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Homework Statement
A hollow cylindrical shell with mass M = 100 g and radius R = 5 cm rolls without
slipping down an inclined plane making an angle [tex]\alpha = 30[/tex]° with the horizontal.
(a) If the initial speed of the shell is zero, what will be the speed of its center of
(c) Calculate the linear acceleration of the center of mass of the shell. How long
does it take the shell to roll 1:5 meters along the plane with zero initial velocity?
(d) If the shell is replaced with a solid cylinder what will be the answer to the
previous question?
Homework Equations
[tex] I =\frac{2}{3}MR^{2} [/tex]
[tex] K = \frac{1}{2}Mv^{2} + \frac{1}{2}I\omega^{2} [/tex]
[tex] \omega = \frac{v}{r} [/tex]
The Attempt at a Solution
(a)
[tex] mgh = \frac{1}{2}Mv^{2} + \frac{1}{2}I\omega^{2} [/tex]
[tex] gh = \frac{1}{2}v^{2} + \frac{1}{3}R^{2}\omega^{2} [/tex]
[tex] gh = \frac{1}{2}v^{2} + \frac{1}{3}R^{2}\frac{v^{2}}{R^{2}} [/tex]
[tex] gh = v^{2}(\frac{1}{2}+\frac{1}{3})[/tex]
[tex] v = \sqrt{\frac{6gh}{5}} [/tex]
(b)
[tex] \sum F_{x} = ma = mgsin(\alpha)[/tex]
[tex]a = gsin(\alpha)[/tex]
(d)
According to my equation it shouldn't change anything...
I don't think b/c are correct though
Thanks for any help.