# Homework Help: Pendulum with constant force

1. Oct 16, 2006

### feelau

Hi, so I'm kinda stuck on this problem, any advise on any part of this problem is appreciated. So the problem states that a ball having mass m is connected to a string with length L and forms a simple pendulum. A wind of constant horizontal F is blowing, the questions asks us to show that the maximum height is H=2L/(1+(mg/F)^2) then it asks us to determine the equilibrium height of ball/ show formula. I tried solving the questions and for the first one, i'm missing the power and for the second one, I get H=L. I'm not sure if they're right, and if they're wrong can someone help? thanks

2. Oct 16, 2006

### OlderDan

The second part is easier than the first. Is this a calculus based course? If H is measured relative to the bottom, the equilibrium height has to be less than L.

3. Oct 16, 2006

### feelau

Yes this is calculus based but I don't think this problem requires calculus though....right? I think I understand why equilibrium height has to be less than L but I still don't/can't get the first part. I don't know how (mg/F) is squared...does anyone else know? It's due tomorow :S

4. Oct 16, 2006

### OlderDan

The equilibrium position is just a statics problem with weight, tension, and constant horizontal force adding to zero. The first part I think has to be done by computing the work done on the ball by the wind force. The work done will equal the change in gravitational potential energy. The problem is, the motion is not parallel to the force, so you will have a position dependent dW (work) to integrate.

5. Oct 16, 2006

### feelau

On the equilibrium one, how do I incorporate height into the force equations?

6. Oct 16, 2006

### OlderDan

Do it in terms of the angle of deflection of the pendulum. The tension in the string will be at an angle to the vertical. You find the angle by summing gravity, tension, and wind forces to zero. When you have the angle, you can compute the height of the ball.

7. Oct 16, 2006

### feelau

So on the first part, how would we relate work to the problem because I don't think there's anyway to relate position like the horizontal component of position

8. Oct 17, 2006

### feelau

well thank you very much anyway, you've helped me a lot

9. Oct 17, 2006

### OlderDan

Work is dW = F<dot>dr, where <dot> is the dot product and F and dr are vectors. dr is an infinitesimal displacement along the path of the ball, so its direction is changing. F is constant. dW = F*dx where F is the magnitude of F and dx is the horizontal component of dr.