It is known that the 10 kg pipe will roll up the ramp and not slide on the ramp when P becomes sufficiently large. Using the rolling assumption, find the minimum P required to cause impending motion of the 10 kg pipe up the ramp. Note that the coefficients of friction for the block/ramp, the pipe/ramp and the pipe/block contacts are each 0.30.

65.73N

Explanation:

The frictional force is a force that opposes the motion of an object on a flat surface or an inclined surface.

It is always acting up an incline plane.

Since the pipe will tend to roll up the plane, then both the impending force P also known as frictional force and the moving force Fm both will be acting up the plane.

The net force acting up the plane is

Fnet = P + Fm ... (1)

The force perpendicular to the plane known as the normal reaction R must be equal to the force acting along the ramp in other to keep the body in equilibrium i. e R = Fnet

If R = W = mgcos (theta)

and Fm = mgsin (theta)

Then mgcos theta = Fnet

mgcos (theta) = P+Fm

mgcos (theta) = P+mgsin (theta)

P = mgcos (theta) - mgsin (theta) ... (2)

Given mass = 10kg

g = 9.81m/s

We can get theta from the formula;

µ = Ff/R = wsin theta/wcos theta

µ = sin theta/cos theta

µ = tan (theta)

0.3 = tan (theta)

theta = arctan0.3

theta = 16.7°

P = 10 (9.81) cos16.7° - 10 (9.81) sin16.7°

P = 98.1 (cos16.7°-sin16.7°)

P = 98.1 (0.67)

P = 65.73N

The minimum force P required to cause impending motion is 65.73N