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23 October, 15:33

An Atwood machine is constructed using two wheels (with the masses concentrated at the rims). The left wheel has a mass of 2.4 kg and radius 24.26 cm. The right wheel has a mass of 2 kg and radius 33.62 cm. The hanging mass on the left is 1.62 kg and on the right 1.09 kg. m3 m1 m4 m2 What is the acceleration of the system

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  1. 23 October, 15:55
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    The acceleration of the system is 0.7305 m/s²

    Explanation:

    Given that:

    m₁ = 2.4 kg, m₂ = 2 kg, m₃ = 1.62 kg, m₄ = 1.09 kg

    Torque (τ) = mra

    For left pulley:

    T₁r₁ - T₂r₁ = m₁r₁a

    Dividing through by r₁

    T₁ - T₂ = m₁a ... 1)

    For right pulley:

    T₂r₂ - T₃r₂ = m₂r₂a

    Dividing through by r₂

    T₂ - T₃ = m₂a ... 2)

    Also

    m₃g - T₁ = m₃a ... 3)

    T₃ - m₄g = m₄a ... 4)

    adding equations 1, 2, 3 and 4 to get:

    (m₁ + m₂ + m₃ + m₄) a = (m₃ - m₄) g

    (2.4 + 2 + 1.62 + 1.09) a = (1.62 - 1.09) 9.8

    7.11a = 5.194

    a = 5.194 / 7.11 = 0.7305

    a = 0.7305 m/s²

    The acceleration of the system is 0.7305 m/s²
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