A block of mass rests on a rough horizontal table

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

Problem

A block of mass

m

rests on a rough horizontal table. The coefficients of friction between the block and the table are

\mu_s

(static) and

\mu_k

(kinetic), with

\mu_s > \mu_k

. A horizontal force

F

is applied to the block. Answer the questions below. (i) Derive an expression for the minimum horizontal force

F_1

required to just start the motion of the block. (ii) Once the block has started moving, derive an expression for the horizontal force

F_2

that must be applied to keep it moving with uniform velocity. (iii) Show that

F_2 < F_1

and explain physically why this inequality holds. (iv) For a

10\,\text{kg}

block with

\mu_s = 0.42

and

\mu_k = 0.30

(take

g = 9.8\,\text{m\,s}^{-2}

), calculate

F_1

and

F_2