Calculating Maximum Height and Equilibrium Height of Pendulum with Wind Force

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To calculate the maximum height (Hmax) of a pendulum ball subjected to a constant wind force (F), the work done by the wind must be equated to the potential energy gained by the ball at height H. The work done can be expressed as F multiplied by the horizontal displacement caused by the wind. Additionally, the equilibrium height of the ball can be determined as a function of the wind force, considering the balance of forces acting on the ball. Understanding the relationship between the force, displacement, and potential energy is crucial for solving the problem. The discussion emphasizes the need for a clear expression of work in the context of the pendulum's motion.
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Homework Statement


A ball of mass m = 300 g is connected by a strong string of length L = 80.0 cm to a pivot and held in place with the string vertical. A wind exerts constant force F to the right on the ball as in the figure below. The ball is released from rest. The wind makes it swing up to attain maximum height Hmax above its starting point before it swings down again.



Homework Equations


(a) Find Hmax as a function of F.
(f) Now consider the equilibrium height of the ball with the wind blowing. Determine it as a function of F.



The Attempt at a Solution


The work done by F is equal to the balls potential energy at height H, but how do I express that work?
 
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F*[the displacement in the direction of that force]?
 

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