Show all the steps of your calculation. Include units in all measurements, calcu
ID: 1991348 • Letter: S
Question
Show all the steps of your calculation. Include units in all measurements, calculations, and answers. This is a timed exam (2% hours). Do not speed too much time is any particular question. This exam is worth 50 pts total. Conservation of Mechanical Energy This problem describes one experimental method for determining the moment of inertia of an irregularly shaped object. The figure below shows a counterweight of mass m suspended by a cord wound around a spool of radius r, forming part of a turntable supporting the object. The turntable table can rotate without friction. When the counterweight is released from rest, it descends through a distance h, acquiring a speed v. Show that the moment of inertia I of the rotating apparatus (including the turntable) is mr2(2gh/v2 - 1).[Hint: use conservation of the total mechanical energy E of the system (E = K + U)].Explanation / Answer
from conservation of energy initial energy= mgh final energy= U+K =E U=0 K= 0.5mv^2+0.5Iw^2 ,w=v/r =0.5mv^2+0.5Iv^2/r^2=0.5v^2(m+I/r^2) equqting these energies 0.5v^2(m+I/r^2)=mgh m+I/r^2=2mgh/v^2 I/r^2= m(2gh/v^2-1) I=mr^2(2gh/v^2-1) so I =mr^2(2gh/v^2-1) proved