Question

An aluminum rod is designed to break when it is under a tension of 600 N. One end of the rod is connected to a motor and a 10-kg spherical object is attached to the other end. When the motor is turned on, the object moves in a horizontal circle with a radius of 6.0 m. If the speed of the motor is continuously increased, at what speed will the rod break

Answer 1

Answer:

v = 18.97 m/s

ω = 3.16 rad/s

Explanation:

During this horizontal circular motion, the centripetal force shall act as the tension force. Therefore, the rod will break when the centripetal force becomes equal to 600 N.

Fc = mv²/r = 600 N

v = √(600 r/m)

where,

m = mass of the spherical object = 10 kg

r = radius of circular path = 6 m

v = tangential speed = ?

Therefore,

v = √[(600 N)(6 m)/(10 kg)]

v = 18.97 m/s

Now, the angular speed of motor is given by:

v = rω

ω = v/r

where,

ω = angular speed of motor = ?

Therefore,

ω = (18.97 m/s)/6 m

ω = 3.16 rad/s