Answer to Question #101368 in Classical Mechanics for Victoria Winters

Question #101368
A horizontal 781 N merry-go-round of radius 1.75 m is started from rest by a constant
horizontal force of 75 N applied tangentially to the merry-go-round.
Find the kinetic energy of the merry-goround after 3.97 s. The acceleration of gravity
is 9.8 m/s2
Assume the merry-go-round is a solid cylinder.
Answer in units of J.
1
Expert's answer
2020-01-20T05:21:33-0500

I=0.5mr2=0.5Wgr2=0.57819.8(1.75)2=122 kgm2I=0.5mr^2=0.5\frac{W}{g}r^2=0.5\frac{781}{9.8}(1.75)^2=122\ kg\cdot m^2

Iα=Fr122α=(75)(1.75)I\alpha=Fr\to 122\alpha=(75)(1.75)

Angular acceleration:

α=1.08rads2\alpha=1.08\frac{rad}{s^2}

Angular velocity:


ω=αt=1.08(3.97)=4.29rads\omega=\alpha t=1.08(3.97)=4.29\frac{rad}{s}

K=0.5Iω2=0.5(122)(4.29)2=1120 JK=0.5I\omega^2=0.5(122)(4.29)^2=1120\ J


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