Question

All the surfaces shown in figure are assumed to be fricitionless. The block of mass m slides on prism which in turn slides backward on the horizontal surface. Find the acceleration of the small block with respect to the prism.

Answer 1

$\frac{g (M+m) \sin \theta}{M + m \sin^2 \theta}$

Answer 2

1. Define the accelerations of the block and the prism in the inertial frame and the acceleration of the block relative to the prism. Use the relation $\vec{a}_m = \vec{a}_M + \vec{a}_{rel}$.

2. Apply Newton's second law to the block in the inertial frame by resolving forces along the horizontal and vertical directions.

3. Apply Newton's second law to the prism in the inertial frame by resolving forces along the horizontal and vertical directions.

4. Use the relationship between the normal forces acting between the block and the prism (Newton's third law).

5. Solve the system of equations to find the acceleration of the block relative to the prism.