Posted by admin | Posted in archery | Posted on 05-05-2010
Tags: archery, bow, bows, bowstring, string
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An archer pulls the bowstring back for a distance of 0.393 m before releasing the arrow. The bow and .....?
An archer pulls the bowstring back for a distance of 0.393 m before releasing the arrow. The bow and string act like a spring whose spring constant is 409 N/m. (a) What is the elastic potential energy of the drawn bow? (b) The arrow has a mass of 0.433 kg. How fast is it travelling when it leaves the bow?
please help...
a)
The formula for the potential energy stored in a spring is
PE = 1/2*k*x^2
Solving for the bow's case, we get:
PE = 1/2*(409 N/m)*(0.393 m)^2
PE = 31.58 J
b)
If the potential energy stored in the bow is completely converted to kinetic energy, we can find the arrow's velocity based on the kinetic energy equation:
KE = 1/2*m*v^2
v^2 = 2*KE / m
v = sqrt(2*KE / m)
Inputting the numbers, we get:
v = sqrt(2*(31.58 J) / (0.433 kg))
v = sqrt(145.9 m^2/s^2)
v = 12.08 m/s
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