Consider a father pushing a child on a playground merry-go-round. The system has
ID: 1606720 • Letter: C
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 perpendicular to its 1.50 m radius to achieve a torque of 375 N · m.
(a) Calculate the rotational kinetic energy (in J) in the merry-go-round plus child when they have an angular velocity of 19.0 rpm. _____J
(b) Using energy considerations, find the number of revolutions the father will have to push to achieve this angular velocity starting from rest._____ revolutions
(c) Again, using energy considerations, calculate the force (in N) the father must exert to stop the merry-go-round in four revolutions.______N
Explanation / Answer
(a)
rotational kinetic energy = (1/2)*I*w^2
w = 19 rpm = 19*2*pi/60 = 1.99 rad/s
KEr = (1/2)*84.4*1.99^2 = 167 J
======================
(b)
total work = chamge in KE
Torque*displacement = KE
375*theta = 167
theta = 0.445 rad = 0.07 revolution
===============
(c)
torque = r*F
theta = 4 rev = 4*2*pi = 8pi rad
work = r*F*theta
work = change in KE
1.5*F*8*pi = 167
F = 4.43 N
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.