Ask Question
15 February, 14:45

A rope of negligible mass passes over a uniform cylindrical pulley of 1.50 kg mass and 0.090 m radius. The bearings of the pulley have negligible friction, and the rope does not slip on the pulley. On one end of the rope hangs a 3.00 kg bunch of bananas, and on the other end hangs a 4.50 kg monkey. Calculate the downward acceleration of the monkey and the tension in both ends of the rope.

+5
Answers (1)
  1. 15 February, 14:50
    0
    1.8 m/s²

    36 N

    34.8 N

    Explanation:

    For the monkey:

    m₁ = mass of monkey = 4.50 kg

    T₁ = Tension force in the rope on monkey's side

    a = acceleration

    From the force diagram, force equation for the motion of monkey is given as

    m₁ g - T₁ = m₁ a

    (4.50 x 9.8) - T₁ = 4.5 a

    T₁ = 44.1 - 4.5 a eq-1

    For the bunch of bananas:

    m₂ = mass of bunch of bananas = 3 kg

    T₂ = tension force in the rope on the side of banana

    From the force diagram, force equation for the motion of bananas is given as

    T₂ - m₂ g = m₂ a

    T₂ - (3 x 9.8) = 3 a

    T₂ = 29.4 + 3 a eq-2

    m = mass of the pulley = 1.50 kg

    r = radius of the pulley = 0.090 m

    α = angular acceleration of pulley = a/r

    Torque equation for the pulley is given as

    (T₁ - T₂) r = I α

    (T₁ - T₂) r = I (a/r)

    T₁ - T₂ = (0.5 m r²) (a/r²)

    T₁ - T₂ = (0.5) ma

    using eq-1 and eq-2

    44.1 - 4.5 a - (29.4 + 3 a) = (0.5) ma

    44.1 - 4.5 a - (29.4 + 3 a) = (0.5) (1.50) a

    a = 1.8 m/s²

    Using eq-1

    T₁ = 44.1 - 4.5 a

    T₁ = 44.1 - 4.5 (1.8)

    T₁ = 36 N

    using eq-2

    T₂ = 29.4 + 3 a

    T₂ = 29.4 + 3 (1.8)

    T₂ = 34.8 N
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “A rope of negligible mass passes over a uniform cylindrical pulley of 1.50 kg mass and 0.090 m radius. The bearings of the pulley have ...” in 📙 Physics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers