SPH3U1
Lesson 01
Dynamics
DYNAMICS
LEARNING GOALS
Students will learn that
 Forces are vector quantities.
 Free-body diagrams are used to analyze forces.
 A net force results from the addition of all forces acting on an object.
THE “WHY” OF MOTION
Mechanics is a branch of physics that is made up of both kinematics and dynamics. While
kinematics describes an object’s motion using displacement, velocity, and acceleration,
dynamics, the “why of motion”, describes “why” objects move the way they do.
FORCES
A force is a push or a pull acting on an object. Applying a force to an object does not
always result in movement. Opposing forces might cancel the applied force. Force is a
vector quantity and therefore has both magnitude and direction. A force can change the
shape and/or the velocity of an object. To deform an object and keep it stationary, at least
two forces are necessary.
The symbol for force is ⃑ and the SI unit is the newton, N. One newton is the amount of
force required to accelerate a 1-kg object at 1 m/s2 (1 N = 1
).
Contact forces are forces that are in direct contact with an object. Your desk is in direct
contact with your books.
Non-contact forces act over a distance, such as two magnets attracting or repelling each
other without touching.
COMMON FORCES
Gravitational Force is an attractive force between any two masses acting at a distance
(non-contact). Any two masses exert a mutual gravitational attractive force on each other.
Two tennis balls will have gravitational forces acting between each other from their centres
of mass but you will not notice this force as gravitational forces are relatively weak.
Weight is the force of gravity acting on a mass. This is dependent upon the acceleration
due to gravity which is given the variable g. There exists different values of g for different
planets and different heights above the centre of the planet.
Normal Force, ⃑ , is a force exerted by any surface on any object in contact with the
surface. The force is perpendicular to the common surface between two objects (normal
means perpendicular).
Friction, ⃑ , is the force that acts parallel to the common surface, in the direction opposite
to the direction of motion.
Applied Force, ⃑
, is a force acting on an object.
Tension Force, ⃑ , is a pulling force acting on a cable or rope.
Page | 1
SPH3U1
Lesson 01
Dynamics
FREE-BODY DIAGRAMS
A free-body diagram is a sketch of a solitary object showing only
forces acting on that object. Force vectors are drawn with their
tails meeting a common point. This does not mean that this
point is where the forces actually act on the object. Each freebody diagram requires a legend indicating the positive direction.
Gravity, ⃑ , always points toward the centre of the Earth. The
length of the vector represents the magnitude of the force.
Draw a free-body diagram for the forces acting on the pail in the
pictorial representation to the right. The free-body diagram starts
with a square and the forces are drawn outwards from a point
representing the centre of mass.
EXAMPLE 1: FREE-BODY DIAGRAM OF A MOVING CAR
A car experiencing a gravitational force of 10 000 N [down] is coasting on a level road. The
car experiences a normal force of 10 000 N [up], a force of air resistance of 2500 N
[backward], and a force of friction exerted by the road on the tires of 500 N [backward].
Draw a free-body diagram for this situation.
While the car is
coasting there is no
forward force acting
on it and the freebody diagram
shows only 4 forces
acting on it.
The picture shown is a pictorial representation.
Page | 2
SPH3U1
Lesson 01
Dynamics
ATTACK OF THE FREE-BODY DIAGRAMS!
1. A book is at rest on a tabletop. Diagram the forces acting on the book.
2. A girl is suspended motionless from the ceiling by two ropes. Diagram the forces acting on
the girl.
3. An egg is free-falling from a nest in a tree. Neglect air resistance. Diagram the forces acting
on the egg as it is falling.
4. A flying squirrel is gliding (no wing flaps) from a tree to the ground at constant velocity.
Include air resistance and diagram the forces acting on the squirrel.
5. A rightward force is applied to a book in order to move it across a desk with a rightward
acceleration. Consider frictional forces. Neglect air resistance. Diagram the forces acting on
the book.
6. A college student rests a backpack upon his shoulder. The pack is suspended motionless by
one strap from one shoulder. Diagram the vertical forces acting on the backpack.
7. A skydiver is descending with a constant velocity. Consider air resistance. Diagram the forces
acting upon the skydiver.
