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    Examination of work done by a pulley system

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    Please help with the following problem. Provide step by step calculations.

    An Atwood machine consists of masses of 1.9 Kg and 1.995 Kg hanging from opposite sides of a pulley.

    As the system accelerates 3.3 meters from rest, how much work is done by gravity on the system?
    Assuming no friction or other dissipative forces, use the definition of KE to determine the velocity of the system after having moved through the 3.3 meters, assuming that the system was released from rest.

    © BrainMass Inc. brainmass.com December 24, 2021, 9:36 pm ad1c9bdddf
    https://brainmass.com/physics/system-work/examining-pulley-sytem-395828

    SOLUTION This solution is FREE courtesy of BrainMass!

    Problem: As the system accelerates 3.3 meters from rest, how much work is done by gravity on the system?
    Assuming no friction or other dissipative forces, use the definition of KE to determine the velocity of the system after having moved through the 3.3 meters, assuming that the system was released from rest.

    Solution:
    Given, two masses of m1 = 1.9 kg and m2 = 1.995 kg

    - Net force (F) is

    F = m2*g - m1*g = g(m2 - m1)

    => F = 9.81(1.995 - 1.900) = 9.81 x 0.095 N

    => F = 0.93195 N

    - Work done (W) is given by

    W = F*d {where F is net force and d is the distance traveled}

    => W = 0.93195 x 3.3 = 3.075 J

    - Now KE of the system is given by

    KE = ½*M*v^2

    Where v is the velocity of the system and the total mass is given as M.

    M = m1 + m2 = 1.9 + 1.995 = 3.895 kg

    Thus KE of the system is

    KE = ½*3.895*v^2 = 1.9475*v^2

    Now after 3.3m we can equate the KE of the system to the Work done.

    1.9475*v^2 = 3.075

    => v^2 = 3.075/1.9475 = 1.579 (m/s)^2

    Thus velocity achieved is

    v = Sqrt {1.579} = 1.257 m/s

    Thank you for using Brainmass.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 9:36 pm ad1c9bdddf>
    https://brainmass.com/physics/system-work/examining-pulley-sytem-395828

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