physics - Force

用戶83992

2013-05-10 7:53 am

In an experiment, one of the forces exerted on a proton is F=<-ax²,0> where a=11.2N/m².
(a) Calculate the work done by this force as the proton moves along a straight line path from the point (0.09m,0) to the point (0.29m,0).
___J
(b) Calculate the work done by this force as the proton moves along a straight line path from the point (0.29m,0) to the point (0.09m,0).
___J

The answer for (a) should be -0.0883J, and the answer for (b) should be 0.0883J. But I am not sure how to get to the answer.

回答 (1)

天同

2013-05-10 3:55 pm

✔ 最佳答案

(a) When the proton moves an infinitetesimal displacement dx,
work done dW = F.dx
Hence, total work done W = integral { F.dx}
W = integral { -ax^2.dx } with limits of integration from 0.09 m to 0.29 m
W = -(1/3).(ax^3)
i.e. W = -(11.2/3).(0.29^3 - 0.09^3) J = -0.0883 J
[the -ve sign indicates that the force F acts in opposite direction to the motion of the proton]

(b) Since W = -(1/3)(ax^3)
the limits of integration are now from 0.29 m to 0.09 m
W = -(11.2/3).(0.09^3 - 0.29^3) J = 0.0883 J

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