Download Force Diagrams

READING: Forces and Motion
DEFINITION: A force is an interaction between 2 objects, usually felt as a push or a pull by those
objects on each other.
Concept #1: An object’s motion can only be described two ways: the object is either Accelerating or in
Equilibrium.
Equilibrium means all the forces acting on that object are balanced, so the object stays at whatever velocity it
already has (zero or some other velocity).
Example 1: A book at rest on a table is in equilibrium. If the table wasn’t strong enough to hold
the book, the book would be accelerating downward because the force downward
would be bigger than the force upward.
Table
Book
Earth
Example 2: A leaf falling at constant speed (terminal velocity) is in equilibrium because the force of gravity
pulling it downward is balanced by the air friction pushing it upward.
Example 3: A person starting from rest and running until she reaches full speed uses traction (friction) to
accelerate. This traction force is unbalanced.
Concept #2 –We can categorize forces in several ways.
I. Some types of forces describe the interaction between objects that are touching each other. Examples of
these types of forces are Friction, Tension, and Normal forces (see below). Other forces such as
electromagnetic forces and gravity can act between objects that aren’t touching each other. These forces act
at a distance. (NOTE: on an atomic scale, it’s hard to define what it means for two different objects to really be “touching” each
other.) Nuclear forces describe interactions between particles in an atom’s nucleus. (We will not be using nuclear
forces in our study of mechanics).
II. In this unit we will be concerned primarily with the following forces. (always an interaction between two
objects):
Ff is the force of Friction –A sticky force. It is always parallel to two surfaces that are touching. This is really
due to the electrons of the atoms of one surface interacting with the electrons of the atoms of another surface.
FN is the Normal force--always perpendicular to two surfaces that are touching. It can be a push or just a
force that supports an object.
Fg is the force of Gravity (also called an object’s weight)- the pull of the earth is always straight towards the
center of the earth (for most of our purposes, this is downward.) Gravity does NOT require the object to be
touching the earth.
FT is a tension force - a pull from something like a rope. This is also due to the electrons between atoms of a
substance attracting each other as the substance is stretched.
Concept #3 - A force diagram is a tool we use to show the interactions between ONE object and all the other
objects in that system. (A system is a group of relevant objects in a situation.)
I. Forces (such as those listed above) are represented by vectors. Vectors are arrows which show what size the
force is (also called its magnitude) and in what direction the force is acting at that instant.
Force arrows are labeled like this example of a weight vector:
The objects are labeled as EARTH on BLOCK (E,B
Fg (E, B)
II. How to draw force diagrams:
1. Draw the object as a dot.
2. List all the other objects in the system. These objects are whatever is touching the object, plus the Earth
if it is in the system (which it usually is in this unit).
3. Match each object with the force it exerts from the list of 4 forces above.
4. Draw the forces as vectors.
5. Label each force with its type and also label the object exerting that force using”by on” notation.
Example: the force of gravity between the earth and a book would be labeled as Fg (E,B)
6. Draw components for forces that are not along an x and y coordinate system.
III. Important ideas about force diagrams:
1. A single force exists between only 2 objects
2. A force diagram shows an instant in time.
3. A force diagram only tells whether the object is accelerating or at constant velocity (including zero), not
what the object’s actual velocity is.
Concept #4 - Forces can be added arithmetically to show whether the object is accelerating or in equilibrium.
I. We can add up (sum) all the forces on an object using the summation symbol ∑ sigma.
∑F means “net force’ which means “sum up all the forces in that coordinate plane”.
 Equilibrium means ∑F = 0 so the object stays at whatever velocity it has (zero or some other velocity)
 Acceleration means ∑F is not equal to 0, so the object accelerates in the direction of the net force.
II. For every force diagram, you can write the net force equation in each direction. For the book in example 1
above :
∑Fx = 0
FN (T, B)
∑Fy = FN + Fg = 0
Fg (E, B)
III. Adding Forces
We can only add forces that are along the same coordinate axis (usually the x or y axis.) Below are two
forces (1 and 2). We CAN’T add force 1 and force 2 together unless we separate FORCE 1 into
components (parts) that are vertical (y) and horizontal (x).
FORCE1
FORCE 2
At the right we have added the vertical
component of force 1 with =
all of force 2
(which only has a vertical component.)
Force 2
Force 1 Y
Net Force
vertical component of FORCE 1
horizontal component
of FORCE 1
Force 1 x
FT
Example: A brick is on a table and is pulled by a rope.
The tension force is drawn with its horizontal and vertical components (dotted lines).
(R,B)
FN (T,B)
F Ty
F Tx
The net force equations are
ΣFx = Ftx < 0 (not equal to zero)
ΣFy = Fty + FN + Fg > 0 (not equal to zero)
Note that only the components of the tension force are in the equation, not the original tension force.
This object is NOT in equilibrium in the x or y directions. The object is accelerating.
The net force is shown as
Fg (E,B)