g cos (\frac{π}{8})$ $R=5gcos(pi/8)$

Resolving forces horizontal to the plane:

$F r = 5 g sin (\frac{π}{8}) - 2 N$ $Fr=5gsin(pi/8)-2N$

Substituting these two equations into $\ \ \ \ \Fr=muR$ :

$5gsin(pi/8)-2=mu*5gcos(pi/8)$

$:.$

$mu=(5gsin(pi/8)-2)/(5gcos(pi/8))$

Taking $g=9.81$

$mu=(5*(9.81)sin(pi/8)-2)/(5*(9.81)cos(pi/8))=0.3700793240N$

$mu=0.37$ 2 d.p.

An object with a mass of 5 kg5kg5 kg is on a ramp at an incline of pi/8 π8pi/8 . If the object is being pushed up the ramp with a force of 2 N2N 2 N, what is the minimum coefficient of static friction needed for the object to remain put?