A sphere has a mass of 150 kg and radii of 0.4 m. Assuming it starts...
A sphere has a mass of 150 kg and radii of 0.4 m. Assuming it starts from rest, how much more work is required to get this sphere rolling on a horizontal surface at 2.5 m/s than to get it sliding at 2.5 m/s on a frictionless horizontal surface.
Please show all work and include explanations! Thanks!
Homework Answers
When rolling, we need to consider linear and rotational kinetic energies.
When sliding, we need to consider only linear kinetic energy.
NOTE - You did not mention if the sphere is solid or hollow.
I am assuming it to be a solid sphere.
-------------------------------------------------------------------------------------------
While rolling,
W = 1/2mv2 + 1/2Iw2
w = v/r
I = 2/5 * m * r2 ( For solid sphere)
W = 468.75 + 1/2 * 2/5 * 150 * 0.42 * (2.5/0.4)2
W = 468.75 + 187.5
W = 656.25 J
---------------------
Now, when its only sliding
W = 1/2 mv2
W = 468.75
Therefore,
we need 187.5 J of more work to get this sphere rolling on a horizontal surface at 2.5 m/s than to get it sliding at 2.5 m/s on a frictionless horizontal surface.
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