Question

A solid uniform sphere rolls without slipping along a horizontal surface with translational speed v, comes to a ramp, and rolls without slipping up the ramp to height h, as shown. Assuming no losses to friction, heat, or air resistance, what is h in terms of v? The moment of inertia of a rolling solid sphere is Icm=2/5MR2. Assume acceleration due to gravity is g= 9.8 m/s2.

A.7v^2/10g

B.v^2/2g

C.v^2/7g

D.3v^2/10g

Answer 1

Using conservation of energy

Initial pE = translational kE + rotational kE

m g h = 0.5 I w^2 + 0.5 m v^2

m g h = 0.5* ( 2/5) mr^2 ( v^2/r^2) + 0.5 m v^2

gh = 0.2 v^2 + 0.5 v^2

h = (7/10) v^2/g

Option (a) is correct

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