An archery bow is drawn a distance d = 0.29 m and loaded with an arrow of mass m = 0.094 kg. The bow acts as a spring with a spring constant of k = 112 N/m, and the arrow flies with negligible air resistance. To simplify your work, let the gravitational potential energy be zero at the initial height of the arrow. How fast will the arrow travel and it leave the bow?

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Question:

An archery bow is drawn a distance d = 0.29 m and loaded with an arrow of mass m = 0.094 kg. The bow acts as a spring with a spring constant of k = 112 N/m, and the arrow flies with negligible air resistance. To simplify your work, let the gravitational potential energy be zero at the initial height of the arrow. How fast will the arrow travel and it leave the bow?

Answer:

The speed of arrow leaving the bow is 10.01 m/s.

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Given data:

The distance drawn by bow is, d = 0.29 m.

The mass of arrow is, m = 0.094 kg.

The value of spring constant is, k = 112 N/m.

The spring potential energy stored during the loading of bow is converted into kinetic energy of arrow. Then,

Spring potential energy = Kinetic energy

?f=U%3DKE%5C%5C%5Cdfrac%7B1%7D%7B2%7Dkd%5E2%20%3D%5Cdfrac%7B1%7D%7B2%7Dmv%5E2%5C%5Ckd%5E2%3Dmv%5E2%5C%5Cv%3D%5Csqrt%7B%20%5Cdfrac%7Bkd%5E2%7D%7Bm%7D%7D%5C%5Cv%3D%5Csqrt%7B%20%5Cdfrac%7B112%20%5Ctimes%200.29%5E2%7D%7B0.094%7D%7D%5C%5Cv%20%3D%2010

Thus, we can conclude that the speed of arrow leaving the bow is 10.01 m/s.

Learn more about spring potential energy here:

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