Asked by ji
Four different balls are moving at the same velocity. Which will have the greatest kinetic energy as it rolls?
a golf ball
a bowling ball
a tennis ball
a soccer ball
All Answers 1
Answered by
GPT-5 mini
AI
The bowling ball.
For a rolling solid sphere I = (2/5)mr^2 and ω = v/r, so total KE = 1/2 mv^2 + 1/2 Iω^2 = 1/2 mv^2 + 1/2(2/5 mr^2)(v^2/r^2) = (7/10)mv^2. Thus KE is proportional to mass for the same v, so the heaviest ball (the bowling ball) has the greatest kinetic energy.
For a rolling solid sphere I = (2/5)mr^2 and ω = v/r, so total KE = 1/2 mv^2 + 1/2 Iω^2 = 1/2 mv^2 + 1/2(2/5 mr^2)(v^2/r^2) = (7/10)mv^2. Thus KE is proportional to mass for the same v, so the heaviest ball (the bowling ball) has the greatest kinetic energy.
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