If we treat a bow as a spring, we can use conservation of energy concerns to est

Question

If we treat a bow as a spring, we can use conservation of energy concerns to estimate the velocity of the arrow. By drawing the arrow back against the bow string, potential energy is stored in the bow material. Upon release of the arrow, that potential energy is transformed into kinetic energy of the arrow. Let's say that an archer draws back the arrow 0.48 m and requires 150 N of force to maintain the arrow in this position. Upon release of the arrow, what will be the speed of the arrow if its mass is 0.02 kg List any assumptions you must make for this simple analysis.

Explanation / Answer

x = stretch of spring = 0.48 m

F = spring force = 150 N

k = spring constant

spring force is given as

F = kx

150 = k (0.48)

k = 312.5 N/m

m = 0.02 kg

v = speed

using conservation of energy

spring energy = kinetic energy

(0.5) kx2 = (0.5) m v2

(312.5) (0.48)2 = (0.02) v2

v = 60 m/s

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