Unit 2 Notes: Newton's Laws of Motion

Unit 2: Newton’s
Laws of Motion and Forces

Laws of Motion

■ formulated by Issac Newton in the late 17th century

■ written as a way to relate force and motion

■ Newton used them todescribe his observations of planetary motion.

History

■ Aristotle was an ancient Greek

philosopher

■ Based on his observations the common belief was that in order for an object to
continue moving, a force must be
exerted in the direction of the motion

■ This lasted until Galileo proposed the idea

of inertia.

■ Then Issac Newton proposed his “Laws of

Motion” based on observations made of
bodies free from earth’s atmosphere.

What is Force?

This Photo by Unknown Author is licensed under CC BY-NC-ND

Mass is…

■ The amount of matter in an

object.

■ Measured in kilograms.

■ NOT a force.

■ The same at any location,

even on another planet.
Not influenced by gravity.

Mass is…

uWe can think of Mass as

a measure of inertia.

uThe more Mass

something has, the more
inertia it has.

A Force is…

■ Measured in Newtons (N) in the

metric (SI) system and pounds
(lbs) in the English system

■ A vector quantity requiring

magnitude and direction to
describe it

■ Represented by drawing

arrows on a diagram

Types of Forces

(that we will study now – there are many

more)

■ Weight - force of gravity

■ Friction - resistance force that opposes

motion

■ Applied force - force you exert, push or

pull

■ Net force – total vector sum of all forces

■ Balanced forces – equal and opposite

forces

■ Unbalanced forces – not equal and

opposite

Newton’s 1st Law

(Law of Inertia)

An object at rest will stay at rest,
and an object in motion will stay in
motion at a constant velocity unless
acted on by an unbalanced or net
force.

This statement contradicted Aristotle’s teaching but
supported Galileo’s idea of inertia. Newton proposed that
there was an unrecognized force of resistance between
objects that was causing them to stop in the absence of an
applied force to keep them moving. This new unseen
resistance force became known as “friction”.

Free-body diagrams

Free-body diagrams are

pictures that show the
size and direction of all
forces acting on an
object.

Steps to drawing a free body

diagram

1. Pick one object to analyze

2. Draw a box to represent the object

3. Draw an arrow to represent each force

acting on the object

4. Make sure the arrow shows the direction and

relative size of the force

Force

Symbol

Definition

Direction

Applied

Force

Fapp

The force beingapplied to an object,
either a push or a pull

Parallel to the
surface and in
the direction of

movement.

Friction

Ff

The contact force that
acts to oppose sliding motion between surfaces

Parallel to surface & opposite direction of sliding

Normal

FN

The contact force exerted by a surface on an object

Perpendicular to & away from the surface

Weight

Fg

A long-range force due to gravitational attraction between two objects

Straight down
toward center

of Earth

Normal Force (FN)

uDefined as the force of a

surface pushing back on an
object.

uAlways directed

perpendicular to the
surface.

uThis is a contact force. No

contact…no normal force.

uNOT always equal to weight.

Examples:

FN

Table

W
a
l l

FN

Draw

Draw the Free Body Diagram for the forces acting on a book sitting at rest on a table.

Draw

An egg is free falling from a nest in a tree. Neglecting air resistance, draw a Free Body Diagram showing the forces involved.

Draw

A flying squirrel is gliding (no wing flaps)
from a tree to the ground at constant
velocity. Consider air resistance. A free
body diagram for this squirrel looks
like…

Draw

A rightward force is applied to
a book at rest, in order to
move it across a desk.
Consider frictional forces.
Neglect air resistance.
Construct a free-body diagram
for the book.

Newton’s 2nd Law
Fnet = ma

If an unbalanced force acts on a
mass, that mass will accelerate in
the direction of the force.

Newton’s 1st Law says that without an unbalanced
force objects will remain at constant velocity
(a=0)…so it seems logical to say that if we apply a
force we will see an acceleration.

2 N

8 N

a

Since 8N is greater than 2N,
the unbalanced force (6N) is to
the right so the acceleration is
to the right.

Dropdown

Which direction will the object move based on the forces acting on the object?​

Select answer

​

Dropdown

Which direction will the object move based on the forces acting on the object?​

Select answer

​

Dropdown

Which direction will the object move based on the forces acting on the object?​

Select answer

Dropdown

Which direction will the object move based on the forces acting on the object?​

Select answer

​

or

u Acceleration and net force are

directly related. If Fnet doubles,
acceleration doubles.

u Acceleration and mass are

indirectly related. If m doubles,
acceleration is half as much.

F=ma

Friction

u A resistance force usually caused by

two surfaces moving past each other.

u Always in a direction that opposes the

motion.

u Measured in Newtons.

u Depends on surface texture and how

hard the surfaces are pressed together.

u Surface texture determines the

coefficient of friction (µ) which has no
units.

u Normal force measures how hard the

surfaces are pressed together.

Types of friction

u Static friction is the force an object must

overcome to start moving. Static means stationary so the object is at rest.

u Kinetic friction is the force an object must

overcome to keep moving. Kinetic means
moving so the object is moving.

Static friction is always greater

than kinetic friction!

