A 50-g bullet is fired from a rifle having a barrel 0.654 m long. Choose the ori

Question

A 50-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 14250 + 9000x - 24500x2, 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 1.10 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

Work done = Force * distance
dw = Integral (F.dx)
dw = Integral ((14250 + 9000x - 24500x^2).dx)

dw = [14250 x + 9000/2 x^2 - 24500/3 x^3]0.654
W = 14250 * 0.654 + 4500* 0.654^2 - 8166.7* 0.654^3 J
W = 8960 J
W = 8.96 KJ

(B)
If the barrel is 1.10 m long ==>
W = 14250 * 1.1 + 4500 *1.1^2 - 8166.7* 1.1^3 J
W = 10,250 J
W = 10.25 KJ

(C)
% increase = (10.25 - 8.96) / 8.96 * 100%
= 14.4 % Increase in Work done

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