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Physics Teacher Notes - Grothaus
Chapter 6 – Newton’s Second Law of Motion
Title: Newton’s Second Law of Motion – Force and Acceleration
** An object accelerates when a net force acts on it **
So far, we’ve been talking about equilibrium, when
(dynamic and static equilibrium)
F  0
This chapter we look at what happens when forces aren’t balanced
F  0
Acceleration?? (definition?)
Example: kicked football
Net force is greater than zero so the ball accelerates.
Its path is not linear, it is curved because of gravity
which is also an acceleration
Most motion we see changes. This is accelerated motion.
Remember a 
v
t
We will now look at the cause of acceleration: FORCE
6.1
Force causes acceleration
Unbalanced forces acting on an object cause the object to accelerate.
Ex: hockey puck
The combination of all forces on an object equals net force
What effect does net force have on acceleration?
Guess?
Let’s try it!
Acceleration depends on net force.
In fact, acceleration is directly proportional to the net force
the more force you apply to something, the more acceleration
6.2
(Review proportionality: directly and inversely)
Mass Resists Acceleration
What effect does mass have on acceleration?
Conceptual Physics
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Physics Teacher Notes - Grothaus
Chapter 6 – Newton’s Second Law of Motion
Guess?
Let’s try it.
For a constant force, an increase in the mass will result in a decrease
in the acceleration. (mass is a measure of inertia and inertia resists a
change in motion - acceleration!!)
Ex: empty grocery cart vs. full grocery cart
For a given force, the acceleration produced is inversely proportional to
the mass
6.3
Newton’s Second Law
Newton was the first to realize that acceleration produced when we move
something depends not only on how hard we push or pull, but also on the
object’s mass.
Newton’s second law states that the acceleration produced by a net
force on an object is directly proportional to the magnitude of the net
force, is in the same direction as the net force, and is inversely
proportional to the mass of the object.
If you use Newtons for force (
kg  m
), kg for mass, and m / s 2 for
2
s
acceleration:
a
Fnet
m
One more thing from 6.3:
Fnet  ma
(triangle)
A special case of Newton’s Second:
W = mg
where g is acceleration due to gravity.
Weight is a force (F) and g is acceleration (a)
W = mg is just a specific case of F=ma !!
Examples:
1. An object with a mass of 5.0 kg accelerates 8.0 m/s2 when an unknown
force is applied to it. What is the amount of the force?
Conceptual Physics
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Physics Teacher Notes - Grothaus
Chapter 6 – Newton’s Second Law of Motion
2. An object accelerates 3.0 m/s2 when a force of 6.0 newtons is applied to
it. What is the mass of the object?
3. An object with a mass of 2.0 kg has a force of 4.0 newtons applied to it.
What is the resulting acceleration of the object?
6.4
Friction
Friction acts on materials that are in contact with each other.
(irregularities of surfaces)
Always acts in a direction to oppose relative motion.
(figure 6.5)
Conceptual Physics
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Physics Teacher Notes - Grothaus
Chapter 6 – Newton’s Second Law of Motion
The force of friction between the surfaces depends on the kinds
of materials in contact and how much the surfaces are pressed
together.
Rubber vs. concrete;
steel vs. steel (fig.6.4)
Friction also occurs in liquids and gases.
Both liquids and gases are called fluids because they flow
Fluid friction happens as an object pushes aside the fluid it is moving
through. Try running through waist deep water!
One common type of fluid friction is Air resistance – the friction
acting on something moving through air. (6.7)
Notice this at higher speeds on bike or skiing, etc.
Why is a car designed the way it is?
When friction is present, an object may move with a constant velocity
even when an outside force is applied to it (figure 6.5 again)
Science friction – the science of curling:
https://www.youtube.com/watch?v=miB7HzUvmM0
A diagram showing all of the forces acting on an object is called a freebody diagram
CD 6.1
Science of skydiving: https://www.youtube.com/watch?v=ur40O6nQHsw
(55 m/s = 123 mi/hour; 5m/s = 11)
Phone book friction: (mythbusters)
Vsauce with fast furious and funny – will it lift?
https://www.youtube.com/watch?v=sGBKZO_sEfU
Free body diagrams
6.5
Applying Force – Pressure
See p. 91 (Figure 6.6) - demonstrate on the scale
No matter how you place the book on the scale, the weight (force) is the
same.
Conceptual Physics
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Chapter 6 – Newton’s Second Law of Motion
Physics Teacher Notes - Grothaus
However, if you balance the book on your hand in different ways, you feel
a difference in how the book presses down on your hand. (still same
weight)
Differences in area of contact.
For a constant force, an increase in the area of contact will result
in a decrease in the pressure.
The amount of force per unit area is called pressure.
When the force is perpendicular to the surface area:
P
F
A
Where P = pressure
A = area over which the force acts (units?)
F = force (units?)
