A hollow sphere of radius 0.150 m, with rotational inertia I = 0.0513 kg·m2 about a line through its center of mass, rolls without slipping up a surface inclined at 25.3° to the horizontal. At a certain initial position, the sphere's total kinetic energy is 54.0 J. (a) How much of this initial kinetic energy is rotational? (b) What is the speed of the center of mass of the sphere at the initial position? When the sphere has moved 1.10 m up the incline from its initial position, what are (c) its total kinetic energy and (d) the speed of its center of mass?
Beforehand, I use rotational inertia to get mass already.
The Attempt at a Solution
I got a and b.
mgh = 54 J
solve for h.
h = 1.61 m
then, sin θ = opp/hyp
solve for hyp , and i got 3.77 m
(3.77 + 1.1 ) sin 25.3° = 2.08 m
mg( 2.08 - 1.61) = 15.75 J
but the answer is wrong. Can someone point out my mistake. Thank you.
I used conservation of energy.
let mgh = 1/2 Iw^2 + 1/2 mv^2
then, I transformed the equation above into
mgh = 5/6 mv^2
solve for v.
I got 4.34 m/s
But the answer is wrong. Can someone point out my mistake. Thank you.