help with this physics question

Question

A 110 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 13000 + 10000x - 26000x2, 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, and how does this value compare to the work calculated in part (a)?

kJ

(work done with the 1.10 m barrel / work done with the 0.580 m barrel)

Answer 1

(a)

 

W = ∫F(x)dx = ∫₀^0.580 (13000 + 10000x - 26000x²)dx

 

Evaluate this integral and the result will be the work done in joules, and then convert to kJ.

 

(b)

 

Evaluate the integral, but with upper limit 1.10 this time.

 

W = ∫F(x)dx = ∫₀^1.10 (13000 + 10000x - 26000x²)dx

 

Then compare to result from part (a).