Question

A man of mass 80 kg stands on a horizontal weighing machine of negligible mass, attached to a massless platform P that slides down at${37}^0$ inclined. The weighing machine reads 72 kg. The man is always at rest w.r.t. weighing machine. Calculate:
a. the vertical acceleration of the man.
b. The coefficient of kinetic friction $\mu$ between the platform and incline.

Answer 1

a) $mg-ma=72g$

$\Rightarrow 80(10-a)=72\times 10$

$\Rightarrow 10-a=9$

$\Rightarrow a=1$ $m/s^2$

b) From figure

$\mu mg{cos37}^0+macos{53}^0=mgsin{37}^0$

$\Rightarrow \mu 80\times 10\times \frac{4}{5}+80\times 1\times \frac{3}{5}=80\times 10\times \frac{3}{5}$

$8\mu +\frac{3}{5}=6$

$8\mu =\frac{27}{5}$

$\mu =\frac{27}{40}$