A block rests on a rough plane that is inclined at above the horizontal
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Force and Translational Dynamics · Force and Translational Dynamics
Problem
A 7.0kg block rests on a rough plane that is inclined at 30∘ above the horizontal. A steady wind exerts a horizontal force of magnitude W on the block, blowing directly uphill (opposite the direction in which the block would slide downhill). The coefficients of friction between the block and the plane are μs=0.55 and μk=0.45.
(a) Draw and label a free-body diagram for the block, clearly indicating all forces and their directions relative to the inclined plane.
(b) Derive an expression for the normal force on the block in terms of W and given constants.
(c) Determine the minimum wind force Wmin required to keep the block at rest.
(d) The wind suddenly increases so that W=100N. Calculate the magnitude and direction (uphill or downhill) of the block’s acceleration immediately after this increase, assuming the block was initially at rest.