If you’re feeling a little perpendicular tonight…

…or, Freebody Diagrams: Part One.

How does a 27-year-old science enthusiast amuse herself on a Saturday night? By doing things like this:

Tiny Einstein is always watching.

So what on Earth is this? (Besides evidence that I’ve really got to get out more…) This is an elaborate photographic representation of a freebody diagram, which is a visual tool that you can use to analyze the forces acting on an object. In a freebody diagram, you draw arrows to represent the strength and direction of all the forces acting on an object. The standard introductory freebody diagram has four forces in it:

  • Earth’s gravitational force: We recently talked about how there’s a gravitational force between any two objects, but generally the only significant one comes from Earth pulling down on an object. The force due to Earth’s gravity is often called weight.
  • Normal force: An object is usually resting on some sort of surface,  and that surface is pushing up on the object. Here, the world normal means “perpendicular to the surface”; it is not intended to imply that other forces are strange in any way.
  • Some kind of applied push/pull: Every force is either a push or a pull; the situations usually described by freebody diagrams involve some kind of horizontal push or pull applied by a dog, horse, person, etc.
  • Friction: Friction is a force that results from two surfaces rubbing together, and it always opposes the direction of motion (or, in the case of a stationary object, the intended direction of motion). The strength of a frictional force depends on what surfaces are involved. You know this from experience: an icy sidewalk has a lot less friction than a non-icy sidewalk.

Without thinking about numbers (because it’s late and there’s plenty of time to be quantitative in Freebody Diagrams: Part Two), let’s stick all of these forces into a freebody diagram of a Standard Physics Box. Note that every force can be qualitatively described as “something pushes/pulls box”; if a force can’t be described that way, then it’s not acting on the box and doesn’t belong in the diagram.

Click to enlarge.

Recall from the Physics Ninja series (which will be finished soon!) that the net force on an object is the sum of all the forces acting on it, taking into account the direction of each force. Even without numbers, it’s apparent from the arrows in our diagram that the vertical forces cancel each other out and the horizontal forces cancel each other out, resulting in a net force of zero. If the net force on the box wasn’t zero, then it would be accelerating: speeding up, slowing down, or changing direction. Since the net force on the box is zero, does it mean the box is not moving? Not necessarily, and that’s a sticking point for a lot of physics students. When the net force on an object is zero, it is not accelerating: the box could be stationary, but it could also be moving at a constant speed without changing direction.

That point is a little non-intuitive because we very rarely see an object with a zero net force that isn’t at rest. Even a bowling ball rolling down a very smooth hallway has a tiny bit of friction acting on it, resulting in a non-zero net force that will eventually slow it to a stop.

However, some of the finer points of a freebody diagram are completely in line with our everyday observations.

Consider the normal force and the chair you’re sitting on. If the normal force of the chair pushed up on you more than Earth pulled down on you, what would your motion look like? If the normal force of the chair pushed up on you less than Earth pulled down on you, what would your motion look like? Since neither of these things are happening, what does the normal force have to be relative to your weight?

Now consider friction. When you push on an object, friction pushes back. Short of tripping over your own feet, have you ever pushed forward on an object and then accelerated backwards? Can friction ever push harder than you do?


3 thoughts on “If you’re feeling a little perpendicular tonight…

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