# Sums of Forces

Published on: Fri Feb 19 2010

Force is a vector. Its magnitude is the Vector sum of it’s x and y component parts. If you hang a bowling ball from a string, there are two forces acting on it. The tension force from the string, and the force of gravity, trying to drag the bowling ball to earth. If you look at the picture, it is the “ghost” bowling ball.

Things get more complicated if you drag your bowling ball to the side, by tying a string to it and pulling it. Now there is another force.

This force is a vector sum, and it can be broken out into

So now we fill in our x and y values based on what we know (which is F String and Mass)

We need to solve for Theta right away. We do this using a trick, since these are vectors they are related to each other and we can combine our x and y values. So we decide to divide our x and y.

This gives us a very neat solution. We can cancel out the |F_{T}| which leaves us with sine of theta over cosine of theta, which is equal to the tangent of theta. So since the other side is already equal to the magnitude of the Force of the string (length of String) divided by mass times gravity… Does this check dimensionally? It doesn’t seem so… but I will continue! Maybe Tangent auto-ignores units.
Ok, now we can get started solving for F_{T}, which we do by performing a neat trick and squaring both sides. I never knew you could play with your math so much.

Ok, here the professor did something to turn the Trig into an identity… and I didn’t catch it. And I’m not to sure how to swing it into the answer, which I do know! Maybe he added x and y instead of dividing? I need to remember I’m working with vectors.

Now, the next example took into consideration acceleration! This was just the example for static force.
**Dynamic Force with acceleration along one axis:**

Ignoring my deadhead passengers, once the elevator takes off and starts accelerating, there is another force to deal with. We need to add “a” into our equations for Force. Lucky it is only in the y direction, which makes things a bit easier.
**If acceleration is not 0**

So that is it for Dynamic forces along the y axis.
What is you place an object on a frictionless surface and tilt it?