Kinetic & Potential Energy / Momentum Problem

AI Thread Summary
The problem involves a small cube of mass m sliding down a circular path on a larger block of mass M, both starting from rest. The initial potential energy of the cube converts to kinetic energy as it descends, leading to the equation v=√(2gR) just before it leaves the block. However, the discussion highlights the need to account for the kinetic energy of the larger block M, which complicates the momentum conservation calculations. The user expresses difficulty in solving the algebraic equations for the velocity of m and questions whether they overlooked any factors. The conversation emphasizes the importance of considering both blocks' kinetic energies in the final solution.
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Homework Statement


From Kleppner and Kolenkow:
A small cube of mass m slides down a circular path of radius R cut into a large block of mass M, as shown. M rests on a table, and both blocks move without friction. The blocks are initially at rest, and m starts from the top of the path.
Find the velocity v of the cube as it leaves the block.

Ans. clue. If m=M, v=√(gR)

http://img390.imageshack.us/img390/5575/blocksbi2.jpg

Homework Equations


KE=(1/2)mv2
PE=mgh
mivi=mfvf
KEi=KEf


The Attempt at a Solution


For m, initial energy PEm=mgR
Just before m leaves block M, KEm=(1/2)mv2=mgR
Thus, v=√(2gR).
From here, I set up equations for conservation of momentum as well as kinetic energy.
I then used substitution and tried to solve for the velocity of m as it leaves the block, M, but the algebra just isn't working out. Did I make a mistake?
 
Last edited by a moderator:
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Do not ignore the KE of the large block. ehild
 
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