Question

A circular disc with a groove along its diameter is placed horizontally. A block of mass $1 \,kg$ is placed as shown. The coefficient of friction between the block and all surfaces of groove in contact is $\mu = 2/5$. The disc has an acceleration of $25 \,m/s^2$ Find the acceleration of the block with respect to disc. _____ $m/s^2$

Answer 1

Normal reaction in vertical direction $N_1 = mg $
Normal reaction from side to the groove $N_2=ma\, \sin\, 37^\circ$
Therefore, acceleration of block with respect to disc
$a_r=\frac{ma\, \cos 37^{\circ} = \mu N_1- \mu N_2}{m}$
Substituting the values we get, $a^r=10 \,m/s^2$