Question

An old hunting weapon was a rock on the end of a string. The hunter would swing the rock in horzontal circles and then throw it. If the rock had a mass of 2.0kg and the 2.0m long string breaks when the tension is 60N, what is the fastest the hunter can swing his rock without breaking the string? (For this question take into account that the string will "droop" because of gravity. Include a diagram of the situation and a free body diagram of the forces).

Answer 1

The string would break when the rock is at the bottom because the force of gravity would be acting against the string and not in the same direction as it would be at the top. So if the free body diagram is drawn with the tension vector pointing up and the gravity vector pointing down then the summation of forces is:
\[T - mg = (mv^{2}/r)\]
where T is tension mg is the force of gravity, m is mass, v is tangential veloctiy and r is radius.

Set T=60 and put in the rest of the numbers and solve for v.