Question

Find weight and coefficient of friction from the given figure ?​

Answer 1

Given : $\</strong><strong>t</strong><strong>h</strong><strong>e</strong><strong>t</strong><strong>a</strong><strong>$ = 30°

W = weight of the body

$R_N$ = Normal reaction

$\mu$ = Coefficient of friction

F = Force of friction

let us consider a pull of 180 N, The force of friction F acts towards left

Resolving the force horizontally,

F = 180 cos 30° = 180 × 0.886 = 156 N

Now, Resolving the force vertically,

$R_N$ = W ― 180 sin 30° = W ― 180 × 0.5 = (W―90)N

We know that F = $\mu$.$R_N$

$\implies$ 156 = $\mu$(W―90) ........ (i)

Now let us consider a push of 220 N Then the force of friction (F) acts towards right.

Resolving the force horizontally

F = 220 cos 30° = 220 × 0.886 = 190.5 N

now, resolving the force vertically

$R_N$ = W + 220 sin 30° = W + 220 × 0.5

= (W + 110) N

F = $\mu$$R_N$

F = $\mu$(W + 110) .........(ii)

After solving eq(i) and (ii) we get,

W = 1000 N, and $</strong><strong>\</strong><strong>m</strong><strong>u</strong><strong>$= 0.1714