A 110-g bullet is fired from a rifle having a barrel 0.552 m long. Choose the or

Question

A 110-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 16050 + 10500x - 22500x2, 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 =  %

Explanation / Answer

here the equation is

F = 16050 + 10500x - 22500*x^2

integrate with respect to x

W = 16050 *x + 5250 * x^2 - 22500 * x^3 / 3

x = 0.552 m

W = 16050 * 0.552 + 5250 * 0.552^2 - 22500 * 0.552^3 / 3

W = 9197.8 J

then

b)

for x = 1.02 m

W = 16050 * 1.02 + 5250 * 1.02^2 - 22500 * 1.02^3 / 3

W = 13874 J

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