Newton

1
Newtons Laws

• The Study of Dynamics

2
Isaac Newton

• Came up with 3 Laws of Motion to explain the
  observations and analyses of Galileo and Johannes
  Kepler.
• Invented Calculus.
• Published his Laws in 1687 in the book
  Mathematical Principles of Natural Philosophy.

3
What is Force?

• A force is a push or pull on an object.
• Forces cause an object to accelerate
• To speed up
• To slow down
• To change direction

4
Newtons First Law

• The Law of Inertia.
• A body in motion stays in motion at constant
  velocity and a body at rest stays at rest unless
  acted upon by an external force.
• This law is commonly applied to the horizontal
  component of velocity, which is assumed not to
  change during the flight of a projectile.

5
The First Law is Counterintuitive
Aristotle firmly believed this. But Physics 1
students know better!
6
A force diagram illustrating no net force
7
A force diagram illustrating no net force
8
A force diagram illustrating no net force
9
A force diagram illustrating no net force
10
Another example illustrating no net force
11
Newtons Second Law

• A body accelerates when acted upon by a net
  external force.
• The acceleration is proportional to the net force
  and is in the direction which the net force acts.
• This law is commonly applied to the vertical
  component of velocity.

12
Newtons Second Law

• ?F ma
• where ?F is the net force measured in Newtons (N)
• m is mass (kg)
• a is acceleration (m/s2)

13
Units of force

• Newton (SI system)
• 1 N 1 kg m /s2
• 1 N is the force required to accelerate a 1 kg
  mass at a rate of 1 m/s2
• Pound (British system)
• 1 lb 1 slug ft /s2

14
The problem of weight

• Are weight and mass the same thing?
• No. Weight can be defined as the force due to
  gravitation attraction.
• W mg

15
Newtons Third Law

• For every action there exists an equal and
  opposite reaction.
• If A exerts a force F on B, then B exerts a force
  of -F on A.

16
Step 1 Draw the problem
Working a Newtons 2nd Law Problem

• Larry pushes a 20 kg block on a frictionless
  floor at a 45o angle below the horizontal with a
  force of 150 N while Moe pulls the same block
  horizontally with a force of 120 N. What is
  acceleration?

17
Step 2 Diagram
Working a Newtons 2nd Law Problem

• Force diagram

• Free Body diagram

18
Step 3 Set up equations
Working a Newtons 2nd Law Problem

• ?F ma
• Fx max
• Fy may

Always resolve two-dimensional problems into two
one-dimensional problems.
19
Step 4 Substitute
Working a Newtons 2nd Law Problem

• Make a list of givens from the word problem.
• Substitute in what you know.

20
Step 5 Solve
Working a Newtons 2nd Law Problem

• Plug-n-chug.
• Calculate your unknowns.
• Sometimes youll need to do kimematic
  calculations following the Newtons 2nd law
  calculations.

21
Gravity as an accelerating force
A very commonly used accelerating force is
gravity. Here is gravity in action. The
acceleration is g.
22
Gravity as an accelerating force
In the absence of air resistance, gravity acts
upon all objects by causing the same
accelerationg.
23
Gravity as an accelerating force
The pulley lets us use gravity as our
accelerating force but a lot slower than free
fall. Acceleration here is a lot lower than g.
24
2-Dimensional problem

• Larry pushes a 20 kg block on a frictionless
  floor at a 45o angle below the horizontal with a
  force of 150 N while Moe pulls the same block
  horizontally with a force of 120 N.
• a) What is the acceleration?
• b) What is the normal force?

25
Flat surfaces 1 D

• N mg for objects resting on horizontal surfaces.

26
Applied forces affect normal force.
friction
applied force
weight
normal
N applied force
27
Elevator Ride going up!
28
Elevator Ride going down!
29
Ramps 2 D
The normal force is perpendicular to angled ramps
as well. Its always equal to the component of
weight perpendicular to the surface.
N mgcos?
30
Ramps 2 D
How long will it take a 1.0 kg block to slide
down a frictionless 20 m long ramp that is at a
15o angle with the horizontal?
N mgcos?
31
Determination of the Coefficients of Friction

• Coefficient of Static Friction
• Set a block of one material on an incline plane
  made of the other material.
• Slowly increase angle of plane until the block
  just begins to move. Record this angle.
• Calculate ?s tan?.

32
Friction

• The force that opposes a sliding motion.
• Enables us to walk, drive a car, etc.
• Due to microscopic irregularities in even the
  smoothest of surfaces.

