An object with a mass of $5 k g$ $5 kg$ is on a plane with an incline of $- \frac{π}{8}$ $- pi/8$ . If it takes $8 N$ $8 N$ to start pushing the object down the plane and $8 N$ $8 N$ to keep pushing it, what are the coefficients of static and kinetic friction?

Question

1493 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-07-11T20:21:04

the static coefficient of friction is $0.5909$ $0.5909$ (4dp)
the kinetic coefficient of friction is $0.5909$ $0.5909$ (4dp)

enter image source here

For our diagram, $m=5 \ kg$ , $theta=pi/8$

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

$R-mgcostheta=0$
$:. R=5gcos(pi/8) \ \ N$

Initially it takes $8N$ to start the object moving, so $D=8$ . If we Apply Newton's Second Law down parallel to the plane we get:

$D+mgsin theta -F = 0$
$:. F = 8+5gsin (pi/8) \ \ N$

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

$F = mu R => 8+5gsin (pi/8) = mu (5gcos(pi/8))$
$:. mu = (8+5gsin (pi/8))/(5gcos(pi/8))$
$:. mu = 0.5909306 ...$

Once the object is moving the driving force remains at $8N$ , so $D=8$ , ie remains unchanged.

Hence:

the static coefficient of friction is $0.5909$ (4dp)
the kinetic coefficient of friction is $0.5909$ (4dp)

An object with a mass of 5 kg5kg5 kg is on a plane with an incline of - pi/8 −π8 - pi/8 . If it takes 8 N8N8 N to start pushing the object down the plane and 8 N8N8 N to keep pushing it, what are the coefficients of static and kinetic friction?