Question

A plane is inclined ${30}^o$ with horizontal. A block is placed on the plane at rest. Assume the coefficient of static friction between block and the plane is $.5$. The block will:

• A. accelerate down the plane
  
• B. accelerate briefly down the plane but then slow down and stop
• C. move with constant velocity down the plane
  
• D. not move
• E. cannot be determined from the information given

Answer 1

The correct option is A accelerate down the plane

Force acting on block down the plane$=mgsin\theta =mgsin{30}^{\circ }=\frac{mg}{2}$

Maximum static friction that can act on the plane$=\mu N=\mu mgcos\theta =0.5\times mgcos{30}^{\circ }=\frac{\sqrt{3}mg}{4}<mgsin\theta$

Thus the block would continue to accelerate down with magnitude$=\frac{\frac{mg}{2}-\frac{\sqrt{3}mg}{4}}{m}$