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
Question
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