Solving Work Done by Gas on a Bullet in a Rifle Barrel

[JamesL]

Heres the problem:

A 103 g bullet is fired from a rifle having a barrel .796 m long. Assuming the origin is placed where the bullet begins to move, the force exerted on the bullet by the expanding gas is F = a + bx - cx^2, where a = 10600 N, b = 5000 N/m, c = 39400 N/m^2, with x in meters.

Determine the work done by the gas on the bullet as the bullet travels the length of the barrel.

Also, if the barrel is 1.136 m long, how much work is done?

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I wasnt sure whether or not to treat this problem as a variable force one... the only way i really know how to do that is by using a "spring-like" constant, but I am not sure if that is really applicable in this problem.

Could anyone point me in the right direction?

 

[Chen]

Yes, the force is not constant in this problem so you have to treat it as a variable force problem. If you draw a graph of F as a function of X, what would it look like? What would the area below the graph represent? How can you find that area? Hint:
$$W_F = \int _{x_1}^{x_2}Fdx$$

 

[sunilkamadolli]

ya...u can think of it this way...the force of the expanding gas on the bullet changes because it depends on the displacement x and the x iz changing...x changes frm what to what? 0 to .796...[so the integral can be interpreted az the force [F] changing with respect to x [dx] from x1 to x2]

- Mr. Kamadolli