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mathmannn
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Homework Statement
A sphere rolling with an initial velocity of 30 ft/s starts up a plane inclined at an angle of 30o with the horizontal as shown. How far will it roll up the plane before it rolls back down?
Homework Equations
[itex] T_1+V_1=T_2+V_2 [/itex]
The Attempt at a Solution
We are doing rigid bodies so I started with
[itex] T_1+V_1=T_2+V_2 [/itex] Where [itex]V_1=T_2=0[/itex] So I have
[itex] T_1=V_2 [/itex]
[itex].5 m v^2 = m g h [/itex]
[itex] h=x\sin(30) [/itex]
Which gives me [itex] .5(30)^2 = (32.2)(x \sin(30)) [/itex]
[itex] x=27.95 [/itex]
And that is not one of the answers, I assume inertia is supposed to be used somewhere but I have no idea where to plug it in because no radius of the circle is give.. Any help would be very much appreciated\
EDIT:
I tried using Inertia like this:
[itex] T_1 = V_2 [/itex]
[itex] T_1 = .5 I \omega^2 + .5mv^2 \quad, \qquad \omega = v/r [/itex]
[itex] I=.5 m r^2 [/itex]
[itex] T_1 = .5((.5 m r^2)(\frac{v}{r})^2) + .5 m v^2 [/itex]
[itex] T_1 = \frac{1}{4} m v^2 + \frac{1}{2} m v^2 = \frac{3}{4}mv^2 [/itex]
[itex] \frac{3}{4}mv^2 = m g x \sin(30) [/itex]
[itex] x = \frac{3v^2}{4 g \sin(30)} \qquad, x=41.9255 [/itex]
Still not an answer but closer than I was.. Any suggestions?
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