- #1
Kaoi
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Homework Statement
Problem:
"A cylindrical 4.91 pulley with a radius of 0.338 m is used to lower a 3.80 kg bucket into a well. The bucket starts from rest and falls for 4.06 s. The acceleration of gravity is 9.81 m/s². What is the linear acceleration of the falling bucket? Answer in units of m/s²."
Givens:
[tex]
\\ m_{p}=4.91 kg\\
\\ r=0.338 m\\
\\ m_{p}=3.80 kg\\
\\ v_{i}=0 m/s\\
\\ \Delta t=4.06 s\\
[/tex]
Unknown:
[tex]
\\ a_{t}=?
[/tex]
Homework Equations
[tex]
\\ a_{t} = r\alpha\\
\\ \Tau\=\I\alpha = Fd sin \theta\\
\\ I_{cylinder}\=\frac{1}{2} r^2\\
[/tex]
The Attempt at a Solution
[tex]
\\ \tau = F_{g}r = I\alpha\\
\\ m_{b}gr = \frac{1}{2}mr^2\alpha\\
\\ \alpha = \frac{2m_{b}g}{m_{p}r}\\
\\ a_{t} = \frac{2m_{b}g}{m_{p}\\
[/tex]
Now, I thought that was a perfectly logical way to get the answer, but when I submitted it, the answer was wrong. Can anyone tell me what I'm doing wrong here?
Edit: And I seem to be having difficulties putting breaks into my TeX, heh.
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