When you throw a ball, the work you do to accelerate it equals the kinetic energ
ID: 1314823 • Letter: W
Question
When you throw a ball, the work you do to accelerate it equals the kinetic energy the ball gains. If you do twice as much work when throwing the ball, does it go twice as fast? Explain.
Yes. Twice as much work will give the ball twice as much kinetic energy. Since KE is proportional to the speed, the speed will double as well.
Yes. Twice as much work will give the ball four times as much kinetic energy. Since KE is proportional to the speed squared, the speed will be the square root of 4, or twice as fast.
No. Twice as much work will give the ball twice as much kinetic energy. But since KE is proportional to the speed squared, the speed will be 2 times larger.
No. Twice as much work will give the ball four times as much kinetic energy. Since KE is proportional to the speed, the speed will be four times larger.
Explanation / Answer
No it does not go twice as fast.
Kinetic energy is defined as: KE = (1/2)mv^2
So if KE is doubled, and since (1/2)m stay constant, v^2 must increase by a factor of 2. The only way for this to happen is for v to increase by a factor of 1.414 (or square root of 2).
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