May the Net Force be with you

u Net force is the vector sum of all the forces

acting on an object.

u Net force is equal to the mass of an object times

the acceleration of that object. The unbalanced
force referred to in Newton’s Law of Motion

u Net force can be found two ways:

1

2

net

net

F

F

F

F

F

=

+
net

ma

F =

2

20

(3

)

60

net

net

net

F

ma

F

kg

m s

F

N

=

=

=

Net force can be found by finding
the sum of the force vectors or by
mass times acceleration.

Example using mass times acceleration:
Find the net force for a 20 kg object that
is being accelerated at 3 m/s2 .

10 kg

40 N

I have a box weighing 10 kg and I push it with
a force of 40 N.

Math Response

I have a box weighing 10 kg and I push it with a force of 40 N. What is the Acceleration in m/s^2? Use the Up and Right directions as the positive direction and the Down and Left directions as the negative directions.

Type answer here

Correct Answer: 4

Deg^°

Rad

10 kg

40 N

40 N

Two kids are fighting over a box that weighs 10 kg.
Both of them are pulling with a force of 40 N.

Math Response

Two kids are fighting over a box that weighs 10 kg. Both of them are pulling with a force of 40 N. What is the Acceleration in m/s^2? Use the Up and Right directions as the positive direction and the Down and Left directions as the negative directions.

Type answer here

Correct Answer: 0

Deg^°

Rad

5 kg

10 N

3 N

Two kids are fighting over a box that weighs 5
kg. One is pulling with a force of 3 N and the
other is pulling with a force of 10 N

Math Response

Two kids are fighting over a box that weighs 5 kg. One is pulling with a force of 3 N and the other is pulling with a force of 10 N. What is the Acceleration in m/s^2? Use the Up and Right directions as the positive direction and the Down and Left directions as the negative directions.

Type answer here

Correct Answer: 1.4

Deg^°

Rad

Newton’s 3rd Law
Action - Reaction

For every action force there is
an equal and opposite
reaction force.

Example: If you punch a wall with your fist in anger,

the wall hits your fist with the same

force. That’s why it hurts!

Action-reaction forces cannot balance each
other out because they are acting on
different objects. The forces acting on an
object determine their motion.

Think about this…

u How do rockets

work?

Open Ended

Describe how Rockets work in the context of Newton's Third Law of Motion.

Think about this…

u How does jumping

work?

Open Ended

Describe how jumping over the high jump work in the context of Newton's Third Law of Motion.

How about this…

u What happens to you

if you throw a ball?

u What about out in

space?

Open Ended

Describe how throwing a ball work in the context of Newton's Third Law of Motion.

Multiple Choice

Calculate the force of gravity (F) between two objects whose masses are m₁ = 100 kg and m₂ = 1000 kg if they are separared by a distance of d = 500 m.

• 2.67 * 10^-11 N

• 0.4 N

• 6.67 * 10^-11 N

• 1.3 * 10^-8 N

Multiple Choice

Find the distance between two objects whose masses are m₁ = 4,500 kg, and m₂ = 8,700 kg; if the gravitational force between them is F = 2.0 x 10^-8 N.

• 130565.25 m

• 361.34 m

• 0.19575 m

• 0.783 m

Multiple Choice

The larger the mass of an object...

• The smaller the force of gravity.

• The larger the force of gravity.

• Mass has no effect on the amount of gravity an object experiences.

Multiple Choice

As the distance between objects increases...

• The smaller the force of gravity.

• The larger the force of gravity.

• Mass has no effect on the amount of gravity an object experiences.

Multiple Choice

Doubling the distance between two objects...

• ...will double the force of gravity.

• ...will half the force of gravity.

• ...will quadruple the force of gravity.

• ...will quarter the force of gravity.

Multiple Choice

Halving the distance between two objects...

• ...will double the force of gravity.

• ...will half the force of gravity.

• ...will quadruple the force of gravity.

• ...will quarter the force of gravity.

Multiple Choice

I man who weighs 1000N on the surface of the earth will weigh how much at twice the distance in the atmosphere.

• 500 N

• 250 N

• 2000 N

• 4000N

Torque

Torque Definition

u Torque, t, is the tendency of a force to

rotate an object about some axis

u Let F be a force acting on an object,

and let r be a position vector from a
rotational center to the point of
application of the force, with F
perpendicular to r. The magnitude of the
torque is given by

𝜏 = 𝑟 ∗ 𝐹

Units for τ are the N*m
(Newton Meters)

With an Angle

u What if the Force is not neatly perpendicular?

u That’s an easy fix, we just need to add a little trig,

and our equation becomes…

u Where r and F are still the radius and Force, and θ

is the angle the Force is applied.

𝜏 = 𝑟 ∗ 𝐹 ∗ sin 𝜃

Force vs. Torque

u Forces cause accelerations

u What cause angular accelerations ?

u A door is free to rotate about an axis through

Point O

u There are two factors that determine the

effectiveness of the force in opening the door:

u The magnitude of the force

u The position of the application of the force

Math Response

A 16 cm wrench is being rotated with a force of 2 N. What is the
torque in N*m?

Type answer here

Correct Answer: 0.32

Deg^°

Rad

Math Response

A door requires a Torque of 180 N*m to open. What is the minimum distance in meters you need to be to open the door if you are applying a force of 200 N?

Type answer here

Correct Answer: 0.9

Deg^°

Rad

Math Response

What is the minimum force in Newtons required to open a door if it is 1.5 m wide and requires 100 N*m of torque?

Type answer here

Correct Answer: 66.67

Deg^°

Rad