Pulley System Question: Find Relationship Between Force and Tension

[GBA13]

Homework Statement

Hi Guys,

I am looking at a simple movable pulley system like the one two in from the left. I am trying to work out the relationship between the force applied to the free end (called F₂ in the picture) and the tension in the cable

Homework Equations

The Attempt at a Solution

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I think that you add the tension in each section of cable so then 2F = T, the tension in the cable is double the force F₂ but I'm not sure. Is that correct?

Thanks!

 

[PhanthomJay]

But the tension in the cable is given in the figure. F2 equals ____?

 

[GBA13]

But the tension in the cable is given in the figure. F2 equals ____?

The tension is 50N so then F = T, as it is for all the options here. Does that mean that F always = T?

 

[Merlin3189]

"Does that mean that F always = T?"
What do you mean? What is F? And what is T?
Depends what F is and what T is. Here F_L certainly doesn't equal the tension in the rope.

When we assume the rope is light and frictionless (which of course it never is!), then the tension in the rope is the same at all points.