Question

A block of mass 2 kg is pushed normally against a rough vertical wall with a force of 40 N, co-efficient of static friction being 0.5. Another horizontal force of 15 N is applied on the block in a direction parallel to the wall. Will the block move? If yes, in which direction and with what acceleration? If no, find the frictional force exerted by the wall on the block.

• A. No Frictional force = 20N
• B. Yes Direction = 53° with horizontal Acceleration = 5 m/s²
• C. No Frictional force = 20N
• D. Yes Direction = 37° with vertical Acceleration = 2.5 m/s²

Answer 1

The correct option is D

Yes

Direction = 37° with vertical

Acceleration = 2.5 m/s²

The force which may cause the tendency of motion or motion in the body is its own weight and the applied horizontal force of 15N.

The resultant of the forces F=$\sqrt{{20}^2+{15}^2}=25N$

Hence net driving force $F_{driving}$ = 25N

In a direction $ta{n}^{-1}\left(\frac{15}{20}\right)$ = 37${}^{\circ }$ with the vertical

The friction will, by its very virtue of opposing the tendency of relative motion, act in a direction opposite to the resultant force.

Maximum resisting force = limiting friction

$F_{lim}=\mu N=0.5\times 40=20N$

As driving force is greater than maximum resisting force, hence the block will move and friction will be kinetic in nature and $f_r$ = 20N

The direction of friction force will be opposite to the direction of net force.

Acceleration of the block a =$\frac{F_{net}-f_r}{m}=\frac{25-20}{2}=2.5m/s^2$