A child\'s merry-go-round in a city park has a radius of 1.7m and a mass of 180

Question

A child's merry-go-round in a city park has a radius of 1.7m and a mass of 180 kg. The merry-go-round is rotating with a period of 2.5 seconds. Four children, each of mass 30 kg, are seated at the edge.

A) The children crawl toward the center of the merry-go-round to where they are all located 60cm from the center. What is the new period? (Assume no friction)

B) What centripetal acceleration did the children feel at the edge of the merry-go-round? What centripetal force did they feel after they moved inward?

C)What is the change in KE between initial and final states? Explain the difference.

D) We know that realistically a spinning merry-go-round loses angular velocity due to friction meaning that the merry-go-round is constantly losing angular momentum. Does this violate the principle of the conservation of angular momentum? Explain.

Explanation / Answer

Here ,

radius , r = 1.7 m

mass of round , m = 180 Kg

time period , T = 2.5 s

A)

let the net period is T

Using conservation of angular momentum

(0.5 *180 * 1.7^2 + 4 * 30 *1.7^2)/2.5 = (0.5 * 180 * 1.7^2 + 4 *30* 0.6^2)/T2

solving for T2

T2 = 1.25 s

the new time period is 1.25 s

B)

at the edge of merry-go-round

centripetal acceleration = (2pi/T)^2 * r

centripetal acceleration = (2pi/2.5)^2 * 1.7

centripetal acceleration = 10.74 m/s^2

centripetal force = mass * centripetal acceleratio

centripetal force = 30 * 10.74

centripetal force = 322.15 N

centripetal force acting on the child on the child at the edge is 322.15 N

c)

change in kinetic energy = -0.5 * (0.5 *180 * 1.7^2 + 4 * 30 *1.7^2) * (2pi/2.5)^2 + 0.5 * (0.5 * 180 * 1.7^2 + 4 *30* 0.6^2) * (2pi/1.25)^2

change in kinetic energy = 1914 J

the change in kinetic energy is 1915 J

d)
No , as the friction will apply an stopping torque on the merry go round.

hence , this does not violate conservation of angular momentum

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.