A girl of 111 lbs (50.5 kg) stands on one end of a 4.00 m horizontal beam suppor

Question

A girl of 111 lbs (50.5 kg) stands on one end of a 4.00 m horizontal beam supported by a fulcrum at DI = 1.00 m. Find the magnitude of the maximum weight (F1) that the girl's weight (F3) can lift, and the force (F2) exerted on the beam by the fulcrum when this max weight is in place as shown (answer in units of Newtons or pounds ...). A merry-go-round full of kids initially has Inertia=5.33 kg m2 while maintaining an angular speed to omegai = 2.55 rad/s. Some kids move closer to the center of the merry-go-round increasing its speed to = 3.00 rad/s. (a) What's the final inertia Ij?. (b) How do the final and initial kinetic energies compare: Kf > Ki, Kf

Explanation / Answer

net torque about the fulcrum = 0

F1 will produce counter clok wise

F3 will produce clock wise

F1*D1 - F3*D2 = 0

F1 = F3*D2/D1

F1 = (50.5*9.8*3)/1 = 1484.7 N <----answer

###

along vertical Fnet = 0

F1 + F3 = F2

F2 = 1484.7+(50.5*9.8) = 1979.6 N <----answer

++++++++++++++++++++++++++

initial moment of inertia I1 = 5.33 kg m^2

initial angular speed w1 = 2.55

final angular speed = w2 = 3 rad/s

final MoI = I2 = ?

from conseevation of angular momentum Lf = Li

I2*w2 = I1*w1

I2 = I1*w1/w2

I2 = (5.33*2.55)/3 = 4.5305 kg m^2   <------answer

part b)

Ki = 0.5*I1*w1^2 = 0.5*5.33*2.55*2.55 = 17.3291625 J

Kf = 0.5*I2*w2^2 = 0.5*4.5305*3*3 = 20.38725 J

Kf > Ki

it come from the kids .

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