Question

A sling-thrower puts a stone (0.250 kg) in the sling's pouch (0.010 kg) and then begins to make the stone and pouch move in a vertical circle of radius 0.725 m. The cord between the pouch and the person's hand has negligible mass and will break when the tension in the cord is 39.5 N or more. Suppose the sling-thrower could gradually increase the speed of the stone. (a) Will the breaking occur at the lowest point of the circle or at the highest point? (b) At what speed of the stone will that breaking occur?

Answer 1

Answer:

Lowest.

$v=10.5m/s$

Explanation:

The breaking will occur at the lowest point of the circle because in that position the weight acts against the tension, to the tension must be higher for one to get the same centripetal force as when it is at the highest point.

The equations of centripetal force is:

$F_{cp}=ma_{cp}=m\frac{v^2}{r}$

Where we also used the equatio for centripetal acceleration.

We calculate then the speed when the centripetal force is 39.5N, which is when the breaking will occur:

$v=\sqrt{\frac{F_{cp}r}{m}}=\sqrt{\frac{(39.5N)(0.725)}{(0.25Kg+0.01Kg)}}=10.5m/s$