Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Simple harmonic motion rope swing problem

  1. Dec 6, 2006 #1
    Jane wants to swing on a rope across a river. What minimum speed does she need to make it across, and once she's across, what minimum speed does she need to make it back?

    Here's what's given:
    mass = 47 kg
    horizontal wind - call it F - (opposite to her swing) = 120 N
    horizontal distance (D) = 50 m
    rope length (L) = 40 m
    theta = 50 degrees

    (hopefully you can see the image)

    Here's how I started:

    D = Lsin(theta) + Lsin(phi)

    Plug in the values, and phi = 28.9 degrees

    Then, Change in height = Lcos(phi) - Lcos(theta)
    Plug in the values, change in height = 9.3 m

    From there:

    PE(o) + KE(o) + wind = PE(f) + KE(f)

    mgh(0) + (1/2)mv(0)^2 - F(w)*D = mgh(f) + (1/2)mv(f)^2

    and v(0) = 8.55 m/s

    I got that part right. But, now how do I find the minimum velocity to go back? I tried switching the h(0) and h(f) in that last equation to go back, but it didn't work. What's wrong?
  2. jcsd
  3. Dec 7, 2006 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Have you considered that she is now swinging with the wind?
  4. Dec 7, 2006 #3
    Yes, I did. Here's what happens:

    mgh(0) + (1/2)mv(0)^2 + F(w)*D = mgh(f) + (1/2)mv(f)^2

    46(9.8)(-9.3) + (1/2)(47)v(o)^2 + 120(50) = 0

    and v(o)^2 = -76.92

    But the fact that it's negative makes me think that it's wrong. Can I still take the square root of it?

    Edit: Apparently I can. I just tried it again and got it right.
    Last edited: Dec 7, 2006
  5. Dec 7, 2006 #4
    But if you got a negative velocity, it means that the wind provides enough energy to Jane to reach that point, so that she doesn't need any initial velocity.
  6. Dec 7, 2006 #5
    That's weird. Are you sure the negative doesn't just mean that Jane is swinging in the opposite direction? Is there something I should have done to make the velocity squared positive?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook