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andyfeynman
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Homework Statement
A uniform solid sphere of radius R rolls without slipping at velocity V on a level surface. It collides with a step of height h. Assume that after the collision, the sphere maintains contact with the step at point A with no slipping.
Find the minimum value of V for the sphere to be able to rise up to the top of the step, in terms of h, R and g. (Hint: If h = R/5, V = (14gR)1/2/6.)
Homework Equations
L = Iω
The Attempt at a Solution
Let the initial and final angular velocities be ω0 and ωf respectively. Let M be the mass of the sphere. Let I be the moment of inertia about point A.
Angular momentum about point A before collision = Iω0 + MV(R-h)
Angular momentum about point A after collision = Iωf
Conservation of angular momentum: Iω0 + MV(R-h) = Iωf
Conservation of energy after collision: (1/2)Iωf2 = Mgh
Then I used the above equations to solve for V in terms of h, R and g, which is different from the answer. What went wrong?
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