A 65-g bullet is fired from a rifle having a barrel 0.546 m long. Choose the ori

Question

A 65-g bullet is fired from a rifle having a barrel 0.546 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 13950 + 10500x - 23250x2, 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.
kJ

(b) If the barrel is 0.97 m long, how much work is done?
kJ

(c) How does this value compare with the work calculated in part (a)?
percent difference = %

Explanation / Answer

W = ?F(x)dx =S (13950 + 10500x - 23250x^2)dx =13950x + 10500x^2/2 - 23250x^3/3 = 13950 + 5250x^2 - 7750x^3 (x -> 0 to 0.546m) = 14253.6 J b)if x=0.97m W =11816.5 J c)( 11816.5-14253.6)/14253.6 *100 = 17.09 % decrement

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