A small child, mass of 9.1 kg sits on the edge of a Merry Go Round. The radius o
ID: 2251219 • Letter: A
Question
A small child, mass of 9.1 kg sits on the edge of a Merry Go Round. The radius of the round platform is 5.5 m. The child has a rubber diaper cover that has a coefficient of friction of o.45. The operator has a heart attack and falls over the control causing the Merry Go Round to start and slowly increase speed. If the speed is 1 rev/min and increasing at a rate of 25% per second at what speed will the child slip off the Merry Go Round?
Calculate the rotational speed in radians /second and revolutions per minute.
Draw a force diagram showing the forces on the child.
Explanation / Answer
mass of child m = 9.1 kg
radius is r = 5.5 m
coefficient of friction is u_k = 0.45
or tanA = 0.45
or A = tan^-1(0.45) = 24.2o = 24.2 x (pi/180) radians
where A is the angle
the angular velocity is w = 1 rev/min = 1 x (2pi/60) rad/s
we know from the relation
w^2 - w_o^2 = 2alpha x A
or alpha = (w^2 - w_o^2/2A)
where w_o = 0 and alpha is angular acceleration
the linear acceleration is
a = r x alpha
the force acting on the child is
F = m x a