Circle motion. Or...

Classical Mechanics Level 2

A little block with mass m rest on a frictionless horizontal table, at a distance r from a hole in the center of the table and is tied by an unelastic cord. The cord is tied by the other edge to another block with mass M . A constant circle motion is given to the little block with a radius r and speed v . Wich v is needed for the big block to stay still once you don't hold it?

v r m \sqrt{\frac{vr}{m}} F r M \sqrt{\frac{Fr}{M}} F r v 3 \sqrt[3]{\frac{Fr}{v}} F r m \sqrt{\frac{Fr}{m}}

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1 solution

Since we have an unelastic cord we know that the centripetal acceleration is equal to gravity acceleration, so a c = g = v 2 r a_c=g=\frac{v^{2}}{r} Then we have a force F that is given by the big block mass and g , and that force pulls the little block, and have g M = F gM=F a c = v 2 r = F M a_c=\frac{v^{2}}{r}=\frac{F}{M} And finally v = F r m v=\sqrt{\frac{Fr}{m}}

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