Work done by expanding gasses on bullet

[bdh2991]

Homework Statement

A 95-g bullet is fired from a rifle having a barrel 0.540 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 16200 + 9400x - 23750x2, 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 0.96 m long, how much work is done?




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

Homework Equations

W = force * displacement

The Attempt at a Solution

after plugging in 0.54 in the force equation i got F = 14,350.5 N

then multiplied it by 0.54 to get work and got 7.75 kJ

same for the second part but i got both answers wrong, i thought it was a simple problem but i guess not.

 

[TSny]

Note that the force is a function of x. So, it is not a constant force. You need to know how to get the work done by a variable force.

 

[bdh2991]

so i basically need to do the integral F dot ds and then plug in the values?

 

[TSny]

so i basically need to do the integral F dot ds and then plug in the values?

Yes, that's it.

 

[bdh2991]

I should have realized that to begin with but thank you for all the help!