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As illustrated below, consider a block that weights m (kg) on a slope that makes

ID: 2001364 • Letter: A

Question

As illustrated below, consider a block that weights m (kg) on a slope that makes an angle alpha with the horizontal. Due to effect of gravity, the block will slide down the slope. The coefficient of friction between the block and the slope is Mu. Find the minimum magnitude of force F that is applied to the object, whose direction is in parallel to the slope, which will prevent the block from sliding. Find the minimum magnitude of force F that is applied to the object, applied in the horizontal direction, that prevents the block from sliding.

Explanation / Answer


along the slope Fnet = F + u*m*g*cosalpha - m*g*sinalpha

normal force N = m*g*cosalpha


friction force up the plane = u*N = u*m*g*cosalpha

along the slope the net force = 0

F + u*m*g*cosalpha - m*g*sinalpha = 0


F =   m*g*sinalpha - u*m*g*cosalpha


++++++++++++++

normal force N = m*g*cosalpha + F*sinalpha

frictional force = f = u*N = u*(m*g*cosalpha + F*sinalpha)

Fnet = F*cosalpha + f - m*g*sinalpha

Fnet = F*cosalpha + u*m*g*cosalpha + u*F*sinalpha - m*g*sinalpha

Fnet = 0


F*(cosalpha + u*sinalpha) = m*g*(sinalpha - u*cosalpha)


F = m*g*(sinalpha - u*cosalpha) / (cosalpha + u*sinalpha)