Work done by expanding gas in a gun on a bullet

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SUMMARY

The discussion focuses on calculating the work done by expanding gas on a bullet fired from a rifle, with a specific force equation given as F(x) = 20000 + 8000x - 22000x². To accurately determine the work done as the bullet travels through a 0.590 m barrel, integration is necessary due to the non-uniform force. The correct approach involves using the integral W = ∫ F(x) dx from 0 to 0.590, rather than simply multiplying force by distance, which is only valid for constant forces. The participant successfully applied this method, resulting in a perfect score on their physics homework.

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TrippingBilly
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A 135 g bullet is fired from a rifle having a barrel 0.590 m long. Assuming the origin is placed where the bullet begins to move, the force (in Newtons) exerted by the expanding gas on the bullet is 20000 + 8000x - 22000x2, 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.
(b) If the barrel is 1.25 m long, how much work is done, and how does this value compare to the work calculated in part (a)?

For part A, i plugged in .590m into x for the equation of the force, multiplied that by .590 because W = Force x Distance, and since they wanted an answer in kJ i divided by 1000, but it says that my answer is incorrect. Any thoughts?
 
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Your answer would be correct if the force is uniform (constant),but since it isn't, some calculus is required. Note that the formal definition of work done by a force is;

W=\int^{x_{1}}_{x_{0}} F(x) \;dx
 
Wow, thanks. Never would have thought of that. Thanks to this forum for the first time ever I got a 100% on my physics homework
Thanks :biggrin:
 

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