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 minS =

750 m/min• S = 1500m / 120 sec

S = 12.5 m/sec

Courtesy U.S. Air Force

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. 

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 = g x t

• 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 5– 2 20– 3 45– 4 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 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

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