Question

A 153 g bullet is fired from a rifle having a
barrel 0
.
794 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
= 12600 N,
b
= 8420 N
/
m,
c
= 10100 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.
Answer in units of J

Answer 1

W = ∫F•dx = a•x + (b/2) •x² - (c/3) •x³

Answer 2

So f = (9.8)(153) and d=.794? And then do I solve for x? How would I solve for x? ( never taken calculus)

Answer 3

W = ∫F•dx = a•x + (b/2) •x² - (c/3) •x³ =
=12600•0.794 +8420•0.794²/2 -10100•0.794³/3=
=10004.4+2654.1-5055.7 =7602.8 J

Answer 4

That answer was wrong :(

Answer 5

I figured it out. The answer is 10973.29 J. You just jsd2272 your x values mixed up. Thanks for the equation though. :)