8. A force is applied horizontally to the right to drag a sled across loosely packed snow with a
rightward acceleration. Diagram the forces acting upon the sled.
9. A football is moving upwards towards its peak after having been kicked by the punter.
Diagram the forces acting upon the football as it rises upward towards its peak.
10. A car is coasting to the right and slowing down. Diagram the forces acting upon the car.
11. A hammer is falling on the moon. Diagram the forces acting upon the hammer before it hits
the ground.
12. A planet is in orbit around the sun. Diagram the forces acting on the planet.
13. A ball experiencing forces of 45 N [up], 60 N [down], and 80 N [up] simultaneously.
14. A plane flying horizontally with its engine exerting a thrust of 1400 N [E] against some air
resistance of 700 N [W].
15. A diver gently falling through water with a downward force of 800 N against the force of
buoyancy of water of 650 N.
BALANCED AND UN-BALANCED FORCES
Consider a physics book resting on a tabletop. There are two forces acting upon the book.
One force - the Earth's gravitational pull - exerts a downward force. The other force - the
push of the table on the book (normal or support force) - pushes upward on the book.
Page | 3
SPH3U1
Lesson 01
Dynamics
Since these two forces are of equal magnitude and in opposite directions, they balance each
other. The book is said to be in equilibrium. There is no unbalanced force acting upon the
book and thus the book maintains its state of motion. When all the forces acting upon an
object balance each other, the object will be in equilibrium; it will not accelerate.
Now consider a book sliding from left to right across a tabletop. Sometime in the prior
history of the book, it may have been given a shove and set in motion from a rest position.
Or perhaps it acquired its motion by sliding down an incline from an elevated position.
Whatever the case, our focus is not upon the history of the book but rather upon the
current situation of a book sliding to the right across a tabletop. The book is in motion and
at the moment there is no one pushing it to the right .
The force of gravity pulling downward and the force of the table pushing upwards on the
book are of equal magnitude and opposite directions. These two forces balance each other.
Yet there is no force present to balance the force of friction. As the book moves to the right,
friction acts to the left to slow the book down. There is an unbalanced force; and as such,
the book changes its state of motion. The book is not at equilibrium and subsequently
accelerates.
Unbalanced forces cause accelerations.
In this case, the unbalanced force is directed opposite the book's motion and will cause it to
slow down.
To determine if the forces acting upon an object are balanced or unbalanced, an analysis
must first be conducted to determine what forces are acting upon the object and in what
direction. If two individual forces are of equal magnitude and opposite direction, then the
forces are said to be balanced. An object is said to be acted upon by an unbalanced
force only when there is an individual force that is not being balanced by a force of equal
magnitude and in the opposite direction.
MEASURING FORCE USING A SPRING SCALE
PURPOSE
To determine how the amount of stretch of a calibrated spring is related to the magnitude of
the force acting on an object.
MATERIALS



set of standard masses with hooks
spring scale (0–10 N)
retort stand with hook arm or test-tube clamp
Page | 4
SPH3U1
Lesson 01
Dynamics
PROCEDURE
1. Create a table to record the masses attached to the spring and the magnitudes of
the gravitational and elastic forces acting on the masses.
2. Hang the spring scale from the arm on the retort stand. Make sure the pointer reads
zero.
3. Gently suspend a 100-g standard mass from the spring scale. Record the reading of
the scale.
4. Hang additional masses from the spring scale, up to a total mass of 1000 g. Each
time, record the mass and the magnitudes of the corresponding gravitational and
elastic forces.
5. Draw a graph of the data you collected in your table with mass as the independent
variable and Force as the dependent variable.
EXTENSION QUESTIONS
1.
What was the reading on the spring scale when the 100-g mass was attached?
2.
What happened to the stretch of the spring when the mass of the object attached to
the spring scale
doubled?
tripled?
increased by a factor of 10?
3.
Why is a spring scale useful for measuring force?
4.
Find the line of best fit on your graph. What does this represent? (Hint: find the
units of the slope based on the units of your independent and dependent variables.)
