The Ordered Universe

1
The Ordered Universe

• Part 3
• Some Calculations

2
Check Prior Knowledge

• Summarize the contributions made by Galileo and
  Newton
• Distinguish between speed, velocity, and
  acceleration
• What are the three laws of motion
• Heavy objects fall faster than light ones. True?
  False? Depends?

3
Mechanics

• --branch of science that deals with motion of
  material objects
• It was not until the 17th century that our modern
  understanding of motion began to emerge.

4
Galileo Galilei (1564-1642)

• Math professor
• Forerunner to modern scientist
• Inventor
• Whats he famous for?

5
Galileo Father of Experimental Science

• At the surface of the earth, all objects speed up
  at the same rate as they fall downward.

6
Analyzing falling objects

• 2 variables distance and time
• Galileo devised an inclined plane to slow motion
  down for study.
• To understand Galileos results, you have to
  distinguish speed, velocity, acceleration.

7

• Speed is the distance an object travels divided
  by the time it takes to travel that distance.
• Speed distance / time
• S d / t
• Velocity is same numerical value as speed, but
  velocity always includes direction of travel.

8
What is the Speed of a race horse that runs 1500m
in 2 minutes?

• S d / t
• S 1500m / 2 min S 750 m/min
• S 1500m / 120 sec
• S 12.5 m/sec

9
Figure 2-10 Colonel John Stapp experienced
extreme acceleration in rocket sled experiments.
The severe contortion of soft facial tissues was
recorded by a movie camera.  
Courtesy U.S. Air Force
10
Acceleration

• Acceleration is the amount of change in velocity
  divided by the time it takes the change to occur.
• Acceleration (m/s2)
• final velocity initial velocity (m/s) / time
  (s)
• A (vf - vi) / t

11
A car traveling at a rate of 10 m/s accelerates
to 90 m/s in 12 seconds. Calculate its
acceleration?

• A (vf - vi) / t
• A 90 m/s 10 m/s / 12 s
• 80 m/s / 12 s
• 6.67 m/s/s
• or 6.67 m/s2

12
3 devices in your car make it accelerate

• Accelerator pedal
• Brake pedal
• Steering wheel
• Whenever an object changes speed or direction it
  accelerates.

13
Figure 2-8 Galileos falling-ball apparatus with
a table of measurements and a graph of distance
versus time.
14
Galileo found the following

• a ball rolling down a ramp moves with constant
  acceleration
• a ball attains a greater acceleration from
  steeper inclines
• regardless of weight, when air resistance is
  negligible, all objects fall with the same
  acceleration

15
Free-Fall Velocity

• The velocity of a falling object is proportional
  to the length of time it has been falling.
• Velocity (m/s) constant g (m/s2) x time (s)
• V g x t
• Galileo found g 9.8 m/s2

16
Acceleration due to Gravity

• Suppose a falling rock is equipped with a
  speedometer
• In each succeeding second of fall, the rocks
  speed increases by the same amount 10 m/s
• Time of Fall (s) Instantaneous Speed (m/s)
• 1                                                 
             10
• 2                                                 
             20
• 3                                                 
             30
• 4                                                 
             40
• 5 50

17
Gravity

• Suppose a falling rock is equipped with an
  odometer
• The readings would indicate that the distance
  fallen increases with time according to the
  relationship d ½ gt2
• Time of Fall (s) Distance of Fall (m)
• 1 5
• 2 20
• 3 45
• 4 80

18
Isaac Newton and the Universal Laws of Motion

• English scientist (1642-1727)
• Synthesized the work of Galileo and others
• 3 laws describe all motion

19
First Law Inertia (matter resists change)

• A moving object will continue moving in a
  straight line at a constant speed, and a
  stationary object will remain at rest, unless
  acted upon by an unbalanced force.
• animation

20
Second Law F m x a

• The acceleration produced by a force on an object
  is proportional to the magnitude of the force,
  and inversely proportional to the mass of the
  object.
• tutorial

21
Free Fall and Air Resistance

• In free-fall, force of air resistance counters
  force of gravity.
• As skydiver falls, air resistance increases til
  it approaches the magnitude of the force of
  gravity. Once the force of air resistance is as
  large as the force of gravity, skydiver is said
  to have reached a terminal velocity.
• Skydiving

22
Third Law action / reaction

• For every action there is an equal and opposite
  reaction.
• See some examples

23
Mass vs Weight

• Quantity of matter in an object
• The measurement of inertia
• Brick 1kg

• The gravitational force exerted on an object by
  the nearest, most massive body (Earth)
• Brick 2.2 pounds

24
The Newton (metric unit)

• In the metric system, the unit of weight, or any
  other force, is the newton, which is equal to a
  little less than a quarter pound.
• Newton force needed to accelerate 1 kg 1 m/s2
• 1 kg brick weighs about 10 N
• Or a baseball 1 N
• Example Problem, page 41 will help

25
calculate the force needed to produce a given
acceleration on a given mass (F ma)

• A 20 kg mass has an acceleration of 3 m/s2.
  Calculate the force acting on the mass.
• F (20 kg) (3 m/s2)
• F 60 kg m/s2 60 N

26
What force is needed to accelerate a 75 kg
sprinter from rest to a speed of 10 meters per
second in half a second?

• First find acceleration.
• Accel final vel initial vel (m/s) / time (s)
• 10 m/s 0 m/s / .5 s 20 m/s/s
• Force (N) mass (kg) x accel (m/s2)
• F 75 kg x 20 m/s2
• F 1500 N

27
Newtons Law of Universal Gravitation

• Between any two objects in the universe there is
  an attractive force proportional to the masses of
  the objects and inversely proportional to the
  square of the distance between them.
• F (G x m1 x m2) / d2
• The more massive 2 objects are, the greater the
  force between them.
• The farther apart 2 objects are, the less the
  force between them.

28
Figure 2-13 An apple falling, a ball being
thrown, a space shuttle orbiting the Earth, and
the orbiting Moon, all display the influence of
the force of gravity.
29
Study Guide The Sciences, Ch 2

• Read pp 24-46
• Discussion Questions 1-10
• Problems 1-7