A body of mass 10 kg is on an inclined plane of inclination 30 degrees with the horizontal as shown. The coefficient of friction between the body and the inclined plane is 0.3 . An external force of 100 N is applied vertically downwards on the body. Find the acceleration of the body along the inclination.

a ) 2.76 m / s 2
b ) 3.46 m / s 2
c ) 4.76 m / s 2
d ) 4.06 m / s 2

 

Let M be the mass of the body ; Na the normal reaction on the block ; m the coefficient of friction and F the external force applied.

The body does not move in the y axis direction.
Writing the equation of motion along the y direction

 Na - F cos q - M g cos q =  0  ;    or
 Na = F cos q + M g cos q  
 Na = 100 ( 0.866 ) + 10( 9.81 )( 0.866 )
 Na = 171.55 N

                
Writing the equation of motion along the x direction

  F sin q + M g sin q - m N a =  M a x  ;    or
 ax = (  F sin
q + M g sin q - m N a ) / M
 ax = [100(0.5) + 10(9.81)(0.5) - 0.3(171.55)] /10
 ax =  4.76 m / s 2

The acceleration of the body along the inclination is 4.76 m / s 2