Asked by Lacey
A solid ball of mass m rolls along a horizontal surface with a translational speed of v. What percent of its total kinetic energy is translational?
Answers
Answered by
bobpursley
KE= 1/2 m v^2
RE=1/2 I w^2 where I is the moment of inertia for a sphere. I sphere= 2/5 m r^2
well, w= v*r, put that in the second formula, and find the ratio.
ratio= mv^2/(2/5)mr^2*v^2*r^2
ratio=5/2 so check that.
so 5/7 of energy is translational
RE=1/2 I w^2 where I is the moment of inertia for a sphere. I sphere= 2/5 m r^2
well, w= v*r, put that in the second formula, and find the ratio.
ratio= mv^2/(2/5)mr^2*v^2*r^2
ratio=5/2 so check that.
so 5/7 of energy is translational
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