Question

# Initially, the monkey is standing on the floor and the bananas are hanging above his head...

Initially, the monkey is standing on the floor and the bananas are hanging above his head near the pulley. The monkey’s mass is 2 kg and the mass of the bananas is 4 kg. The pull is 12 cm in diameter and has a mass of 2.0 kg. As the pulley turns, friction at the axle exerts a constant torque of magnitude 0.50 N. If the bananas and the monkey are released from rest with the bananas 1.0 m off the floor, how long does it take the bananas to reach the ground?

Newton's second law : F = ma. and Tr = I

Linear for bananas

T1 - 4g = -4a
T1 + 4a = 40 ...i

Linear for monkey

T2-2g = 2a
T2-2a = 20 ..... ii

Angular for pulley

T1 - T2 -Tf = I

T1x0.06 - T2x0.06 - 0.5 = (2 x 0.06^2 / 2) x

0.06T1 - 0.06T2 -0.0036 = 0.5

but = a/r = a/0.06

0.06T1 - 0.06T2 - 0.06a = 0.5 .... iii

solving 3 eqns

T1 = 33.33N

T2 = 23.33N

a = 1.67 m/s^2

using second kinematical equations

s = 1/2 a t^2

t^2 = 2s/a = 2x1/1.67 = 1.2

t = 1.09 s

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