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1 answer:
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Answer:
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
