A 130-g bullet is fired from a rifle having a barrel 0.654 m long. Choose the or

Question

A 130-g bullet is fired from a rifle having a barrel 0.654 m long. Choose the origin to be at the location where the bullet begins to move. Then the force (in newtons) exerted by the expanding gas on the bullet is 16050 + 9100x - 26000x2, where x is in meters.

(a) Determine the work done by the gas on the bullet as the bullet travels the length of the barrel.
kJ

(b) If the barrel is 0.90 m long, how much work is done?
kJ

(c) How does this value compare with the work calculated in part (a)?
percent difference =  %

Explanation / Answer

W = integration F*x

W = 16050*x + 9100*x^2/2 - 26000*x^3/3

a) W1 = (16060*0.654) + ((9100*0.654*0.654)/2)-((26000*0.654*0.654*0.654)/3) = 10.025 kJ

b) W2 = (16060*0.9) + ((9100*0.9*0.9)/2)-((26000*0.9*0.9*0.9)/3) = 11.8215 kJ

c) % = W2-W1/W1 *100 = 17.9 %

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