Acceleration with constraint

Classical Mechanics Level 5

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

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

If the acceleration of the smaller block with respect to the bigger block, as soon as the system is released, is \(a\), enter the value of \(3a\).

Details and Assumptions:

  • \(m= \dfrac{1}{3} \text{ kg}\)

  • \(M= \dfrac{1}{2} \text{ kg}\)

  • \( \theta = 45^\circ\)

  • \(g=10 \text{ ms}^{-2} \)


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