Please I want someone to answer it clearly and step by step A child of mass 30 k
ID: 1560861 • Letter: P
Question
Please I want someone to answer it clearly and step by step
A child of mass 30 kg runs at a speed of 3.0 m/s tangent to the edge of a playground merry-go-round, which is initially at rest. The child jumps onto the edge of the merry-go-round and then remains at rest relative to it. The merry-go-round has a mass of 150 kg and a radius of 1.5 m, and it may be considered to be a uniform solid disk (I = 1/2 mr^2). (a) Find the angular velocity of the merry-go-round plus child just after the child jumps on. (b) What is the magnitude and direction of the force required to keep the child on the merry-go-round immediately after jumping on? (c) If the combination of merry-go-round plus child comes to a stop in 10 complete revolutions, how long does it take to come to rest assuming constant deceleration?Explanation / Answer
(a)
initial angular momentum Li = m*v*r
final angular momentum Lf = (Idisk + m*r^2)*w
from conservation of angular momentum
Lf = Li
(Idisk + m*r^2)*w = m*v*r
(((1/2)*150*1.5^2) + (30*1.5^2))*w = 30*3*1.5
w = 0.57 rad/s <<<<<-----ANSWER
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(b)
force = m*r*w^2 = 3*1.5*0.57^2 = 1.46 N <<<<<-----ANSWER
direction towards the centr
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(c)
final nagualr velocity wf = 0
theta = (wf+wi)*t/2
theta = angular displacement = 10 rev = 10*2*pi rad
10*2pi = (0.57+0)*t/2
t = 220.5 s <<<<<------answer