Question

A stone with a mass of 0.70 kg is attached to one end of a string 0.80 m long. The string will break if its tension exceeds 65.0 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

Answer:

The maximum speed the stone can attain without breaking the string is 8.62 m/s .

Explanation:

Given :

Mass of stone , m = 0.7 kg .

Length of string , l = 0.8 m .

It is also given that the stone will break if its tension exceeds 65.0 N.

Now , we know tension in the rope due to rotation is equal to the centripetal acceleration .

Therefore , the maximum speed the stone can attain without breaking the string is less than or equal to 65 N .

So , $\dfrac{mv^2}{r}=65$

Putting all value in above equation we get :

$\dfrac{0.7\times v^2}{0.8}=65\\\\v= 8.62\ m/s$

Therefore , maximum speed the stone can attain without breaking the string is 8.62 m/s .