An object with a mass of $7 k g$ $7 kg$ 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 · 2017-01-15T00:07:44

minimum friction coefficient is $0.3827$ $0.3827$ (4dp)

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For our diagram, $m = 7 k g$ $m=7kg$ , $θ = \frac{π}{8}$ $theta=pi/8$

If we apply Newton's Second Law up perpendicular to the plane we get:

$R - m g cos θ = 0$ $R-mgcostheta=0$
$:. R=7gcos(pi/8) \ \ N$

It takes $2N$ to keep the object in equilibrium, so $D=2$ . If we Apply Newton's Second Law down parallel to the plane we get:

$mgsin theta -D-F = 0$
$:. F = 7gsin (pi/8) -2\ \ N$

And the friction is related to the Reaction (Normal) Force by

$F le mu R => 7gsin (pi/8) -2 le mu (7gcos(pi/8))$
$:. mu ge (7gsin (pi/8) -2)/(7gcos(pi/8))$
$:. mu ge 0.382656 ...$

An object with a mass of 7 kg7kg7 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?