USING FREE-BODY DIAGRAMS TO FIND NET FORCE
The existence of an unbalanced force will cause an object's motion to change, whether it is
already in motion or at rest. The unbalanced force refers to that force that does not
become completely balanced (or cancelled) by the other individual forces. If either all the
vertical forces (up and down) and/or all horizontal forces do not cancel each other, then
an unbalanced force exists.
Free-Body Diagrams (FBDs) can be used to identify the existence of an unbalanced force.
Draw an FBD for a sled being pulled across the snow in a horizontal direction with a
horizontal applied force of 20 N and a friction force of 10 N.
The net force, ⃑ , is the vector sum of all the forces acting on an object at one instant in
time. The magnitude and direction must be considered when determining the net force.
Parallel vectors are collinear even if they point in opposite directions.
Find the sum of the forces in the x-direction, ⃑ (horizontal), and the sum of the forces in
the y-direction, ⃑ (vertical), for the sled above.
Page | 5
SPH3U1
Lesson 01
⃑
Dynamics
⃑
The pulling force acting on a cable or rope is called the
tension force, ⃑ .When considering tension forces, we
assume the rope or cable has no mass, no thickness and
does not stretch.
EQUILIBRIUM RULE
When an object is stationary, it is said to be in equilibrium.
All forces are balanced in both the x-direction and the ydirection. The scaffold below has the weights of the workers
acting on it as well as gravity acting down while the two
ropes exert tension forces upwards. These forces all
balance if the scaffold is stationary.
⃑
⃑
This soldier is rappelling from a
helicopter. There is considerable
tension force on the rope from
which he is suspended.
EXAMPLE 1: FINDING THE NET FORCE
Two people are dragging a canoe out of a lake onto a beach using light ropes (Figure 4.8).
Each person applies a force of 60.0 N [forward] on the rope. The force of friction exerted by
the beach on the canoe is 85.0 N [backward]. Draw a free-body diagram of the canoe, then
calculate the net force on the canoe.
Page | 6
SPH3U1
Lesson 01
Dynamics
WEIGHT VS. MASS
The weight of an object is defined as the force of gravity exerted by the earth on the
object. Weight is a force and has a unit of newtons (N).
Most people use the word weight incorrectly. When you ask someone how much they
weigh, you are really asking for their mass. The mass of an object is a measure of the
amount of matter in an object. What you should really ask a person is, “How massive are
you?”
EXAMPLE 2: STANDING ON A SCAFFOLD
When Burl stands alone in the exact middle of his
scaffold, the left scale reads 500 N. Fill in the reading
on the right scale in the first picture.
The total weight of Burl and the scaffold must be
______________ N.
Now fill in the missing forces in the right scale in the
second and third diagrams.
Page | 7
SPH3U1
Lesson 01
Dynamics
ADDING THE FORCES
For each FBD below, determine the net force acting upon the object.
𝐹⃑𝑁
2 N
𝐹⃑𝑓
𝐹⃑𝑁
3N
5N
𝐹⃑𝑔
2 N
𝐹⃑𝑔
3N
𝐹⃑𝑇
4 N
𝐹⃑𝑁
3N
𝐹⃑𝑓
5N
𝐹⃑𝑎𝑝𝑝
3N
𝐹⃑𝑔 3 N
In the
following
, the net force is provided for each FBD; however, the magnitudes of some of the forces
acting on the object are unknown. Analyze each FBD to determine the magnitude of the
unknown forces.
𝐹⃑𝑔
𝐹⃑1
𝐹⃑2
25 N
?
𝐹⃑𝑛𝑒𝑡
?
𝐹⃑𝑛𝑒𝑡
9
N [up]
?
𝐹⃑4
𝐹⃑3
𝐹⃑1
5 N
3N
𝐹⃑2
?
𝐹⃑𝑛𝑒𝑡
𝐹⃑2
𝐹⃑1
N
𝐹⃑1
6 N [down]
2 N
𝐹⃑2
𝐹⃑2
𝐹⃑3
N
2
3
N
N
𝐹⃑𝑛𝑒𝑡
3 N [ri ht]
8 N
?
𝐹⃑3
𝐹⃑4
?
?
Page | 8