A 120-g bullet is fired from a rifle having a barrel 0.654 m long. Choose the or
ID: 1331774 • Letter: A
Question
A 120-g bullet is fired from a rifle having a barrel 0.654 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 15900 + 9700x - 26250x2, 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 1.05 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
a.
the work done is defined as follows:
W = integral [F.dx]
W = integral {[15900 + 9700x - 26250x2]dx}
= 15900x+9700[x2 / 2] - 26250[x3 /3]
from 0 to L, the work done is
W = 15900L + 4850 L2 - 8750 L3
If L = 0.654 m, the work done is,
W = 15900(0.654) + 4850(0.654)2 - 8750(0.654)3
= 10 kJ
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b.
If L = 1.05 m, the work done is,
W = 15900(1.05) + 4850(1.05)2 - 8750(1.05)3
= 11.9 kJ
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c.
The difference in % is,
Difference = [11.9 kJ - 10 kJ /11.9 kJ ]*100 = 15.96%
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