A 80 g bullet is fired from a rifle having a barrel 0.580 m long. Assuming the o

Question

A 80 g bullet is fired from a rifle having a barrel 0.580 m long. Assuming the origin is placed where the bullet begins to move, the force (in newtons) exerted by the expanding gas on the bullet is 17000 + 9000x - 20000x2, 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. (b) If the barrel is 1.10 m long, how much work is done, and how does this value compare to the work calculated in part (a)? (i): ................... (ii) .............. (work done with the 1.10 m barrel / work done with the 0.580 m barrel

Explanation / Answer

a) work done by the gas on the bullet = integral Fdx = 17000x + 9000x*x/2 - 20000x*x*x/3 = 12674.55 N-m ; b) x=1.10m ; work done = 17000x + 9000x*x/2 - 20000x*x*x/3 = 33018.33 N-m ;;;;; work done with the 1.10 m barrel / work done with the 0.580 m barrel = 2.6 ;; In b) part the work done is more than in a) part

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