*Now onto more of the Mathematics you will need to solve these problems. Every vector has a horizontal and vertical component.*

This 'reactionary' pullback force is tension in the rope. [Notice the rope feels this force but does not exert it in a direction.

The rope is not pulling, so there is no true direction to this, hence why tension is not a true force.] This is all one needs to know about tension to understand how to do the problems involving tension in Calculus III.

Tension is a result of Newton's Three Laws, which summed up rather loosely are 1st Law: An object with no external force acting on it does not change velocity.

2nd Law: 3rd Law: Every force has an equal and 'opposite' force - a reaction force. Well if I pulled on a rope tied to a tree with 100N of force, the rope 'pulls back' with 100N of force.

[mathjax] Many of my students find tension in rope problems to be rather difficult.

This does not come at a surprise because there are many moving parts to these problems: the strange phenomenon of tension, basic Physics knowledge, breaking vectors into components, solving simultaneous equations, and some usually not so fun numbers.

Well then the problem is no harder, it's just given us more busy work.

Notice that the components are completely horizontal or vertical, respectively.

So as because it's horizontal component would pointing in the negative direction.

Notice that negatives play no role in the magnitude of the vector. After all, exerting a fixed amount of force in a direction should be the same force no matter what direction you decide to face!

## Comments Solving Tension Problems

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