Force Diagrams (A.K.A. "Free-Body Diagrams")



Force diagrams, also known as "free-body" diagrams, are diagrams which display the magnitude and direction of forces acting on a single, isolated body. This single body is also known as a "free" body, hence the name. They assist in being able to determine the magnitude or direction of other forces in problem-solving situations which require such information without having to reference the objects creating the forces.

All forces on a force diagram are non-contact or contact. The only non-contact force there is is Fg (force of gravity). The core contact forces are Ff (friction), Fn (normal force), and Ft (tension force).

The first step to drawing a force diagram is by drawing a point to represent our free body. Be sure to provide ample space surrounding the point for future steps, and while this is just a point, do not forget the object's placement in reality as we'll need to reference it later.


H_PHYSICS1.PNG
The next step is to begin drawing our forces. We'll begin with our most obvious known force, which is most often a normal or gravity force. We'll start with gravity here. It is displayed as a vector leading from the point in the direction the force is affecting the object. Gravity is a downward vertical force on the object, so that is how we'll draw it.
H_PHYSICS2.PNG
Gravity is ALWAYS present in any force diagram that takes place on Earth, but is not always a vertical, downward force. Though if the object is placed on a ramp, and gravity is pulling it at an angle, the force is displayed vertically on a diagram, at least to begin with.

Next, we'll draw the other forces. This particular object does happen to be on a (frictionless) ramp with a rope keeping it from sliding downwards. It is not moving, there is no acceleration in any direction, so all forces should be equal, as Newton's Laws of Motion have taught us. If we step back, we'll now see that the forces in the diagram should be:
- Ft - a tension force from the rope
- Fg - a gravity force from the earth
- Fn - a normal force from the ramp
We'll draw them in the same fashion as the gravity force above.
H_PHYSICS4.PNG
Now, all forces should be parallel or perpendicular if they're all equal. You can see that the normal force is perpendicular to the tension force. It all makes sense if you imagine it visually:
H_PHYSICS5.PNG
But once you imagine it realistically, the gravity doesn't make sense (though it is correct at this stage!). In reality, gravity would be pulling the object down the ramp, so we'll have to dissect the force, in order for it to make sense. We now have an "x" and "y" component for or gravitational force. (Note: vectors are always decomposed based on the normal force-- this is much easier in the long run!)
H_PHYSICS6.PNG

Fgx has to be equal to Ft because the object is not accelerating because there is no net force. Fgy and Fn have to be equal as well. Sometimes decomposition of vectors requires right angle trigonometry. This may be daunting at first but will soon become second nature.

sCIENCe.JPG
Now let's see what happens when we add another force. Let's say the ramp the object is on is covered in carpet, making it harder for the object to move. This is obviously a significant force so we'll have to write it down. Since it is acting against the direction the object is moving in, we'll draw it in the oposite direction of gravity x. Since there is already a tension force there, we'll add it on top as another extended arrow in green. Fun fact: the length of an arrow usually determines the magnitude, or size of the force. Friction is a minimal force so its arrow is small.
Capture.PNG

Now that you have all your vectors, all that's left is to label them! If any of the object's forces are equal, you will show this with a small hash mark. Any vector with the same amount of hash marks as another will be equal to that one, no matter its size.
Some quick tips to find out magnitudes can be drawn from previous physics knowledge. Fg will always be mass x gravity, a.k.a. mass x 9.81. Once you've found out your Fg, you can utilise other factors to use trigonometry to solve for other forces. In the diagram we've made, you could use an angle and the Fg to solve for either the x or y of the gravity force using right triangle equations such as sine, cosine or tangent.