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!

Homework Help: Pendulum swings into a peg

  1. Apr 14, 2016 #1
    1. The problem statement, all variables and given/known data
    With this problem I have to get the answer: cosθ = r/L * cosα - √(3)/2 * (1 - r/L)
    which in other words mean I need to find angle θ with arccos[r/L * cosα - √(3)/2 * (1 - r/L)].

    Here's the picture:

    Lcosθ is the vertical length of the string at its lowest point.

    rcosα is a fraction of that same vertical string in terms of displacement "r" (which is from the start of the string to the peg)

    ∠β is the angle between the peg and the horizon.

    (L-r) sinβ is the height from the end of the peg and the horizontal

    (L-r) cosα is the horizontal length of that same peg.

    (L-r)cosα is the vertical length of the string from the ball to the peg.

    So, this is not really a physics issue but more like a math issue but since this is a physics problem I've decided to put it under here.

    My problem is that I am unable to continue from this point as shown on the picture of my attempt. I don't know where to continue from here on out. I am trying to find "t" for the equation but I am unsure how. Where do I continue from now?

    2. Relevant equations

    Newtonian Position Formula:
    yf = yi +viyt + .5gt2
    xf = xi +vixt + .5gt2

    Energy Equation:
    Work of hand - force of friction * displacement = delta Kinetic Energy + delta Potential Energy

    Wh - fF*d = [.5*mvf2 - .5*mvi2] - [mghf - mghi]

    3. The attempt at a solution
    Picture of Attempt:
  2. jcsd
  3. Apr 14, 2016 #2


    User Avatar
    Science Advisor
    Homework Helper
    2017 Award

    Hello Stranger, :welcome:

    Your position formula is only valid for uniform acceleration. You don't have that here !
    Can you think of a condition you can impose on ##\beta## ?
  4. Apr 14, 2016 #3
    Thanks for the welcome :).
    The only method I can think of when dealing with changing acceleration by breaking it into parts. Each part for every time the value of acceleration changes. I have not yet learned ho to derive very well but I know it exists. As for angle β I am clueless on what to impose.
  5. Apr 15, 2016 #4


    User Avatar
    Science Advisor
    Homework Helper
    2017 Award

    Well, then perhaps you can conquer this one without dealing with changing acceleration ?
    The sketch suggests a trajectory, but is it realistic ? Where must the mass run out of sped to fall on the peg ? What would happen if it ran out of speed at e.g. 85 degrees ?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted