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Jesse2789
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Homework Statement
Find the mass, M, of a rotating wheel of radius r that has an attached mass, m, suspended by a string using conservation of energy. The mass is suspended a height, h, above the ground and it takes a time of t seconds to reach the ground.
Homework Equations
[tex] U_g,mass = K_f,mass + K_f,wheel [/tex]
[tex] mgh = 1/2(m_b)(v_f)^2 + 1/2(Iω_f^2) [/tex] (m_b is the hanging block's mass)
[tex] I_(disk) = 1/2(Mr^2) [/tex]
The Attempt at a Solution
[tex] a_y,block = (-2h)/(t^2) [/tex]
[tex] v_f,y,block = (a_y,block)*t [/tex]
^At this point the only two unknowns in the conservation equation are I and ω. To find ω_f could I just say that v_f,y,block is the same as the final tangential velocity of the wheel?
So then it would just be [tex] ω_f=v_t/r [/tex], then you could find M through [tex] I=Mr^2 [/tex]?
EDIT: I just tried this with numbers and came out to an unreasonably high mass of 1879kg. I did this in lab and could lift the wheel, so obviously there's an error somewhere in my reasoning.
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