This means that P is in
𝑜𝑜 𝑜𝑜𝑜𝑜𝑜𝑜𝑜
What does this mean?
P
F
A
A and P are indirectly proportional
P and F are directly proportional
(in book, notice that symbols are in italic and units are not: m
is meters where m is mass)
Bed of Nails???
https://www.youtube.com/watch?v=dyMaIA2-zGs
6.6
Free Fall Explained
Free fall assumes no air resistance.
2
Accelerates at 10 m / s regardless of mass
Only if air resistance is negligible or if air resistance is
very small compared to the mass of the object
https://www.youtube.com/watch?v=5C5_dOEyAfk (moon)
https://www.youtube.com/watch?v=frZ9dN_ATew (vacuum tube)
Conceptual Physics
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Chapter 6 – Newton’s Second Law of Motion
Physics Teacher Notes - Grothaus
Galileo showed that two objects of different masses hit the ground at
approximately the same time.
Proved Aristotle wrong, but had no idea why this was true
So, why?? Newton’s second law shows why:
Remember mass is proportional to weight Force (W=mg)
on Earth’s surface, 1 kg of mass weighs 10N;
weighs 20 N, etc.
2 kg of mass
10N 1,000N

1kg 100kg
so g = 10 m / s
2
Always! (on Earth)
Textbooks normally represent this as:
F
m
F

m
All freely falling objects fall with the same acceleration because the
net force on an object is only its weight, and the ratio of weight to
mass is the same for all objects.
6.7
Falling and Air Resistance
Let’s leave physics world and jump into the real world for a little bit:
What if we have air resistance?
(fluid friction, air molecules moving out of the way)
A feather and a coin, the coin falls much more quickly than a feather
when there is air.
Conceptual Physics
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Physics Teacher Notes - Grothaus
Chapter 6 – Newton’s Second Law of Motion
Paper and tennis ball demo
Think about it:
Stick your hand out of the window in a moving car.
What happens as you increase speed?
(do it with your see saw)
The faster you go the more resistance so the air
resistance force seems to depend on speed.
Try putting your palm flat against the air and then put it
sideways (parallel to the ground)
(do it with your see saw)
The more surface area, the more air resistance as well.
(ball up the paper)
The air resistance force an object experiences
depends on the object’s speed and surface area.
Physics of skydiving video (55 m/s = 123 mi/hour; 5m/s = 11)
https://www.youtube.com/watch?v=ur40O6nQHsw
Terminal Speed: The speed at which the acceleration of a falling
object is zero because friction balances the weight
If you are concerned with direction (down for falling
objects), you talk about terminal velocity
*****Show free body diagram of what happens
Acceleration vs. Velocity
Terminal velocity is dynamic equilibrium.
A feather reaches terminal velocity quickly – its area is large
compared to its very small weight.
A coin has a relatively small surface area compared to its
weight, so will have a faster terminal speed.
Terminal speed for a sky diver -- 150 to 200 km/hour
What can this depend on?
Parachutes greatly increase air resistance – terminal
speed reduced to about 15 to 25 km/hour
Conceptual Physics
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Chapter 6 – Newton’s Second Law of Motion
Physics Teacher Notes - Grothaus
How could a heavy and a light person descend
together?
CD 6.1
(55 m/s = 123 mi/hour; 5m/s = 11)
** paper and book demonstration
Recap: Galileo / Tower of Pisa
Newton – changed the way of looking at how things are
connected to each other -- acceleration, mass, force
Free body diagram notes:
Type of Force
Gravity / Weight
Fg
N
Characteristics
Always straight down
Normal / Support
FN
N
Perpendicular to the surface
Applied Force
(push, pull, etc.)
Friction
Fapp
N
Ff
N
In the direction of the force (always draw
going away from the object)
Acts against the movement / force
FD
FT
N
Acts against the movement
N
Goes up the rope, string, arms, chain,
etc
Air Resistance
Tension
Conceptual Physics
Symbol
Units
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Chapter 6 – Newton’s Second Law of Motion
Physics Teacher Notes - Grothaus
Net Force
Fnet
N
Sum of all forces
Suggestions for drawing free body diagrams:
 Represent each force with an arrow that points in the direction the force is applied.
Always draw the force vectors pointing away from the object, even when the force is a
push.
 Make the length of each arrow proportional to the size of the force. Often you will draw
these diagrams before you know the magnitudes of all the forces. In such cases, make
your best estimate.
 When forces are supposed to be balanced, make sure it is clear that the magnitudes are
equal. If they are supposed to be unbalanced, make it clear that they are of different
magnitudes.
 Label each force. Use the symbol F with a subscript label to identify the type of force.
Is it moving?
No
static equilibrium – net force is equal to 0 in every direction
Yes
Is it constant velocity?
Yes – dynamic equilibrium – net force is equal to 0 in every direction
No – non-zero net force and there is acceleration
Conceptual Physics
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