Question

A cylinder and a wedge of same mass (m) with a vertical face, touching each other, move along two smooth inclined planes forming an angle and respectively with horizontal as shown in the figure. Determine the force of normal N (In newton) exerted by the wedge on the cylinder, neglecting the friction between them. Consider $m=\frac{1}{\sqrt{3}}kg;\alpha ={60}^{\circ };\beta ={30}^{\circ }andg=10m/s^2.$ ___

Answer 1

5
By constrained motion

$acos\beta =bcos\alpha$ $\cdots$ (i)

$mgsin\beta -Ncos\beta =ma$ $\cdots$ (ii)
For wedge:

$Ncos\alpha -mgsin\alpha =mb$ $\cdots$ (iii)
From (i), (ii) and (iii), we get
N = 5 newton