A 85-g bullet is fired from a rifle having a barrel 0.552 m long. Choose the ori

Question

A 85-g bullet is fired from a rifle having a barrel 0.552 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 15900 + 10300x - 26250x2, 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 0.91 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=Intedral(Fds), so you have to integrate the above equation from 0 to .0.552 in the fifst case and from 0 to 0.91 in the second

W = (15900 x + 10300X^2/2 -26250x^3/3) from 0 to .0.552 = 8867.31J
W = (15900 x + 10300X^2/2 -26250x^3/3) from 0 to 0.91 = 12139.965J

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