Displacement of a Pendulum to find Work done by Force

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Homework Help Overview

The discussion revolves around calculating the work done by a force on a pendulum, focusing on the relationship between the force, displacement, and energy conservation principles.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the relationship between the force acting on the pendulum and the displacement, with one participant attempting to derive the force equations. Others question the direction of displacement and suggest considering conservation of energy as an alternative approach.

Discussion Status

Participants are actively engaging with the problem, raising questions about the direction of displacement and the application of energy conservation. Some guidance has been offered regarding the integration approach to calculate work done, but no consensus has been reached on the best method to proceed.

Contextual Notes

There is a discussion about the nature of the forces involved, including potential energy, kinetic energy, and frictional losses, which may influence the approach taken. The specific setup of the problem and assumptions about the system are also under consideration.

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I'm having trouble with this problem. I did: FTcosθ-mg= 0, solving for FT, getting FT= mg/cosθ. Then, along the x-axis, F-FTsinθ=0, solving for F, getting F= mgtanθ. Not sure how to go about it from here. What is the direction of the displacement?
 
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The force is always horizontal, so for the work done you want the horizontal displacement. But.. why not just use conservation of energy?
 
What do you mean?
 
The force has done work on the system. Where has that work gone? There are three possibilities: PE, KE and frictional losses. Which apply here?
If you want to do it by integration, ∫F.ds, since the force acts horizontally that becomes ∫F.dx, where F is the scalar magnitude of F and dx is the horizontal component of ds. You have F as a function of θ, so next you need dx in terms of θ and dθ.
 

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