A sphere of mass of 1.55 kg is accelerated upwards by a string to which the sphere is attached. Its speed increases from 2.81 m/s to 4.60 m/

Question

A sphere of mass of 1.55 kg is accelerated upwards by a string to which the sphere is attached. Its speed increases from 2.81 m/s to 4.60 m/s in a time of 2.64 s. Calculate the tension in the string, assuming that the tension remains constant during that time.

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Thiên Thanh 2 months 2021-07-23T04:38:43+00:00 1 Answers 4 views 0

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    2021-07-23T04:39:54+00:00

    Answer:

    The tension in the string is 16.24 N

    Explanation:

    Given;

    mass of the sphere, m = 1.55 kg

    initial velocity of the sphere, u = 2.81 m/s

    final velocity of the sphere, v = 4.60 m/s

    duration of change in the velocity, Δt = 2.64 s

    The tension of the string is calculated as follows;

    T =  ma  + mg\\\\T = m(a + g)\\\\where;\\\\a \ is \ upward \ acceleration \ of \ the \ sphere\\\\g \ is \ acceleration \ due \ to \ gravity =9.8 \ m/s^2\\\\a = \frac{\Delta V}{\Delta t} = \frac{v- u}{ t} = \frac{4.6 - 2.81 }{2.64} = 0.678 \ m/s^2

    T = 1.55(0.678 + 9.8)

    T = 1.55(10.478)

    T = 16.24 N

    Therefore, the tension in the string is 16.24 N

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