Question

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?

Answer 1

Answer:

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:

$F_c=\frac{mv^2}{R}$

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,

$R=L = 0.61\ m$

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

$F_c=T=7.9\ N$

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

$7.9= \frac{0.170v^2}{0.61}\\\\v^2=\frac{7.9\times 0.61}{0.170}\\\\v^2=28.347\\\\v=\sqrt{28.347}\\\\v=5.32\ m/s$

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