Find the potential energy of the particle

[1v1Dota2RightMeow]

Homework Statement

A small bead of mass m is constrained to move on a helix: r (θ) = (R cos(θ), R sin(θ), q θ) where R and q are constants, and θ=θ(t) describes the position of the bead along the helix at time t. The bead is also subjected to a gravitational acceleration g downward (-z direction). Find the following quantities in terms of θ and dθ/dt.

c) The potential energy U

Homework Equations

r (θ) = (R cos(θ), R sin(θ), q θ)

θ=θ(t)

The Attempt at a Solution

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I'm only asking because my attempt at a solution proved to be so simple that I'm a bit nervous about it. If I define the position vector (given above) to have coordinates (x,y,z) and claim that as the particle moves in an upwards (+z) directed helical path, then the potential energy is entirely due to gravity and therefore it is U=mg(qθ). Although I'm not sure if I might have missed something...

 

[PeroK]

If only it were always as simple!

 

[1v1Dota2RightMeow]

If only it were always as simple!

Yay! Thank you!

Just out of curiosity though, how would I derive this from U(r)=-W(r_0 -> r) (the definition of potential energy)?

 

[PeroK]

Yay! Thank you!

Just out of curiosity though, how would I derive this from U(r)=-W(r_0 -> r) (the definition of potential energy)?

I'm not sure what you mean. The PE in a uniform gravitational field is just $mgh$.