** A 100-g bullet .is fired from a rit1e having a barrel 0.600 m long. Choose th

Question

** A 100-g bullet .is fired from a rit1e 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 + 10,000x- 25,000x2, where x is in meters. (a) Determine the work clone by the gas on the bullet as the bullet travels the length of the barrel. (b) What is the exit speed of the bullet? (c) If the barrel is 1.00 m long, how much work is clone and how does this value compare to the work calculated in part (a)?

Explanation / Answer

a) work done = integral of Fdx

W = 15000x + 10000x2/2 - 25000x3/3

b) work done = K

15000x + 10000x2/2 - 25000x3/3 = (!/2)mv2

put x = 0.6m and solve for v

c) put x = 1 in work expression

and take the ratio with work done when x = 0.6

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