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!

Ball on massless pendulum

  1. Dec 25, 2012 #1
    1. The problem statement, all variables and given/known data

    A rod of neligeable mass is released from the horizontal position. As a ball at the end of the rod falls, it reaches a point at which the tension, T, in the rod equals the ball's weight. At what angle from the verticle does this occur. I am not getting the same answer as my book--Halliday and Resnick 7th ed, problem 69, p 195.


    2. Relevant equations

    Let the verticle height the ball falls, h, h = R sinθ where R is the length of the rod.
    Fnet on the ball = ma = T - Fg. T = mg(weight of ball). Fg = mgsinθ.
    ma = mv^2/R(centripital force).
    So if T = mg, then mg = mv^2/R + mgsinθ and hence sinθ = 1 - v^2/Rg.

    3. The attempt at a solution

    Forging on, 1/2mv^2 = mgh because the kinetic energy of the ball equals the gravitational work done on the ball at the point in question.
    So v^2 = 2Rgsinθ.
    Solving for θ, sinθ = 1 - 2Rgsinθ/Rg, 3sinθ = 1, θ = 19.47°
    Thus the angle from the verticle is 45° + 19.5° = 64.5°.
    The book gives ans answer of 71°
     
  2. jcsd
  3. Dec 25, 2012 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Not sure why you are adding 45°. θ is the angle from the horizontal.
     
  4. Dec 25, 2012 #3
    θ, the angle from the horizontal, was used to simplify the solution. Since the question asks, "what is the angle from the verticle" I added 45°.
     
  5. Dec 25, 2012 #4

    Doc Al

    User Avatar

    Staff: Mentor

    So you think the angle between vertical and horizontal is 45°? :wink:
     
  6. Dec 25, 2012 #5

    Doc Al

    User Avatar

    Staff: Mentor

    Try this: If something makes an angle of 0° with the horizontal what angle does it make with the vertical?
     
  7. Dec 25, 2012 #6
    Done. Thanks.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Ball on massless pendulum
Loading...