A block of mass rests on a rough horizontal surface

PHYSICS · Multi-part · CBSE · Physics · Laws of Motion · Laws of Motion

Problem

A block of mass

m

rests on a rough horizontal surface. A horizontal force

F

acts on the block while an additional vertical force

P

is applied on the top of the block. The positive direction for

P

is taken upward (so

P

is negative if the block is pressed downward). The coefficient of static friction between the block and the surface is

\mu_s

. (a) Write an expression for the normal reaction

N

on the block in terms of

m

g

and

P

. (b) Hence derive an expression for the minimum horizontal force

F_{\text{min}}

required to just start moving the block in terms of

m

g

P

and

\mu_s

. (c) Discuss qualitatively how

F_{\text{min}}

changes when

P

acts (i) upward and (ii) downward, and comment on the physical reason for this behaviour.