can some one help me solve this answer thank you so much Do not just quote a res
ID: 1494467 • Letter: C
Question
can some one help me solve this answer thank you so much
Do not just quote a result, show your work dearly step by step.** A 100-g bullet is fired from a ritle having a barrel 0.6 m long. Assuming the origin is placed where the bullet begins to move, the force exerted on the bullet by the expanding gas is in the positive x direction, with a magnitude 15,000 + lO.OOOx - 25,000 x^2, where x is in meters. Determine the work done by the gas on the bullet as the bullet travels the length of the barrel. If the barrel is 1.00 m long, how much work is done? How does the value you got for part (b) compare with the value you got in part (a)?Explanation / Answer
Here ,
force , F = 15000 + 10000 x - 25000 x^2
a) for the length of barrel , L = 0.6 m
work done by the gas = integration(F .dx) from 0 to 0.6 m
work done by the gas = integration(15000 + 10000 x - 25000 x^2 .dx) from 0 to 0.6 m
work done by the gas = (15000 * x + 10000 * x^2/2 - 25000 * x^3/3)
work done by the gas = (15000 * 0.6 + 10000 * 0.6^2/2 - 25000 * 0.6^3/3)
work done by the gas = 9000 J
b) if the barrel is 1 m long
work done by the gas = integration(F .dx) from 0 to 0.6 m
work done by the gas = integration(15000 + 10000 x - 25000 x^2 .dx) from 0 to 0.6 m
work done by the gas = (15000 * x + 10000 * x^2/2 - 25000 * x^3/3)
work done by the gas = (15000 * 1 + 10000 * 1^2/2 - 25000 * 1^3/3)
work done by the gas = 11667 J
c)
the value of part b is larger than the value found in part a)
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