A 80-g bullet is fired from a rifle having a barrel 0.582 m long. Choose the ori

Question

A 80-g bullet is fired from a rifle having a barrel 0.582 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 14100 + 9100x - 24250x2, 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

W=Integral(Fds), so you have to integrate the above equation from 0 to .582 in the first case and from 0 to 1.10 in the second a) W = (14100x + 9100X^2/2 - 24250x^3/3) from 0 to .582 = 8153.86J b) W = (14100x + 9100X^2/2 - 24250x^3/3) from 0 to 1.10 = 10256.58J c) % difference = [10256.58J- 8153.86J/8153.86J]*100 = 25.78 %

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