The Ordered Universe
Part 3:
Some Calculations
Check Prior Knowledge:
• Summarize the contributions made by
Galileo and Newton
• Distinguish between speed, velocity, and...
Mechanics
--branch of science that deals with motion of
material objects
It was not until the 17th century that our
modern...
Galileo Galilei (1564-1642)
• Math professor
• Forerunner to modern
scientist
• Inventor
• What‟s he famous for?
Galileo:
Father of Experimental Science
At the surface of the
earth, all objects
speed up at the
same rate as they
fall do...
Analyzing falling objects
• 2 variables: distance and time
• Galileo devised an inclined plane to “slow
motion down” for s...
• Speed is the distance an object travels
divided by the time it takes to travel that
distance.
• Speed = distance / time
...
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 / 12...
Figure 2-10
Colonel John Stapp
experienced extreme
acceleration in rocket
sled experiments. The
severe contortion of
soft ...
Acceleration
• Acceleration is the amount of change in
velocity divided by the time it takes the
change to occur.
• Accele...
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
...
3 devices in your car make it accelerate:
•
•
•
•

Accelerator pedal
Brake pedal
Steering wheel
Whenever an object changes...
Figure 2-8

Galileo’s falling-ball apparatus with a table of
measurements and a graph of distance versus time.
Galileo found the following:
• a ball rolling down a ramp moves with
constant acceleration
• a ball attains a greater acce...
Free-Fall Velocity
• The velocity of a falling object is
proportional to the length of time it has
been falling.
• Velocit...
Acceleration due to Gravity
• Suppose a falling rock is equipped with a
speedometer:
• In each succeeding second of fall, ...
Gravity
• Suppose a falling rock is equipped with
an odometer:
• The readings would indicate that the
distance fallen incr...
Isaac Newton and
the Universal Laws of Motion
• English scientist
(1642-1727)
• Synthesized the work
of Galileo and others...
First Law: Inertia
(matter resists change)
• A moving object will continue moving in a
straight line at a constant speed, ...
Second Law: F = m x a
• The acceleration produced by a force on an
object is proportional to the magnitude of
the force, a...
Free Fall and Air Resistance
• In free-fall, force of air
resistance counters force
of gravity.
• As skydiver falls, air
r...
Third Law: action / reaction
• For every action there is an equal and
opposite reaction.
• See some examples
Mass
• Quantity of matter in
an object
• The measurement of
inertia
• Brick = 1kg

vs

Weight
• The gravitational force
ex...
The Newton (metric unit)
• In the metric system, the unit of weight, or any
other force, is the newton, which is equal to ...
calculate the force needed to produce a
given acceleration on a given mass
(F = ma)
• A 20 kg mass has an acceleration of ...
What force is needed to accelerate a 75 kg
sprinter from rest to a speed of 10 meters
per second in half a second?

• Firs...
Newton’s Law of Universal
Gravitation
• Between any two objects in the universe there
is an attractive force proportional ...
Figure 2-13

An apple falling, a ball being thrown, a space shuttle
orbiting the Earth, and the orbiting Moon, all display...
Study Guide: The Sciences, Ch 2
• Read pp 24-46
• Discussion Questions 1-10
• Problems 1-7
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Ch 2 mechanics, motion, gravity

  1. 1. The Ordered Universe Part 3: Some Calculations
  2. 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. 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. 4. Galileo Galilei (1564-1642) • Math professor • Forerunner to modern scientist • Inventor • What‟s he famous for?
  5. 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. 6. Analyzing falling objects • 2 variables: distance and time • Galileo devised an inclined plane to “slow motion down” for study. • To understand Galileo‟s results, you have to distinguish speed, velocity, & acceleration.
  7. 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. 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. 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. 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. 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. 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. 13. Figure 2-8 Galileo’s falling-ball apparatus with a table of measurements and a graph of distance versus time.
  14. 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. 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=gxt • Galileo found g = 9.8 m/s2
  16. 16. Acceleration due to Gravity • Suppose a falling rock is equipped with a speedometer: • In each succeeding second of fall, the rock‟s 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. 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 2 3 4 5 20 45 80
  18. 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. 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. 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. 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. 22. Third Law: action / reaction • For every action there is an equal and opposite reaction. • See some examples
  23. 23. Mass • Quantity of matter in an object • The measurement of inertia • Brick = 1kg vs Weight • The gravitational force exerted on an object by the nearest, most massive body (Earth) • Brick = 2.2 pounds
  24. 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. 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. 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. 27. Newton’s 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. 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. 29. Study Guide: The Sciences, Ch 2 • Read pp 24-46 • Discussion Questions 1-10 • Problems 1-7

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