Question

A 110-g bullet is fired from a rifle having a barrel 0.636 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 + 11000x - 25750x2, 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 1.02 m long, how much work is done?
___kJ

(c) How does this value compare with the work calculated in part (a)?
percent difference = ___%

Answer 1

Data:
mass =  110-g bullet
d = 0.636 m
Force = 13500 + 11000x - 25750x^2, newtons.

a) Work, W

W = ∫( F* )(dx) =∫[13500+ 11000x - 25750x^2] (dx) =

W =  13500x + 5500x^2 - 8583.33 x^3 ] from 0 to 0.636  =

W = 8602.6 joule

b) x= 1.02 m

W =  13500x + 5500x^2 - 8583.33 x^3 ] from 0 to 1.02

W = 10383.5

c) %

[W in b / W in a] = 10383.5 / 8602.6 = 1.21 => W in b is 21% more than work in a.