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joemama69
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Homework Statement
U(x,y) = 3x2 - 7y
A) Calculate the force at the coordinate point (3,3)
B) Determine if the following forces are conservative and find the change in potential energy correspoinding to each for an interval 0 to x
i) Fx = ax + bs2 a and b are constants
ii) Fx = AeBx (A and B are constants)
c) a force F = 6i - 2j acts on a particle that undergoes a displacement of S = 3i + 5j
i)find the work done by the force on the particle
ii) find the angle between F and S
Homework Equations
The Attempt at a Solution
Part A)
by book says F(x,y) = -dU/dx i - dU/dy j those are partial derivatives
so F = -6xi + 7j
then F(3,3) = -18i + 7j and the magnitude is 19.31 N, the answer is given as 21.2 what's my mistake
Part B)
it says you need to take the curl and if it is 0, then it is conservative
i) curl F = (-a - 2bx)j + (a + 2bx)k = 0
ii) curl F = -ABeBx i + ABeBx k = 0
Part C)
i) W = F dot S = 18 - 10 = 8 N
ii)thetaF = arctan -2/6 = -18.4 degress
thetaS = artcan 5/3 = 59.0 degrees
59.0-18.4 = 77.5 degrees