thank you for your help! A student tics a mass 925 g to the end of a 0.65 m long

Question

thank you for your help!

A student tics a mass 925 g to the end of a 0.65 m long string and then swings it in a circle around his head (the mass rotates in a horizontal plane). The largest tension that the string can sustain before breaking is 17.8 N. What is the highest speed the mass can achieve before the string breaks? Suppose the student from the previous question uses the same string and mass, but this time instead of swinging the mass in a circle around his head, he extends his hand in front of him and rotates the mass in a vertical plane. What is the highest speed the mass can achieve before the string breaks?

Explanation / Answer

m = 0.925 kg, r = 0.65 m, T = 17.8 N, find v
T = mv2/r
so v = (Tr/m) = 3.54 m/s

motion in a vertical plane:

at the highest point: T + mg = mv2/r, T = m(v2/r - g) 0, so v (gr) = 2.52 m/s

The largest tension happens at the lowest position.

T - mg = mv2/r

v = [(T - mg)r/m] = 2.48 m/s < 2.52 m/s

so it is impossible to move it in a vertical plane if tension is not more than 17.8 N

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