Physics 30S – Free Body Diagrams
Free body diagrams (otherwise known as FBD's) are simplified
representations in a problem of an object (the body), and the force vectors
acting on it. This body is free because the diagram will show it without its
surroundings; i.e. the body is 'free' of its environment. This eliminates
unnecessary information, which might be given in a problem.
Let's take this figure to be a pictorial representation of a situation: a sled on snow, with horses
pulling it. First we will represent the sled (the 'body' in our problem) as a (really) simplified
figure, a square resting on a flat surface.
In this tutorial, we will review some of the main forces which you
will encounter in physics, and discuss their contribution to an FBD.
Gravity
Normal Force
Friction
Push or Pull
Gravity
The first force we will investigate is that due to gravity, and we'll
call it the gravitational force. We know that the acceleration due to
gravity (if on Earth) is approximately g = 9.8 m/s2. The force, by
Newton's Second Law is
Fmg = Fw
Fg = m g
where g is the acceleration due to gravity and m is the mass of the carriage. Let's add this to our
diagram.
Note that the force vector, labelled Fg (or Fw), points downward, as this is the direction in which
the gravitation force acts.
Note also that this force is commonly called “weight”. This 'weight' (mg) is different from our
everyday use of the word 'weight' (which is known in physics as 'mass').
Normal
The normal force is one that prevents objects from 'falling' into whatever it is they are sitting
upon. It is always perpendicular to the surface with which an object is in contact. For example, if
there is a crate on the floor, then we say that the crate experiences a normal force exerted by the
floor; and because of this force, the crate does not fall into the floor. The normal force on the
crate points upward perpendicular to the floor.
It is called the normal force because “normal” and “perpendicular” mean the same thing.
The normal force is always perpendicular to the surface with which a body is in
contact. For a body on a sloping surface (say a ramp) the normal force acting on
body is still perpendicular to the slope.
FN
Fmg = Fw
Let's add the normal force to our FBD
represent the normal force with the letter FN.
FN
that
and
Physics 30S – Free Body Diagrams
Friction
Related to the normal force is the frictional force. The two are related because they are both due
to the fact that the body is in contact with the surface. Whereas the normal force was
perpendicular to the surface, the frictional force is parallel. Furthermore, friction opposes motion,
and so its vector always points away from the direction of movement.
Friction is divided into two types-static and kinetic. These are represented by Ff, with a
further subscript 's' for static friction, and a subscript 'k' for kinetic friction. As its name suggests,
static friction occurs when the body is not moving with respect to the surface. It is the force that
makes it difficult to start something moving. On the other hand, kinetic friction occurs when the
body is sliding over the surface. (Of course rolling objects experience friction as well.) This is
the force that causes objects to slow down and eventually stop. Friction is usually approximated
as being proportional to the normal force. The proportionality
constant is called the coefficient of (static or kinetic) friction.
FN
The coefficient is represented as s for static friction, and k for
Ff
kinetic friction; the numerical value of  depends on the nature
of the surface with which the body is in contact.
We've added (kinetic) friction to our free body diagram.
Fmg = Fw
Push and Pull
Another force that may act on an object could be any physical push or pull. This could be caused
by a person pushing a crate on the floor, a child pulling on a wagon, or in the case of our
example, the horse pulling on the carriage.
We will label the applied push (or pull) force with Fa – Applied Force
Tension
Tension in an object results if the pulling force acts on its ends, such as in a rope used to pull a
boulder.
If we say that our carriage is being pulled by a bar (by
the horse) at its front end, then we can add this force to
Ff
our FBD.
FN
Fa
And there we have it: all the forces acting on our
carriage have been labeled in this figure. This is the
Fmg = Fw
complete FBD for our problem of a carriage being
pulled along a road.
EXAMPLE 1: The Sled
Question
The child next door wants to take his German Shepherd
(named Spot) for a ride on his sled. He chases Spot (who is
Physics 30S – Free Body Diagrams
running away) while dragging his sled behind him. What forces are acting on the sled?
Hints
The forces we discussed were:
1. gravity
2. normal
3. friction
4. push or pull
Solution
Let's consider each of the above forces in turn.
1. Since the question does not state otherwise, we will assume that this is all happening on Earth.
So gravity is a force acting on the sled. The gravitational force, Fmg, vector points downward.
2. The sled is being dragged on the ground, which we can take to be another surface. This
surface exerts a force on the sled, preventing it from
falling into the ground. Thus there is a normal force N
on the sled.
3. Because the sled is in motion, and the surface with
which it has contact (i.e. the ground) is not frictionless
then there is kinetic friction.
4. The child is pulling on the sled, and so there is a pull
force, Fpull. The pull may not be parallel to the ground
but at an angle as shown in the drawing.
EXAMPLE 2: Dot and Spot
Question
Spot, the German Shepherd, is being walked by his best pal, Dot, the Siamese cat. Actually, Dot
is pulling Spot across the ice rink, and disturbing the neighbourhood hockey game. What are the
forces acting on Spot?
Solution
Since this is taking place on Earth, we can assume a gravitational force Fmg on Spot.
Also, because Spot is on the surface of the
ice is exerting a normal force N on him.
We assume that ice is frictionless, and so
static friction nor kinetic friction acts on
(which he probably appreciates).
The push/pull force may be misleading.
is true that Spot is being pulled along by
is not the force acting on Spot. This is
Dot is actually pulling on the rope. The
turn through its tension T, exerts a force on
EXAMPLE 3: King Kong's Pendulum
Question
ice, the
neither
Spot
While it
Dot, this
because
rope, in
Spot.
Physics 30S – Free Body Diagrams
While climbing the Empire State Building, King Kong peaks into one of the corporate windows,
and sees a poster with Tarzan swinging from a vine. Our furry friend decides he'd much rather be
swinging from vines instead of hanging outside of skyscrapers When King Kong is swinging
from a vine, what forces are acting on him?
Solution
1. We assume that King Kong has travelled to the
jungles on Earth, so he still experiences the Earth's
gravitational force, Fmg.
2. The overgrown gorilla is not in contact with any
surface, so there is no normal force.
3. Again, he is not in contact with any surface, so
neither static friction nor kinetic friction is exerted on
him.
4. No one or thing is pushing or pulling on King Kong (and who or what would want to?), but
there is a tension T in the vine holding him up.
EXAMPLE 4: The Elevator
Question
Our furry friend, King Kong, has had enough of
monkey-ing around, and has returned to the Big
Apple. Once again he is up to his tricks with
the Empire State Building. Only this time, he has
taken the elevator instead. While he is riding up to
the top of the building (at a constant speed), what
forces are acting on him?