A 90-g bullet is fired from a rifle having a barrel 0.654 m long. Choose the ori

Question

A 90-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 13500 + 9900x - 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 1.04 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

E = integral F dx

= integral [13500 + 9900 x - 24500 x2] dx

= [13500 + 4950 x2 - 8166.7 x3] (0 to 0.654)

= 13500 + 4950 (0.654)2 - 8166.7 (0.654)3

= 13333 J = 13 KJ

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If barrel is 1.04 m long

= [13500 + 4950 x2 - 8166.7 x3] (0 to 1.04)

= 13500 + 4950 (1.04)2 - 8166.7 (1.04)3

= 9667 J = 9.6 KJ

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