Question

A small object of mass mm slides down a wedge of mass 2 m2 \mathrm{~m} and exits smoothly onto a frictionless table. The wedge is initially at rest on the table. If the object is initially at rest at a height hh above the table, find the velocity of the wedge when the object leaves it.

Solution

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Key Idea:

Let our system be composed of the wedge and the small object. The system is not subjected to a net external force, hence the total momentum of the system is conserved. There is also no non-conservative force exerted on the system, hence the conservation of mechanical energy also applies.

We only know the following:

  • Mass of the small object: mo=mm_o = m
  • Mass of the wedge: mw=2mm_w = 2m
  • Initial height of object: ho,i=hh_{o,i} = h

From these information, we must be able to determine the final velocity of the wedge (vw,f)(v_{w,f}) after the contact with the small object.

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