Analyzing Work and Potential Energy for a Uniform Force at an Angle µ

AI Thread Summary
The discussion revolves around calculating the minimum work required to move a point mass under a uniform force at an angle µ and determining the direction of constant potential energy. The user seeks assistance in expressing the work in vector notation and acknowledges the conservative nature of the force, which implies path independence. They initially struggle with integrating the angle into their calculations but receive guidance on resolving the force into orthogonal components to simplify the problem. The user is encouraged to visualize the problem geometrically to aid in understanding the direction of work and potential energy. Overall, the conversation emphasizes the importance of vector notation and geometric interpretation in solving physics problems related to forces and energy.
jd102684
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Hello, I need some help on a two part question. Thanks in advance!

Consider a uniform force, similar to the gravitation force but pointing at an angle µ to the vertical direction, F = ma sin µ ¡ ma cos µ j (i and j represent vector notation...)

1) What is the minimum work required to move a point mass with mass equal to m from the origin (0,0) to a point P (x,y)? (answer in vector notation in terms of µ)

2) in what direction r (also a vector) is the potential energy constant?


Thanks so much for all your help!


EDIT: I forgot to post my current work. I've tried to mess with changing the axis so I can treat the force like gravity. I know that the force is conservative, so the work required to move the mass from point A to point B is the same no matter what path is taken. I'm just really having trouble getting an answer in terms of the angle in vector notation... As for part 2, I would guess it would be in the direction oposite of the uniform force being applied, but when i submitted what i got for that answer, it came back as wrong.
 
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You have the force resolved into orthogonal components, so for all practical purposes you can treat them as independent of each other. Work out the work in the i direction and the work in the j direction, then add them. You'll get the direction with a little Euclidean geometry - just make a sketch and I think you'll see what I mean.
 
Thanks, that did help! I got the first part, but before I try to crank out an answer to the second part of the question can you tell me if my line of thinking is correct as far as what I say in the original post? Maybe give me a boost in the right direction again? Thanks so much!
 
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