An arrow, starting from rest, leaves the bow with a speed of 27.2 m/s. If the average force exerted on the arrow by the bow was increased 4 times and the arrow was accelerated over the same distance, then with what speed would the arrow leave the bow?
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It will not be 4 times as fast.
Work and energy are the same thing right? Work is force times distance, and the distance is constant. So 4 times more force means 4 times more work. 4 times more work means 4 times more energy for the arrow.
KE=(1/2)m*v^2. So if energy is increased by a factor of 4, then velocity is increased by a factor of 2.
So your final answer is 27.2 m/s * 2 = 54.4 m/s
Work and energy are the same thing right? Work is force times distance, and the distance is constant. So 4 times more force means 4 times more work. 4 times more work means 4 times more energy for the arrow.
KE=(1/2)m*v^2. So if energy is increased by a factor of 4, then velocity is increased by a factor of 2.
So your final answer is 27.2 m/s * 2 = 54.4 m/s
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4 times faster than it originally did?