Consider a father pushing a child on a playground merry-go-round. The system has

Question

Consider a father pushing a child on a playground merry-go-round. The system has a moment of inertia of 84.4 kg m2. The father exerts a force on the merry go-round perpendicufar to its 1.50 m radius to achieve a torque of 375 N·m. (a) Calculate the rotational kinetic energy (in ) in the merry- go-round plus child when they have an angular velocity of 28.6 rpm energy considerations, find the number of revolutions the father will have to push to achieve this angutar velocity starting from rest. revolutions Again, using energy considerations, calculate the force (in N) the father must exert to stop the merry go-round in three (c) Additional Materials Reading

Explanation / Answer

Given Data,

Moment of Inertia, I = 84.4 Kg.m^2

radius, r = 1.5 m

Torque, T = 375 N-m

Solution: -

T = I*

= T / I

= 375 / 84.4

= 4.44

a) K.E rotational = 0.5*I*^2

Here = 28.6*(2 / 60)

= 2.995 rad/s

K.E = 0.5*84.4*2.995^2

K.E = 378.53 J

b) Number of revoltuions :-

= T *

= / T

= K.E / T

= 378.53 / 375

= 1.01 radians

Radians to REV is 1.01 * (1 rev / 2 rad)

                           = 0.16 rev

c) Force in 3 revolutions is

W = r*

= r*F*

Here 3 rev = 3*(2) rad = 6 rad

F = W / r*

= 378.53 / 1.5* (6)

= 13.4 N

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