- #1
Hamiltonian
- 296
- 190
- Homework Statement
- The figure shows a block A of mass 9m having a smooth semicircular groove of radius R placed on a smooth horizontal surface. A block B of mass m is released from a position in groove where its radius is horizontal. Find the speed of the bigger block when the smaller block reaches its bottom-most position.
- Relevant Equations
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since there is no external force in the x-direction linear momentum can be conserved. Hence I get the equation $$0 = mv^2 - 9mV^2$$
where ##v## is the velocity of B towards the right and ##V## is the velocity of A toward the left.
also the conservation of energy gives $$1/2(9m)V^2 + (1/2)mv^2 = mgR$$
solving these two equations yields ## V = (\frac {gR}{45})^{1/2}## which differs quite a bit from the correct answer. Also, I thought maybe I would have to account for the work done by the normal reaction between B and A but shouldn't they get canceled out is that assumption wrong?