Unit 3: Balanced Force Particle Model Lesson 1: Force, Force Diagrams
Name ______________________________ Date __________
3.1.1 What causes motion?
Your teacher will have a block of wood on the teacher’s desk and ask two students to move the desk
without lifting it off from the table.
After observing this activity, make a list of things that one has to do in order to move an object.
All of the things that will make an object start moving can be written as a “pull” or a “push”. These
represent an interaction between two objects. Force is a physical quantity that characterizes the
interaction between two objects. The two objects are usually in contact during the interaction, with the
exception of objects interacting with very large objects like planets or stars; interactions with magnets;
electrically charged objects and some other rare cases. The unit of measurement of Force is Newton,
which is named after the scientist who studied forces.
3.1.2 Representing Force
Consider an example of you holding a grocery bag in your hand. Identify an object of interest that you
choose to analyze, say the grocery bag. The object of interest that you choose to analyze is also called
“system”. One or more “external objects” interact with the “system”. Make a list the objects that interact
with our system, the grocery bag.
Each interaction between an external object and the system is characterized by a force. For example,
“your hand exerted a force on the grocery bag.” Think of a way to represent each interaction between our
system and the external objects. Is direction important when representing force?
One possible way to represent a force is using an arrow. A diagram that shows all interactions with a
chosen system for analysis is called a force diagram or a free body diagram. The force diagram helps
us to analyze and evaluate processes involving forces.
In order to draw a force diagram, follow the steps listed and shown below.
1. Sketch the situation.
2. Identify and circle the “system” or the object of interest for analysis.
3. Represent the system with a dot.
4. Identify the external objects interacting with the system (ask what’s touching, pulling or pushing the
system?)
5. Show which way is positive for the X & Y axes in your force diagram.
6. Draw a force arrow for each interaction. The length of the arrow is proportional to the magnitude of the
force. The direction of the arrow shows the direction of the force (push or pull). All arrows are drawn
such that the tail of the arrow touches the dot.
7. Label the forces as F subscript external object on system. Use a little arrowhead above F to show that it
is a vector quantity (direction is important).
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Unit 3: Balanced Force Particle Model Lesson 1: Force, Force Diagrams
Name ______________________________ Date __________
HOW TO DRAW A FORCE DIAGRAM or A FREE BODY DIAGRAM
Consider a box on a floor which is being
pulled by a rope.
1. Sketch the situation
2. Circle the object of
interest, the system
5. Show which way
is positive for the Y
axis
Y
3. Draw a dot
representing the
system, the box
4. Identify interactions between
the system and other objects.
Here: Earth, floor, rope and
surface
Use congruent lines to
show equal length arrows
7. Label the
forces
FFloor on Box
=
FRope on Box
=
FEarth on Box
Check for understanding:
What does the length of
an arrow on the diagram
show?
6. Draw force arrows to
represent interactions,
watch the length of arrows
3.1.3 Mathematical Representation
How can we represent the force diagram above with a math statement? Write a math statement for the box
in the above force diagram. Write one sentence for the vertical direction and one for the horizontal
direction.
Remember that only forces in the same direction can be added together! Forces that are not along the
same straight line, can be added using “vector addition”, not by simple addition!
For the force diagram above, adding the forces in the vertical direction gives us:
ΣF y = F floor on box + ( - F Earth on box)
The symbol ( Σ ), read as “sigma”, refers to “the sum of” or “the total” and is found by adding all values
of the variable that follow sigma.
Since the two forces in the vertical direction are equal and in opposite directions, they cancel out,
therefore ΣF y = 0 [N]. In other words, there is no “unbalanced force” or "net force" in the Y direction.
When there is no unbalanced force or no net force on an object, the object is in "equilibrium".
ΣF x = + F rope on box
There is an unbalanced force in the positive X direction in the force diagram above.
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Unit 3: Balanced Force Particle Model Lesson 1: Force, Force Diagrams
Name ______________________________ Date __________
Physicists are interested in finding the “sum of forces” or the “unbalanced force” or the "net force" since
it helps them figure out other variables (that we will see later in this unit.)
3.1.4 Lesson Summary
New Physical Quantity
Unit of measurement
Symbol
New Representation
Mathematical expression
for total force
Force
[Newton] or [N]; Example F person on box = 10 [N]
F external object on system
Force Diagram
ΣF = F object 1on system + F object 2 on system +….
3.1.5 Practice
Write the following interactions using the symbol for force. Also, circle the system and underline the
external object in each sentence.
1. The force exerted by the Earth on Moon.
2. The force exerted by Johnny on ground.
3. The force exerted by ground on Johnny.
4. The force exerted by baseball bat on ball
Write the following interactions in words.
1. F Earth on tennis ball
2. F hand on tennis ball
3. F crane on container
4. F Earth on container
3.1.6 Practice
1. Define the term “force” so someone new to the class will understand what it means from your words.
Page 3 of 4
Unit 3: Balanced Force Particle Model Lesson 1: Force, Force Diagrams
Name ______________________________ Date __________
2. Draw force diagrams for the following situations. Follow the steps listed in the lesson.
Problem
Sketch
List of
objects
interacting
with the
system
1. You are holding a
heavy suitcase. The
suitcase is the object
of interest.
Mathematical sentence
representing the force diagram:
2. A boat floats in the
ocean. The boat is the
object of interest.
Mathematical sentence
representing the force diagram:
3. You are pulling a
sled on fresh snow
horizontally, at
constant velocity. The
sled is the object of
interest.
Mathematical sentence
representing the force diagram:
4. You are pushing a
lawnmower
horizontally at
constant velocity. The
lawnmower is the
object of interest.
Mathematical sentence
representing the force diagram:
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Force diagram