Answer:
The kinetic energy of the merry-go-round is 632.82 J
Explanation:
Given;
weight of the merry-go-round, W = 649 N
radius of the merry-go-round, r = 1.05 m
applied horizontal force, F = 61.3 N
acceleration due to gravity, g = 9.8 m/s²
mass of merry-go-round, m = W/g
= 649/9.8 = 66.225 kg
moment of inertia of merry-go-round, I = ¹/₂mr²
= ¹/₂ x 66.225 x (1.05)²
= 36.507 kg.m²
Angular acceleration of the merry-go-round, α
τ = Iα = Fr
α = Fr / I
Where;
α is angular acceleration
α = (61.3 x 1.05) / 36.507
α = 1.763 rad/s²
Angular velocity of the merry-go-round, ω
ω = αt
ω = 1.763 x 3.34
ω = 5.888 rad/s
Finally, the kinetic energy of the merry-go-round, K.E
K.E = ¹/₂Iω²
K.E = ¹/₂ x 36.507 x (5.888)²
K.E = 632.82 J
