A block of mass m slides on a smooth prism of mass M and inclination α. The prism is free to move on a smooth horizontal floor. The acceleration of the block relative to the prism down the incline is:

Question

G1 Physics · Accepted Answer

Let prism acceleration be a₀. From the prism FBD, a₀=mg sinα cosα/(M+m sin²α). The block's relative acceleration is a=a₀cosα+g sinα=(M+m)g sinα/(M+m sin²α).