Question

On the International Space Station an object with mass m = 280 g is attached to a massless string L = 0.97 m. The string can handle a tension of T = 7.7 N before breaking. The object undergoes uniform circular motion, being spun around by the string horizontally. What is the maximum speed v the mass can have before the string breaks? Give your answer in units of m/s.

Answer 1

Answer:

5.16 m/s

Explanation:

The tension in the string provides the centripetal force that keeps the object spinning in circular motion, therefore we can write:

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

where

T is the tension

m is the mass of the object

v is the speed

r is the radius of the circle

Here we have:

m = 280 g = 0.280 kg

r = L = 0.97 m (the radius of the circle is the length of the string)

The maximum tension allowed is

T = 7.7 N

Therefore, by solving for v, we find the maximum speed allowed before the string breaks:

$v=\sqrt{\frac{Tr}{m}}=\sqrt{\frac{(7.7)(0.97)}{.280}}=5.16 m/s$