Question

A 140 g bullet is fired from a rifle having a barrel 0.600 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 10000 + 6000x - 26000x^2, 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 (suggestion: enter your answer in kJ = kilojoules).

(b) If the barrel is 1.00 m long, how much work is done?

Answer 1

a) Workdone on the bullet, W = intgerla F*dx

= integral (10000 + 6000*x - 26000*x^2)*dx (x = 0 to x = 0.6m)

= (10000*x + 6000*x^2/2 - 26000*x^3/3) (x = 0 to x = 0.6m)

= (10000*(0.6 - 0) + 6000*(0.6^2/2 - 0) - 26000*(0.6^3/3 - 0) )

= 5208 J

= 5.208 kJ

b)

Workdone on the bullet, W = intgerla F*dx

= integral (10000 + 6000*x - 26000*x^2)*dx (x = 0 to x = 1.0 m)

= (10000*x + 6000*x^2/2 - 26000*x^3/3) (x = 0 to x = 1.0 m)

= (10000*(1 - 0) + 6000*(1^2/2 - 0) - 26000*(1^3/3 - 0) )

= 4333 J

= 4.333 kJ