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21 January, 07:33

Two objects (38.0 and 17.0 kg) are connected by a massless string that passes over a massless, frictionless pulley. The pulley hangs from the ceiling. Find (a) the acceleration of the objects and (b) the tension in the string.

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  1. 21 January, 07:53
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    a) 3.7 m/s^2

    b) 231.8 N

    Explanation:

    Let m1 be mass of the first object (m1 = 38.0 kg) and let m2 be the mass of the second object (m2 = 17.0 kg). Let a be the acceleration of the two objects. Let F1 be the force of gravity exerted on m1 and F2 be the force of gravity exerted on m2. Let M = m1 + m2

    a)

    F1 = m1g and F2 = m2g

    So Fnet = F1 + F2

    Since the pulleys will move in different directions when accelerating ...

    Fnet = F1 - F2

    M*a = m1g - mg2

    M*a = g * (m1 - m2)

    a = g * (m1 - m2) / M

    a = 9.8 * (38 - 17) / (38 + 17)

    a = 3.7 m/s^2

    b)

    Looking at the part for m2

    Fnet = T - m2g

    -m2*a = T - m2g

    T = m2 (g - a)

    T = 231.8 N
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