A block with a mass of 3.07 kg is placed at rest on a surface inclined at an angle of 44.6° above the horizontal. The coefficient of static friction between the block and the surface is 0.540, and a force of magnitude pushes upward on the block, parallel to the inclined surface. The block will remain at rest only if is greater than a minimum value, Fmin, and less than a maximum value, Fmax. Calculate Fmin.

Question

A block with a mass of 3.07 kg is placed at rest on a surface inclined at an angle of 44.6° above the horizontal. The coefficient of static friction between the block and the surface is 0.540, and a force of magnitude  pushes upward on the block, parallel to the inclined surface. The block will remain at rest only if  is greater than a minimum value, Fmin, and less than a maximum value, Fmax. Calculate Fmin.

drwls · Answer

To keep the block from sliding downhill the block uphill, the applied force must exceed

Fmin = M*g*sin44.6 - M*g*cos44.6 * 0.540

That is the component of weight down the hill, minus the maximum possible friction force