Transcript ppt

The Ordered Universe
Part 3:
Some Calculations
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?
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.
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 downward.
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.
• 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.
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
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
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
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
3 devices in your car make it accelerate:
•
•
•
•
Accelerator pedal
Brake pedal
Steering wheel
Whenever an object changes speed or
direction it accelerates.
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 acceleration from
steeper inclines
• regardless of weight, when air resistance
is negligible, all objects fall with the same
acceleration
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
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
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
Isaac Newton and
the Universal Laws of Motion
• English scientist
(1642-1727)
• Synthesized the work
of Galileo and others
• 3 laws describe all
motion
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
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
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
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
exerted on an object
by the nearest, most
massive body (Earth)
• Brick = 2.2 pounds
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
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
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
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.
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.
Study Guide: The Sciences, Ch 2
• Read pp 24-46
• Discussion Questions 1-10
• Problems 1-7