Question

A 0.50-kg toy is attached to the end of a 1.0-m very light string. The toy is whirled in a horizontal circular path on a frictionless tabletop. If the maximum tension that the string can withstand without breaking is 350 n. What is the maximum speed the mass can have without breaking the string?

Answer 1

Answer:

26.5 m/s

Explanation:

The tension in the string provides the centripetal force that keeps the toy in circular motion. So we can write:

$T=m\frac{v^2}{r}$

where:

T is the tension in the spring

m = 0.50 kg is the mass of the toy

r = 1.0 m is the radius of the circle (the length of the string)

v is the speed of the toy

The maximum tension in the string is

T = 350 N

If we substitute this value into the equation, we find the maximum speed that the mass can have before the string breaks:

$v=\sqrt{\frac{Tr}{m}}=\sqrt{\frac{(350)(1.0)}{0.50}}=26.5 m/s$