Question

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.

Answer 1

Answer:

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

Answer 2

When The minimum force of P required to cause approaching motion is 65.73N. It is always operating up an inclined plane.

What is the Friction?

Then frictional force is a force that resists the motion of an object on a flat surface or a willing surface.

Since the pipe will manage to roll up the plane, then both the impending force P is also understood as frictional force, and also the moving force Fm both will be serving up the plane.

The net force operating up the plane is

Then Fnet = P + Fm... (1)

The force perpendicular to the plane learned 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 is = W = mgcos (theta)

and Fm is = mgsin(theta)

Then mgcos theta is = Fnet

mgcos (theta) = P+Fm

mgcos (theta) = P+mgsin(theta)

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

Given mass = 10kg

g = 9.81m/s

Now, We can get theta from the formula;

Then µ = Ff/R = wsin theta/wcos theta

After that µ = sin theta/cos theta

Then µ = tan(theta)

Now, 0.3 = tan (theta)

theta is = arctan0.3

theta is = 16.7°

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

P is = 98.1(cos16.7°-sin16.7°)

P is = 98.1(0.67)

P is = 65.73N

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

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