Calculating Maximum Height and Equilibrium Height of Pendulum with Wind Force

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SUMMARY

The discussion focuses on calculating the maximum height (Hmax) and equilibrium height of a pendulum-like ball subjected to a constant wind force (F). The mass of the ball is specified as 300 g, and the string length is 80.0 cm. The relationship between the work done by the wind force and the potential energy of the ball is central to the calculations. The participants explore how to express the work done by the wind force in relation to the displacement of the ball.

PREREQUISITES
  • Understanding of potential energy and work-energy principles
  • Basic knowledge of pendulum mechanics
  • Familiarity with forces acting on objects in motion
  • Ability to manipulate algebraic equations for physical calculations
NEXT STEPS
  • Calculate the maximum height (Hmax) of the pendulum as a function of wind force (F)
  • Determine the equilibrium height of the ball under the influence of wind force (F)
  • Explore the relationship between displacement and work done by a constant force
  • Review the principles of energy conservation in dynamic systems
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and forces, as well as educators looking for practical examples of pendulum dynamics influenced by external forces.

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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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