A solid sphere of radius R is placed at a height of 40 c m on a 15 ? slope. It i
ID: 2245407 • Letter: A
Question
A solid sphere of radius R is placed at a height of 40cm on a 15? slope. It is released and rolls, without slipping, to the bottom.From what height should a circular hoop of radius R be released on the same slope in order to equal the sphere's speed at the bottom? A solid sphere of radius R is placed at a height of 40cm on a 15? slope. It is released and rolls, without slipping, to the bottom.
From what height should a circular hoop of radius R be released on the same slope in order to equal the sphere's speed at the bottom?
Explanation / Answer
For any circular object,
V = sqrt[2gh/(1+k)] where k is the factor in the moment of inertia formula: I = k*m*R^2
sphere: k = 0.40
hoop: k = 1.0
Vs = sqrt[2*g*0.40/(1+.4)] = 2.366 m/s
Solving for h: h = V^2(1+k)/(2g)
For the hoop with V = 2.366 m/s,
h = (2.366)^2*(2.0)/(2g) = 0.571 m
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