On the International Space Station an object with mass m = 170 g is attached to a massless string L = 0.61 m. The string can handle a tension of T = 7.9 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?

The maximum speed with which the mass can rotate before breaking is 5.32 m/s.

Explanation:

Given:

Maximum tension in the string (T) = 7.9 N

Length of the string (L) = 0.61 m

Mass of the object (m) = 170 g = 0.170 kg

Object is under uniform circular motion.

Maximum speed the mass can rotate is 'v'.

Now, we know that, for a uniform circular motion, the force required for moving in a circular path is called centripetal force and is given by the formula:

Where, 'R' represents the radius of the circular path.

Here, the object rotates in a circle around the string of length 'L'. So, the radius of the circle is equal to the length of the string. Therefore,

Also, the centripetal force is provided by the tension in the string. So,

Now, substitute the values given and solve for 'v'. This gives,

Therefore, the maximum speed with which the mass can rotate before breaking is 5.32 m/s.