Lecture I

Physics 367
 
 Problems, Units, Estimates and Limits

 

Problems
 

We live in a world in a state of flux
 

Everything affects everything  

Nothing is really free
 
 Everything we do counts  
 What we do matters  
 Everything has a cost  
 TANSTAAFL  

Tragedy of the Commons  

10 farmers each have 20 cattle
 
 The cattle graze on a common area
 
 The common area can support 200 cattle
 
 One farmer (you) gets a "good" idea
add 1 cow and make a 5% gain!  
 20 + 1 21             +1
 
 But there is a cost to everyone, since now  
   200 cattle each get  

 200/201 food etc.   -1/201
 

Why does this appear to be a "good idea" for you?

For 20 cattle ...you make an overall gain of  

 +1 -20/201       +9/10

What is really going on?

Nothing is really free

Units: The Metric System (SI)

Time: Measurement of Duration

units: seconds (s)
  minutes (min)   1 min = 60 s
  hour (h)   1 h = 60 min = 3600 s
  day (d)   1 d = 24 h = 86,400 s
  year (yr)   1 y = 31,557,600 s ~ 3.14 x 107 s

Length: Measurement of Distance

units: meters (m)

  centimeters (cm)   1 m = 100 cm

Mass: Measurement of the Quantity of Matter

units: kilograms (kg)

  gram (g)   1 kg = 1000 g
  pounds mass (lb)   1 kg = 2.2 lb

Prefixes used with the METRIC SYSTEM

  From the gigantic to the very small

exa- E     1,000,000,000,000,000,000 = 1018

peta- P      1,000,000,000,000,000 = 1015

tera- T      1,000,000,000,000 = 1012

giga- G     1,000,000,000 = 109

mega- M  1,000,000 = 106

kilo- k      1,000 = 103

hecto- h   100  

deka- dk  10  

 

deci- d   1/10  

centi- c   1/100  

milli- m   1/1000 = 10-3

micro- µ  1/1,000,000 = 10-6

nano- n   1/1,000,000,000 = 10-9

pico- p    1/1,000,000,000,000 = 10-12

femto- f   1/1,000,000,000,000,000 = 10-15

atto- a   1/1,000,000,000,000,000,000 = 10-18

How we use prefixes:

kilo-  means   One thousand

milli-  means   One one-thousandth

centi-  means   One one-hundredth

 

For the meter--the unit of length

 millimeter   mm   1/1,000 m

 kilometer   km   1,000 m

A meter is 1,000 mm.
A kilometer is 1000 m or 1,000,000 mm.

 

For the kilogram--the unit of mass

  gram   g   1/1,000 kg

  milligram   mg   1/1,000,000 kg = 1/1,000 g

A gram is 1,000 mg.
A kilogram is 1,000 g or 1,000,000 mg.

Energy-related units

  • Speed is (distance traveled)/(time taken) [m/s]

  • Velocity (change in position)/(time taken) [m/s]

  • Acceleration is (change in velocity)/(time taken) [m/s2]

  • Force is required for change in motion (speed or velocity) i.e. acceleration or deceleration. [N] It is defined by Newton's First Law.
    A body will remain in a state of rest or continue to move as it had been moving with no change in its speed or the direction in which it moves, unless it is acted on by an unbalanced force.

  • Mass or inertia is the quantity of matter which resists change in motion [kg]

  • Weight of a mass is the force exerted on it.
    Newton's 2nd Law states force is the product of mass and acceleration. F = ma -> [kg m/s2, N]

  • Work is the product of the force in the direction of motion times the distance moved in that direction. [J = N m]

  • Energy is the ability to do work. [J = N m]

A force is that thing that causes a body to change its motion [by which we mean a change in the body's velocity].

Forces cause bodies to change the way they are moving--to accelerate. Since velocity has a direction, so does acceleration, the change in the velocity with time.

Force is measured in units of Newtons (N). The force on a body is proportional to the amount of mass the body has.

Newton's Second Law is written as F = ma, where F is the total force on a body and a is the body's acceleration. Force has a direction associated with it.

A body with a mass of 1 kg has a weight of about 10 N.
     [9.8 Newtons, to be exact].
Where did the 9.8 come from?
In what direction?

Work is defined as W = F•x the product of the force in the direction of motion times the distance moved in that direction

Work is measured in Newton meters [N m].

Energy is the ability to do work. Thus, the unit of energy is the same as the unit of work.

The most important unit of energy is the joule (J). 1 J = 1 N m

A force of 1 N moving a body 1 m does 1 J of work.
A force of 100 N moving a body 1 m does 100 J of work.
A force of 10 N moving a body 10 m does 100 J of work.

Machines are useful because they allow us to amplify forces. Machines cannot create more work. They merely trade force against distance moved.

No work is created by use of a machine--you get out what you put in, except that the force you had to exert was smaller and the distance was longer.

We believe it is a principle of the universe that work cannot be created or destroyed. Since energy is the ability to do work, we believe this of energy also.

Energy can neither be created nor destroyed but merely changed from one form to another.

Estimates - Problem Solving.

What is important in the problem?

What is needed?

Where can it be found?

Problem of the day

How many dentists are there in Columbus?

People go to dentists

.... how many people in Columbus?
.... look in a book about Columbus

106 people in Columbus

How often do people go to dentists?

.... I go twice a year
.... young kids don't go at all
.... an average person goes once a year

106 visits/year

How many patients can a dentist see?

.... dentists work
.... 40 hrs/wk · 50 wks=2000 hrs
.... a typical visits take 1 hr?

A dentist handles 2000 visits/yr

There are 500 dentists in Columbus!