Chapter 4: Newton’s Laws

of Motion [A Tale of Force, Friction and Tension]

4.1. Newton’s Laws of Motion

Force

Force is a push or pull.

Force is a vector – it has magnitude and

direction.

Newton’s First Law of Motion

“An object moving with constant velocity

continues to move at that velocity as long as

no net force acts on it.”

“An object at rest remains at rest as long as

no net force acts on it.”

E.g.: A book does not start moving by itself. A force is

required to make it move.

An object stops moving only if there is friction, which is a

force. (Demonstrate pushing a book and a steel ball.)

Zero velocity is a constant velocity. Hence the first

sentence includes the case of the second sentence.

Also known as the Law of Inertia (“laziness”).

Newton’s First Law of Motion

“An object moving with constant velocity

continues to move at that velocity as long as

no net force acts on it.”

“An object at rest remains at rest as long as

no net force acts on it.”

The “net force” is the vector sum of all forces. The law

says “no net force” because typically more than one force

acts on an object. For example, gravity is acting on all

objects in this room. However a book on a table does

not fall because the table is supporting it i.e. exerting a

force on the book equal and opposite to gravity, resulting

in no net force. Remove the table and the book will fall.

What surfaces have little friction, on which it

can be observed that objects keep sliding at

(nearly) constant velocity?

• Ice

• A wet or oily surface

– Exceptions: a golf ball on wet grass, a hockey

puck on wet ice

• Air hockey table

• Outer space

Inertia

Newton’s Second Law of Motion

“Force equals mass times acceleration.”

Or, equivalently,

The SI units of Force are kg m/s2 = N (Newtons).

Newton’s Second Law of Motion

Newton’s Second Law of Motion

E.g. it takes more force to push a car than a

baby carriage.

Two equal weights

exert twice the

gravitational force of

one.

Example

A 1800-kg car has an acceleration of 3.8

m/s2. What is the force acting on the car?

F = ma

F = (1800 kg)(3.8 m/s2)

F = 6840 kg m/s2 = 6800 N

Newton’s Second Law of Motion

An object may have several forces acting on it. The

net acceleration is due to the net force, determined

by summing the x-, y- and z- components:

Σ Fx = m ax

Σ Fy = m ay

Σ Fz = m az

Newton’s Second Law of Motion

To solve for the acceleration of an object, draw a

free-body diagram which shows (with arrows) the

direction of all the forces acting on that object

only. The forces are considered to act on the

object’s center.

Σ Fx = m ax

Σ Fy = m ay

Σ Fz = m az

Example 2 Moe, Larry and Curly push on a 752-kg boat that floats next

to a dock. They each exert an 80.5-N force parallel to the

dock. (a) What is the boat’s acceleration if they all push in

the same direction? (b) What is the boat’s acceleration if

Larry and Curly push in the opposite direction from Moe?

Answer

Vector Forces in Two Dimensions

The easiest way to add forces in two dimensions

is to (a) choose a coordinate system that

simplifies resolving forces into perpendicular

components, and (b) apply Newton’s 2nd Law

(ΣF=ma) in each coordinate direction separately.

Newton’s Third Law of Motion

“For every action force acting on object 1 by

object 2, there is a reaction force acting on

object 2 by object 1. The action and reaction

forces are equal in magnitude and opposite in

direction.”

Forces always come in pairs. If object 1 exerts a

force F on object 2, then object 2 exerts the force

–F on object 1.

These forces are called action-reaction pairs.

E.g. if you push or pull someone, you both feel

the same magnitude pressure.

Newton’s Third Law of Motion

Some action-reaction pairs:

Newton’s Third Law of Motion

“For every action force acting on object by

object 2, there is a reaction force acting on

object 2 by object 1. The action and reaction

forces are equal in magnitude and opposite in

direction.”

Note: Forces equal in magnitude and opposite in

direction acting on the same object cancel.

However, forces equal in magnitude and opposite

in direction acting on different objects do not

cancel. Both objects will move---unless one is

much more massive, or has other forces acting

on it.

Example 3

Two groups of canoeists meet in the middle of a

lake. After a brief visit, a person in canoe 1

pushes on canoe 2 with a force of 46 N to

separate the canoes. The mass of canoe 1 and its

occupants is 150 kg, and the mass of canoe 2 and

its occupants is 250 kg. What is the acceleration

of each canoe?

Answer

Newton’s Third Law of Motion

Rocket propulsion can also be explained using

Newton’s third law. Combustion causes gases at

high pressure to push on the inside of the rocket.

Because the gases are allowed to exit the tail, the

net force on the

rocket is upward.

Note that the

rocket does not

need the ground

or air to “push”

against; it can

accelerate in

outer space.

The Limits of Newton’s Laws

The Limits of Newton’s Laws

The Limits of Newton’s Laws

• 4.1 Clicker Questions