physics question

Question

A 75-g bullet is fired from a rifle having a barrel 0.620 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 18,000 + 10,000x − 26,000x²,

 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. (Enter your answer to at least two decimal places.)

b- If the barrel is 0.95 m long, how much work is done? (Enter your answer to at least two decimal places.)

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

The work is greater by ____ %.

Answer 1

Work is force times distance. In this case the force is a function of distance, so you have to integrate the expression 18,000 + 10,000x − 26,000x²,dx.

work is ∫ (18000 + 10000x -26000x²) dx between the limits of zero and either 0.620 m or 0.95 m.

Once you do this, divide the work difference between the two distances and divide by 0.620 m times 100 to get percent.