An archer pulls the bowstring back for a distance of 0.400 m before releasing the arrow. The bow and string act like a spring whose spring constant is 490 N/m.

Question

(a) What is the elastic potential energy of the drawn bow?
(b) The arrow has a mass of 0.0300 kg. How fast is it traveling when it leaves the bow?

Answer 1

a) Elastic P.E. = (1/2) k X^2, where
k = 490 N/m and X = 0.400 m

b) Set Elastic P.E = (1/2) M v^2 and solve for V.

kX^2 = mV^2
V = X sqrt (k/m)