Acceleration With Constraint

A block of mass mm can slide freely in a slot made in a bigger block of mass M,M, as shown in the diagram above. There is no friction anywhere in the system.

The block mm is connected to one end of a string whose other end is fixed at point PP. The system is released from rest when the string at PP makes an angle θ \theta with horizontal.

What is the acceleration of the smaller block with respect to the bigger block, as soon as the system is released?

Details and Assumptions:

  • m=13 kgm= \dfrac{1}{3} \text{ kg}
  • M=12 kgM= \dfrac{1}{2} \text{ kg}
  • θ=45 \theta = 45^\circ
  • g=10 ms2g=10 \text{ ms}^{-2}

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