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24 July, 15:57

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.

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  1. 24 July, 17:02
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    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
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