Classroom Change

1
Classroom Change

• Our class will be in Hamilton Hall 302 from now
  on !

2
Vector Review

• Scalars and Vectors
• Vector Components and Arithmetic

3

• 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.
4
Notation

• Scalars ordinary or italic font (m, q, t . .
  .)
• Vectors - Boldface font (v, a, F . . .)
• - arrow notation
• - underline (v, a, F . . .)
• Pay attention to notation
• constant v and constant v mean
  different things!

5
Coordinate Systems
In 2-D describe a location in a plane
y

• by polar coordinates
• distance r and angle ?
• by Cartesian coordinates
• distances x, y, parallel to axes with
  xrcos? yrsin?
• These are the x and y components of r

( x , y )
r
y
?
x
0
x
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Addition
If A B C , then
Tail to Head
Three scalar equations from one vector equation!
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Newtons Laws of Motion

• Newtons Laws
• Forces
• Mass and Weight

8
Newtons 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
• Force is a vector.
• In Newtons dynamics, all influences on a
  particle from its surroundings are expressed as
  forces exerted on that particle.

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Newtons Second Law

• Fnet (or Ftotal) is the vector sum of all forces
  acting on the particle of mass m
• The acceleration a is parallel to the total
  force, and proportional to it. The
  proportionality constant is the particles mass.
  Newton defines mass as a measure of an objects
  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 the moon, a baseball weighs 0.40 N
On Earth, a baseball weighs 2.40 N
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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

Weights are equal when masses are equal
14
Newtons Third Law (action and reaction)

• If object A exerts a force on object B, object B
  exerts an equal, opposite force back on A.

15
Newtons Third Law examples
What is the reaction to the following forces?
You push on a block
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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?

1. The forces are always equal.
2. The larger wrestler always exerts a larger force.
3. 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
Forces on Block
Examples A heavy block on a table

• The table must push up on the block to prevent it
  from falling
• 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)

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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 contactforce into two
components
!_at_
friction has a more complex behaviour than the
normal force (next lecture)