Newton’s Laws of Motion

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Transcript Newton’s Laws of Motion

Classroom Change
Our class will be in
Hamilton Hall 302
from now on !
Physics 1D03 - Lecture 6
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Vector Review
• Scalars and Vectors
• Vector Components and Arithmetic
Physics 1D03 - Lecture 6
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Physical quantities are classified as scalars, vectors, etc.
Scalar : described by a real number with units
examples: mass, charge, energy . . .
Vector : described by a scalar (its magnitude) and a direction
in space
examples: displacement, velocity, force . . .
Vectors have direction, and obey
different rules of arithmetic.
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Notation
•
Scalars : ordinary or italic font (m, q, t . . .)
•
Vectors : - Boldface font (v, a, F . . .)
  
- arrow notation ( v, a, F . . .)
- underline (v, a, F . . .)
•
Pay attention to notation :
“constant v” and “constant v” mean
different things!
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Coordinate Systems
In 2-D : describe a location in a plane
y
• by polar coordinates :
(x,y)
distance r and angle 
r
y
• by Cartesian coordinates :

0
x
x
distances x, y, parallel to axes
with:
x=rcosθ y=rsinθ
These are the x and y components of r
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Addition:
If A + B = C ,

A
Ay
Ax

B
By
Bx
then:
Cx  Ax  Bx
Tail to Head
Cy  Ay  By

B

C
Cz  Az  Bz
Three scalar
equations from one
vector equation!
Cy
Bx

A
Ax
By
Ay
Cx
Physics 1D03 - Lecture 6
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Newton’s Laws of Motion
• Newton’s Laws
• Forces
• Mass and Weight
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Newton’s First Law (Law of Inertia)
An isolated object, free from external forces, will
continue moving at constant velocity, or remain at rest.
Earlier, Aristotle said objects were “naturally” at rest, and needed a
continuing push to keep moving.
Galileo realized that motion at constant velocity is “natural”, and
only changes in velocity require external causes.
Objects in equilibrium (no net external force) also move
at constant velocity.
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Forces
• A force is a push or pull that tends to cause motion
(more exactly, changes in motion)
• From the Second Law, force should have units of
1 kg  m/s 2  1 newton (N)
• Force is a vector.
• In Newton’s dynamics, all influences on a particle
from its surroundings are expressed as forces
exerted on that particle.
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Newton’s Second Law


Fnet  ma
Fnet (or Ftotal) is the vector sum of all forces acting on the
particle of mass m:



Fnet   Fi   mai
i
i
The acceleration a is parallel to the total force, and proportional
to it. The proportionality constant is the particle’s mass.
Newton defines mass as a measure of an object’s inertia.
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Contact Forces : direct contact is required
examples - normal forces, friction, air resistance,
buoyancy, ...
Non-Contact Forces :
gravity, electromagnetic, weak and strong forces
The gravitational force is also called weight and is
measured in Newtons.
Weight is proportional to mass : Fw = mg, where g is the
gravitational field (and is also the acceleration of an object
in free fall).
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Weight and Mass
Weight is a force; it can be measured using a spring scale
On Earth, a baseball
weighs 2.40 N
On the moon, a
baseball weighs 0.40 N
Physics 1D03 - Lecture 6
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•
Mass is a measure of inertia : on the earth or on the moon, a
24.5 N force applied to the baseball will give it an acceleration of
100 m/s2 (its mass is m = F/a = 0.245 kg)
•
We can compare masses with a balance, because of the
remarkable property :
weight  mass
Weights are equal
when masses are
equal

Fg ,1

Fg,2
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Newton’s Third Law (action and reaction)
If object A exerts a force on object B, object B
exerts an equal, opposite force back on A.
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Newton’s Third Law : examples
What is the “reaction” to the following forces?

Fg

 Fg
Gravity (of block)
pulls earth up
Block pushes down on table
You push on a block
Balloon pushes on
air outside
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Quiz
A 140-kg wrestler and a 90-kg wrestler try to push each other
backwards out of the ring. At first they are motionless as they push;
then the large wrestler moves the other one backwards. Compare the
forces they exert on each other. Which statement is correct?
a) The forces are always equal.
b) The larger wrestler always exerts a larger force.
c) When they are motionless, the forces are equal; they start to
move when the large wrestler exerts a larger force on his
opponent than his opponent exerts back on him.
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Contact Forces
Examples : A heavy block on a table
• The table must push up on the
block to prevent it from falling
Forces on Block

Fg
• The type of contact force is
called a normal force if it is
perpendicular (normal) to the
surfaces in contact.
• The normal force will be as large
as necessary to hold the block
(until the table breaks)

Ftable
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If we look closely, the normal force
arises from the table being bent :
as the table tries to straighten, it
pushes back.
This is really an elastic force; the table behaves like a
spring.
At the atomic level, all contact forces are due to
electromagnetic forces.
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We divide the contact
force into two
“components”

Fg

FA

f

n

- normal force : n is perpendicular to the surfaces
in contact

- friction : f is parallel to the surface
friction has a more complex behaviour than
the normal force (next lecture)
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