Finding Work Done by a Force on a Particle Along a Triangular Path

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To find the work done by the force F=(5y+3x-6)i + (2x-y+4)j on a particle moving along a triangular path with vertices (0,0), (4,0), and (4,3), the user initially attempted to integrate the force equation but expressed uncertainty about the method. They questioned whether line integrals were necessary for calculating work in a non-uniform 2D field and sought clarification on the correct approach. The user is looking for guidance on solving this problem effectively, emphasizing the need for a clear explanation. The discussion highlights the complexity of work calculations in multidimensional force fields. Overall, the user seeks assistance in understanding the proper techniques for this type of physics problem.
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Homework Statement


F=(5y+3x-6)i + (2x-y+4)j. find work done by the force on a particle following a triangular path with verticies (0,0),(4,0),(4,3) where the positions are given in meters.


Homework Equations


Int(F(x,y))dx*dy ? not really sure for 2 dimensional problems


The Attempt at a Solution


I integrated the force equation with respect to x and then y to obtain...
2xy(5y+3x-3)i + xy(x-(1/2)y+4)j and then calculated the work for each section of the path and added them together. i don't think its the right way to do it though. Is there a way to solve this without the need for line integrals!? Please help
 
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bump. basically i need to know how to figure out work done over a non uniform 2 dimensional field. even if it requires line integrals, if someone could walk me through it
 
nobody knows? did i phrase my question wrong or something?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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