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Free-Body Diagrams: An Introduction

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Free-Body Diagrams: An Introduction

A couple of basic free-body diagrams.

Andrew Zimmerman Jones
In any problem where you are considering the forces acting on an object - which is a large percentage of the problems in physics - one of the first steps is to create a free-body diagram to depict the situation. Here you will learn what is necessary to create a free-body diagram and apply it toward your physics problem-solving.

What is a Free-Body Diagram?

A free-body diagram is a picture of the physical situation you are analyzing, which depicts all of the relevant forces acting on the objects of interest.

The complexity of the free-body diagram is dependent upon the idealized model you are applying in that situation. In other words, if your model indicates ignoring a force, it shouldn't show up in the free-body diagram.

Forces are vector quantities and should, therefore, be indicated with a magnitude and direction. In the free-body diagram, you can indicate the magnitude of the force either with a variable or numerically, as you prefer for the given situation.

Coordinate Systems & Free-Body Diagrams

When creating a free-body diagram, you must orient it in a coordinate system, typically a two-dimensional one. This is almost always done so that the force of gravity is pulling straight down (in the negative-y direction). It's generally preferred to orient things so that any horizontal movement will be in the positive-x direction (i.e. to the right), although so long as you maintain the same orientation you will get physically identical results.

Some Types of Forces

The majority of forces in free-body diagrams, at least as they relate to classical mechanics, come from the application of Newton's Three Laws of Motion and the Law of Universal Gravitation.

Free-body diagrams of other situations can involve other forces. When creating the free-body diagram of an electron, for example, you would want to include electromagnetic forces acting on it.

Gravitational Force

You will almost always consider the gravitational force, or weight, in a free-body diagram. The magnitude of this force is calculated by mass (m) times the acceleration of gravity (g), typically treated as a constant of 9.8 m/s2 on the Earth's surface.

In the case of an airborn object, such as a basketball player who is jumping, the only force that is typically acting on it while in the air is the weight of the object.

Normal Force

The normal (or perpendicular) force is the contact force the surface an object rests or moves on against the object. It is directed perpendicular to the surface.

In most cases, these surfaces are depicted in a free-body diagram as horizontal, with gravity down, so the normal force is directed upwards and is equal to the total force into the surface.

When you stands on the floor, gravity exerts a force downward and the floor exerts a normal force upward, resulting in a net force of 0. This is why you don't get sucked through the floor by gravity (unless the floor breaks, in which case the normal force ceases to exert itself on you).

If you are standing on a chair, which is in turn resting on the floor, then the chair is exerting a normal force upward to counteract your weight. The floor, however, is exerting a normal force on the chair to counteract the total weight of both you and the chair.

Remember that the total normal force, assuming the surface is solid, will be enough to counteract the net downward force - and no more. If you're pulling at an angle on a rope attached to an object, then you're introducing an upward force. The net downward force will be less, and the normal force will, in turn, have to compensate for less. The normal force never creates a net force upward - that would be like the floor spontaneously throws you into the air.

Frictional Force

An object resting on a surface interacts with the surface. The force of this interaction is the frictional force, or just friction. Friction requires a bit more of an in-depth discussion than what I will present here, but for the moment I will state that friction is:
  • always parallel to the surface the object is interacting with.
  • always in the opposite direction of the force moving an object across the surface.
  • proportional to the normal force.

Tension

Often, free-body diagrams will depict one component of a larger system. When we discuss a man pulling a stone slab with a rope, and we're interested in the motion of the slab, we don't care about all the forces acting on the man. As such, what we really care about is the tension - the force that the rope is exerting on the stone slab. Tension at any point is the magnitude of the force at that point, so tension at the point where the rope meets the object is what we care about.

Final Words

Consider the forces carefully when creating a free-body diagram and you'll find that it's pretty easy. Keep in mind that artwork is irrelevant in this case - you care about the forces, not how good a box or basketball player you can draw. Stick figures work fine.
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