Question

A box (m = 20 kg) is sliding on a horizontal surface. it is connected to a massless hook by a light string passing over a massless pulley wheel. the coefficients of friction between the box and the surface are 0.80 (static) and 0.30 (kinetic). if 15 kg (in total) are placed on the hook, calculate the acceleration of the box.

Answer 1

mass of the box = 20 kg

force of friction on the box due to surface

$F_s = \mu_s N$

$F_s = 0.80 * 20 * 9.8$

$F_s = 156.8 N$

similarly kinetic friction on it

$F_k = \mu_k N$

$F_k = 0.30* 20 * 9.8$

$F_k = 58.8 N$

now the weight of the suspended block will be

$W = mg = 15*9.8 = 147 N$

so here the weight of the suspended block is less than the limiting friction on it

So here we will say that friction will counter balance the weight of the suspended block and it will not move at all

So acceleration of the box will be zero