Question

"A 0.4 kg mass, attached to the end of a 0.75 m string, is whirled around in a circular horizontal path. If the maximum tension that the string can withstand is 450 N, then what maximum velocity can the mass have if the string is not to break?"

Answer 1

Explanation:

Below is an attachment containing the solution.

Answer 2

Answer:

The maximum velocity the mass can have if the string is not to break = 29.05 m/s

Explanation:

The force balance in the mass:

The tension in the string must always be equal to the force keeping the mass in horizontal circular motion.

The force keeping the mass in circular motion is given by

F = mv²/r

m = mass of body = 0.4 kg

v = speed of the body in circular motion

r = radius of the circular motion = 0.75 m

Maximum tension the string can withstand will correspond to the maximum velocity of the body in horizontal circular motion

T = F = mv²/r

450 = (0.4)(v²)/(0.75)

v² = 450×0.75/0.4 = 843.75

v = 29.05 m/s