- #1
FaiKT
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Homework Statement
A solid sphere starts from rest at the upper end of the track, as shown in figure below, and rolls without slipping until it rolls off the right-hand end. If H = 12.0 m and h = 2.0 m and the track is horizontal at the right-hand end, how far horizontally from point A does the sphere land on the floor?
Homework Equations
mgH = 1/2 I w^2 + mgh
y = vot + 1/2gt^2
The Attempt at a Solution
I'm not exactly sure how i went wrong here.
the moment of inertia for a solid sphere is 2/5 mr^2 and w^2 = v^2/r^2 so the radius cancels out...after cancelling out the mass as well i come out with
gH = 1/5 v^2 + gh which becomes sqrt(5(gH-gh)) = 22.136 m/s
Since it starts at rest... you use the equation 2 = -4.9t^2 to get a time of 0.639s
Since its asking for horizontal distance i multiplied the velocity by time to get 14.145m, but that's wrong somehow...is there something I'm missing?