- #1
onelove8187
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Homework Statement
The problem is I need to estimate the mass of a (solid equally distributed mass) disc which has an axle on which a string is tied and then attached to a (hanging) 1.022 kg mass. We wound the wheel up moving the hanging mass to a height of 0.64 m off the ground. At this point we recorded the time it would take for the mass to fall to the floor (spinning the wheel in the process). for this first run we have an average time t=10.42s. We did this several times varying the height off the floor of the hanging mass. We also ran several tests varying the mass. I have spent probably ten hours banging my head against a wall, I do not know what mistake I am making. This is what I tried to solve for the mass of the wheel in the first run:
E_pot=E_k+E_rot
E_pot=mgy
E_k(at bottom)=.5mv^2
E_rot=.5Iω^2 where I=.5MR^2 and ω=v/R
where m=known mass and M=mass of wheel
Combining all this I got:
mgy=.5mv^2+.5(.5MR^2)(v/R)^2
simplifying to
M=4m(gy-.5v^2)/v^2
for the first fun it gives≈1600kg as the answer which can't be right!
I also tried to solve this from a torque perspective and got the same answer!
possible other relevant equations:
angular acceleration=torque_net/Moment of Inertia
a_y=angular acceleration
Torque=Tension*d (where d=R in this case)
More than anything I want to see where my error in logic is here so I can better understand the material. Any help will be greatly appreciated. Thank you!