Question

A stone with a mass of 0.600 kg is attached to one end of a string 0.600 m long. The string will break if its tension exceeds 55.0 N. The stone is whirled in a horizontal circle on a frictionless tabletop; the other end of the string remains fixed.Find the maximum speed the stone can attain without breaking the string.

Answer 1

The maximum speed the stone can attain without breaking the string is 7.416 m/s

Step-by-step explanation:

Given;

mass of the stone, m = 0.600 kg

length of string, L = 0.600 m

maximum tension on the string, T = 55.0 N

Total force acting on the stone in horizontal direction is given as;

∑
`F_x =T =(mv^2)/(r)`

This force corresponds to maximum tension on the string;

`T_(max) =m(v_(max)^2)/(r)`

where;

m is the mass of the stone

`v_(max)` is the maximum speed the stone can attain without breaking the string, which corresponds to maximum tension on the string.

r is radius of the circular path of the string

`v_(max)^2 = (Tr)/(m) \\\\v_(max) = \sqrt{(Tr)/(m)} \\\\v_(max) = \sqrt{(55*0.6)/(0.6)} = 7.416 \ m/s`

The maximum speed the stone can attain without breaking the string is 7.416 m/s