Question

In the given figure all surface are smooth. Find acceleration of block A with respect to wedge. If acceleration of wedge with respect to ground is :

(i) $a=5m/s^2$
(ii) $a=10m/s^2$
(iii) $a=7.5m/s^2$

Answer 1

F.B.D for block A with respect to Wedge having acceleration $=a$

pseudo force on mass A $=ma$

$\frac{mg\sin 37-am\cos 37}{m}=a^{\prime }$

$\frac{m(g\sin 37-a\cos 37)}{m}=a^{\prime }$

$\therefore a^{\prime }=g\sin 37-a\cos 37$

As, $\sin {37}^{\circ }=\frac{3}{5}\&\cos {37}^{\circ }=\frac{4}{5}$

a) $a_1=10\left(\frac{3}{5}\right)-5\left(\frac{4}{5}\right)=6-4=2m/s^2$ down the inclination.

b) $a_2=10\left(\frac{3}{5}\right)-10\left(\frac{4}{5}\right)=6-8=-2m/s^2$ up the inclination.

c) $a_3=10\left(\frac{3}{5}\right)-7.5\left(\frac{4}{5}\right)=6-6=0m/s^2$ remains at rest.