A ball is attached to a horizontal cord ...

A ball is attached to a horizontal cord of length `l` whose other end is fixed. (a) If the ball is released, what will be its speed at the lowest point of its path? (b) A peg is located a distance `h` directly below the point of attachment of the cord. If `h=0.75l`, what will be the speed of the ball when it reaches the top of its circular path about the peg?

Text Solution

Verified by Experts

Apply conservation of energy between A and B.
`1/2mv_1^2=mgLimpliesv_1=sqrt(2gL)`

We see that `v_1gtsqrt(5g(0.25L))`
So the ball will complete the circular motion about peg.
Apply conservation of energy between A and C:
`1/2mv_2^2=mg(0.5L)impliesv_2=sqrt(gl)`

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