How do you relate work to the problem of a pendulum with a constant force?

[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

 

[OlderDan]

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

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.

 

[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

 

[OlderDan]

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

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.

 

[feelau]

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

 

[OlderDan]

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

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.

 

[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

 

[feelau]

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

 

[OlderDan]

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

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.