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A 97.1 kg horizontal circular platform rotates freely with no friction about its center at an initial angular velocity of 1.63 rad/s . A monkey drops a 8.97 kg bunch of bananas vertically onto the platform. They hit the platform at 45 of its radius from the center, adhere to it there, and continue to rotate with it. Then the monkey, with a mass of 22.1 kg , drops vertically to the edge of the platform, grasps it, and continues to rotate with the platform. Find the angular velocity of the platform with its load. Model the platform as a disk of radius 1.73 m .

Sagot :

Nuhulawal20idn

Answer:

the final angular velocity of the platform with its load is 1.0356 rad/s

Explanation:

Given that;

mass of circular platform m = 97.1 kg

Initial angular velocity of platform ω₀ = 1.63 rad/s

mass of banana [tex]m_{b}[/tex] = 8.97 kg

at distance r = 4/5  { radius of platform }

mass of monkey [tex]m_{m}[/tex] = 22.1 kg

at edge = R

R = 1.73 m

now since there is No external Torque

Angular momentum will be conserved, so;

mR²/2 × ω₀ = [ mR²/2 + [tex]m_{b}[/tex] ([tex]\frac{4}{5}[/tex] R)² + [tex]m_{m}[/tex]R² ]w

m/2 × ω₀ = [ m/2 + [tex]m_{b}[/tex] ([tex]\frac{4}{5}[/tex] )² + [tex]m_{m}[/tex] ]w

we substitute

w = 97.1/2 × 1.63 / ( 97.1/2 + 8.97(16/25) + 22.1

w = 48.55 × [ 1.63 / ( 48.55 + 5.7408 + 22.1 )

w = 48.55 × [ 1.63 / ( 76.3908 ) ]

w = 48.55 × 0.02133

w = 1.0356 rad/s

Therefore; the final angular velocity of the platform with its load is 1.0356 rad/s

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