A 55-g bullet is fired from a rifle having a barrel 0.564 m long. Choose the ori

Question

A 55-g bullet is fired from a rifle having a barrel 0.564 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 13800 + 9500x - 23250x2, 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 0.94 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 = ?F(x)dx = Integral of [13800 + 9500x - 23250x2]dx
W = 13800x + 4750x^2 - 7750x^3

(a)
at x = 0.564
W = 13800 * 0.564 + 4750 * 0.564^2 - 7750 * 0.564^3
W = 7783.2 + 1510.956 - 1390.4
W = 7903.756 J

(b)
W = 13800 * 0.94 + 4750 * 0.94^2 - 7750 * 0.94^3
W = 12972 + 4197.1 - 6437.026
W = 10732.074 J

(c)
% difference = (10732.074 J - 7903.756 J) / 7903.756 J
% difference = 35.78%

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