An archer pulls the bowstring back for a distance of 0.440 m before releasing th

Question

An archer pulls the bowstring back for a distance of 0.440 m before releasing the arrow. The bow and stringact like a spring whose spring constant is 435 N/m. (a) What is the elastic potential energy of thedrawn bow?
1 J

(b) The arrow has a mass of 0.0300 kg. How fast is it travelingwhen it leaves the bow?
2 m/s

Section 10.3 Energy and SimpleHarmonic Motion (a) What is the elastic potential energy of thedrawn bow?
1 J

(b) The arrow has a mass of 0.0300 kg. How fast is it travelingwhen it leaves the bow?
2 m/s

Explanation / Answer

(a)     Elastic potential energy = ( 1/2 ) K x2 = 0.5 * 435 * 0.44 2 = 42.108 J (b)     kinetic energy of the arrow = potentialenergy            ( 1/2) m V 2 = 42.108             0.5 * 0.03 * V2 = 42.108                             V = 52.98 m/s

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