33
There are two types of friction

• Static friction
• exists before sliding occurs
• Kinetic friction
• exists after sliding occurs
• In general fk lt fs

34
Friction and the Normal Force

• The frictional force which exists between two
  surfaces is directly proportional to the normal
  force.
• Thats why friction on a sloping surface is less
  than friction on a flat surface.

35
Static Friction

• fs ? ?sN
• fs static frictional force (N)
• ?s coefficient of static friction
• N normal force (N)
• Static friction increases as the force trying to
  push an object increases up to a point!

36
A force diagram illustrating Static Friction
Normal Force
Applied Force
Frictional Force
Gravity
37
A force diagram illustrating Static Friction
Normal Force
Bigger Applied Force
Bigger Frictional Force
Gravity
38
A force diagram illustrating Static Friction
The forces on the book are now UNBALANCED!
Normal Force
Frictional Force
Even Bigger Applied Force
Gravity
Static friction cannot get any larger, and can no
longer completely oppose the applied force.
39
Kinetic Friction

• fk ?kN
• fk kinetic frictional force (N)
• ?k coefficient of kinetic friction
• N normal force (N)
• Kinetic friction (sliding friction) is generally
  less than static friction (motionless friction)
  for most surfaces.

40
Determination of the Coefficients of Friction

• Coefficient of Kinetic Friction
• Set a block of one material on an incline plane
  made of the other material.
• Slowly increase angle of plane until the block
  just begins to move at constant speed after
  giving it a slight tap. Record this angle.
• Calculate ?k tan?.

41
Magic Pulleys
m1
m2
42
Pulley problem

• Mass 1 (10 kg) rests on a frictionless table
  connected by a string to Mass 2 (5 kg). Find (a)
  the acceleration of each block and, (b) the
  tension in the connecting string.

m1
m2
43
Pulley problem

• Mass 1 (10 kg) rests on a table connected by a
  string to Mass 2 (5 kg) as shown. What must the
  minimum coefficient of static friction be to keep
  Mass 1 from slipping?

m1
m2
44
Pulley problem

• Mass 1 (10 kg) rests on a table connected by a
  string to Mass 2 (5 kg). If ms 0.3 and mk
  0.2, what is a) the acceleration and b) the
  tension in the string?

m1
m2
45
Tension

• A pulling force.
• Generally exists in a rope, string, or cable.
• Arises at the molecular level, when a rope,
  string, or cable resists being pulled apart.

46
Step 1 Identify the body to analyze.
Working a Newtons Law Problem

• This may not be all that easy!
• It may be a knot, a nail, a hinge, a person, an
  object or a particle.
• It is the focus of your subsequent analysis.

47
Step 2 Select a reference frame.
Working a Newtons Law Problem

• This should be an inertial reference frame which
  may be moving but not accelerating.
• Think of this as a coordinate system with a
  specific origin!

48
Step 3 Make a diagram of forces.
Working a Newtons Law Problem

• Force diagram

• Free Body diagram

49
Step 4 Set up force equations.
Working a Newtons Law Problem

• ?F ma
• Fx max
• Fy may

Always resolve two-dimensional problems into two
one-dimensional problems.
50
Step 5 Calculate!
Working a Newtons Law Problem

• Substitute in what you know into the second law
  equations.
• Calculate unknown or unknowns.

51
Ramp (frictionless)
The normal force is perpendicular to angled ramps
as well. Its usually equal to the component of
weight perpendicular to the surface.
N mgcos?
52
Ramp (frictionless)
What will acceleration be in this situation? SF
ma mgsinq ma gsinq a
N mgcos?
53
Ramp (frictionless)
How could you keep the block from accelerating?
N mgcos?
54
Tension (static 1D)

• The horizontal and vertical components of the
  tension are equal to zero if the system is not
  accelerating.

SF 0 T mg
15 kg
55
Tension (static 2D)

• The horizontal and vertical components of the
  tension are equal to zero if the system is not
  accelerating.

SFx 0 SFy 0
30o
45o
15 kg
56
Tension (elevator)

• When an elevator is still, the tension in the
  cable is equal to its weight.

M
57
Tension (elevator)

• What about when the elevator is just starting to
  head upward from the ground floor?

M
58
Tension (elevator)

• What about when the elevator is between floors?

M
59
Tension (elevator)

• What about when the elevator is slowing at the
  top floor?

M
60
Tension (elevator)

• What about if the elevator cable breaks?

M
61
Pulley problems

• Magic pulleys simply bend the coordinate system.

SF ma m2g (m1m2)a
m1
m2
62
Pulley problems

• Tension is determined by examining one block or
  the other

SF2 m2a m2g - T m2a
SF1 m1a T-m1gsinq m1a
m1
m2
q