1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Find the potential energy of the particle

Tags:
  1. Oct 16, 2016 #1
    1. The problem statement, all variables and given/known data
    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

    2. Relevant equations
    r (θ) = (R cos(θ), R sin(θ), q θ)

    θ=θ(t)

    3. The attempt at a solution

    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...
     
  2. jcsd
  3. Oct 16, 2016 #2

    PeroK

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    If only it were always as simple!
     
  4. Oct 16, 2016 #3
    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)?
     
  5. Oct 16, 2016 #4

    PeroK

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I'm not sure what you mean. The PE in a uniform gravitational field is just ##mgh##.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted