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23 August, 11:53

The weights in atwoods machine, starting at rest, attain a velocity of 2ft/sec in one sec. Find the ratio of the masses

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  1. 23 August, 12:17
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    Refer to the figure shown below.

    Let m₁ and m₂ e the two masses.

    Let a = the acceleration.

    Let T = tension over the frictionless pulley.

    Write the equations of motion.

    m₂g - T = m₂a (1)

    T - m₁g = m₁a (2)

    Add equations (1) and (2).

    m₂g - T + T - m₁g = (m₁ + m₂) a

    (m₂ - m₁) g = (m₁ + m₂) a

    Divide through by m₁.

    (m₂/m₁ - 1) g = (1 + m₂/m₁) a

    Define r = m₂/m₁ as the ratio of the two masses. Then

    (r - 1) g = (1 + r) a

    r (g-a) = a + g

    r = (g - a) / (g + a)

    With = 2 ft/s from rest, the acceleration is

    a = 2/32.2 = 0.062 ft/s²

    Therefore

    r = (32.2 - 0.062) / (32.2 + 0.062) = 0.9962

    Answer:

    The ratio of masses is 0.9962 (heavier mass divided by the lighter mass).
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