What's the shortest length?

Question

A certain cord will break if its tension exceeds 360 N. Suppose the cord is attached to a 0.40 kg ball. If the ball is to be swung with a speed of 25 m/s, what's the shortest length of cord that can be used?

Answer 1

Sun, just as in the cornering problem this is a rotational acceleration and force problem. 

 

F= m v²/r, but this time we want to solve for r given a mass, velocity and maximum force.

 

rearranging the equation:

 

r= mv²/F , given the values in the problem

 

r_min= (.4)(25²)/360 = .6944 meters

Answer 2

T = mv^2/r

Plug in the maximum tension force to get the shortest length of the cord.

360 = 0.40(25^2)/r

Solve for r,

r = 25/36 = .69 m <==Answer