Question

A park merry-go-round consists of a 255 kg circular wooden platform 4.10 m in diameter.?

Four children running alongside push tangentially along the platform's circumference until, starting from rest, the merry-go-round reaches a steady speed of one complete revolution every 2.8 s.
(a) If each child exerts a force of 26 N, how far does each child run?
(b) What is the angular acceleration of the merry-go-round?
(c) How much work does each child do?
(d) What is the kinetic energy of the merry-go-round?

Answer 1

Answer: a) 12.9 m b) 0.40 rad/s² c) 335.4 J d) 1349.06 J

Step-by-step explanation:

a)

Distance traveled= R∅

where ∅=
`((2\pi )^2 )/((2.8)^2)` / 2*α

To find α we have

Sum of torque= Iα

F x r x number of children = m*r²/2 * α

26 x
`(4.1)/(2)` * 4 = (255) * (4.10/2)² /2 *α

Solving we get,

α=
`(213.2)/(535.82)`

α= 0.40

So,

∅=
`((2\pi )^2 )/((2.8)^2)` / 2*α

Becomes

∅= 6.29

Now,

Distance traveled= 4.1/2 * 6.29

Distance traveled= 12.9 m

b)

Angular acceleration= 0.40

c)

Work done= F x distance traveled

Work done= 26 x 12.9

Work done= 335.4 J

d)

Kinetic energy=
`(1)/(2)* I * ((2\pi )/(2.8))^2`

Putting values we get,

Kinetic energy= 267.91 * 5.03

Kinetic energy= 1349.06 J