Simple harmonic motion rope swing problem

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

p5-73.gif

(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?
 

Hootenanny

Staff Emeritus
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Have you considered that she is now swinging with the wind?
 
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:
P

PSOA

Guest
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.
 
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?
 

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