**Free Body Diagrams**

Created March 2020, Offline version here

*Videos by Flipping Physics, also on their YouTube channel.
*

Anytime you have a problem that involves forces, you should first draw a free body diagram (FBD), otherwise known as a
. The first step to start an FBD is to
. Weight = mass x gravity (mg), known as the
. Next, the force vectors are represented by arrows. An object at rest on a table will have two forces acting on it. These are
. If there are unbalanced forces acting on an object it is
. The normal force is always
to the surface it is contact with and is always a
. Unequal force vectors indicate that these forces are not matched and we know that the object is
in that direction. If a force is applied to our object at rest on the table but it still does not move, we know that there is an equally opposing force called
. The size of the force vectors matters because it represents the
.

If numerical values are being solved for in various directions, it is important to write out the variables we are given and the variable that we are solving for. We can then find the sum of the forces by
. If the forces are going in the same x or y direction, we can simply add the vectors across that plane. If they are not, we must
. This step should be done by using trigonometry to calculate the force of each component of the vector and redrawing the FBD to
. Once you have the vectors split into x and y components, you can then setup the net force equations for each
. You will then have two net force equations: the
. You may start by solving for the net force for either the x or y. The net force equation is the
of the vectors across one plane. Splitting a vector into x and y components will require the use of trigonometry (sin = opposite/hypotenuse, cos=adjacent/hypotenuse, tan=opposite/adjacent) to find each component’s value. Calculating the angle will also require this. Let’s try an example! If a 150 N wind is applied to a kite 20 degrees East of North, it’s x component value would be equal to
. There is now a new tension pulling our kite West at 57 N. The ΣFx =
. The only force acting on our y axis is the y value of our East of North wind, making it our total for the ΣFy for this problem. Once you have the net force in both coordinate directions, you can use both values to solve for the total net force. The equation for this is:
. Therefore, the magnitude of the ΣF of our kite example would equal the square root of
. Force is measured in
. Since force is a vector component, it has both a magnitude and a(n)
.