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 o

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

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Amity 4 years 2021-08-22T05:41:27+00:00 1 Answers 15 views 0

Answers ( )

  1. Sapo1
    0
    2021-08-22T05:42:44+00:00
    Reply

    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

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