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

[jd102684]

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.

 

[Diane_]

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.

 

[jd102684]

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!