An archer pulls the bowstring back for a distance of 0.530 m before releasing th

Question

An archer pulls the bowstring back for a distance of 0.530 m before releasing the arrow. The bow and stringact like a spring whose spring constant is 475 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 Simple HarmonicMotion (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 Simple HarmonicMotion

Explanation / Answer

spring constant k = 475N/m archer pulls the bowstring back for a distance of x =0.530 m a) the elastic potential energy of the drawn bow is PE = 1/2*k*x2        =1/2*475*0.532        = 66.71J b) mass of arrow m = 0.30kg when arrow leaves the bow the potential energy isconvertd in to kinetic energy    so KE = PE       1/2mv2 =66.71J      or v = 2*66.71J / 0.3kg            =21.08 m/s

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