# Homework Help: Displacement of a Pendulum to find Work done by Force

1. May 10, 2013

### shinify

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?

2. May 10, 2013

### haruspex

The force is always horizontal, so for the work done you want the horizontal displacement. But.. why not just use conservation of energy?

3. May 10, 2013

### shinify

What do you mean?

4. May 11, 2013

### haruspex

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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