Question

A 100-g bullet is fired from a rifle having a barrel 0.600 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 15 000 1 10 000x 2 25 000x2, 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) What If

Answer 1

9000 J

Step-by-step explanation:

weight of bullet = 100 g

length of gun barrel = 0.6m

A) determine the work done by the gas on the bullet as the bullet travels the length of the barrel

The work done is an integral of force over distance in this scenario

lets represent the force using some constants ( arbitrary )

Fx = a + bx + cx^2

where : a = 15000, b = 10000, c = - 25000

hence work done ( W ) =
`ax_(f ) + (bx^(2) _(f) )/(2) + (cx^(3) _(f) )/(3)`

where ; xf = 0.6

hence work done(W)

= 15000(0.6) + [(10000*0.6^2)/2] + [(-25000*0.6^3)/3]

= 9000 J