1. Potential energy is, as the word suggests, the energy “locked up” up somewhere and which
can do work. Potential energy kam karnay ki salahiat hai! Potential energy can be converted
into kinetic energy, 1 2
2 mv . As I showed you earlier, this follows directly from Newton’s
Laws.
2. If you lift a stone of mass from the ground up a distance , you have to do work against
gravity. The (constant) force is , and so . By conservation of energy,
the work done by you
m x
mg W = mgx
was transformed into gravitational potential energy whose
values is exactly equal to . Where is the energy stored? Answer: it is stored neither
in the mass or in the earth - it is stored in
mgx
the gravitational field of the combined system
of stone+earth.
3. Suppose you pull on a spring and stretch it by an amount away from its normal
(equilibrium) position. How much energy is sto
x
red in the spring? Obviously, the
spring gets harder and harder to pull as it becomes longer. When it is extended by
length x and you pull it a further distance dx, the small amount of work d
2
0 0
one is
. Adding up all the small bits of work gives the total work:
1
2
This is the work you did. Maybe you got tired working so
x x
dW Fdx kxdx
W Fdx k xdx k x
= =
=∫ =∫ =
1 2
2
hard. What was the result
of your working so hard? Answer: this work was transformed into energy stored in the
spring. The spring contains energy exactly equal to .
4. Kinetic energy obvi
k x
ously depends on the frame you choose to measure it in. If you are
running with a ball, it has zero kinetic energy with respect to you. But someone who is
standing will see that it has kinetic energy! Now consider the following situation: a box
of mass 12kg is pushed with a constant force so that so that its speed goes from zero to
1.5m/sec (as measured by the person at rest on the cart) and it covers a distance of 2.4m.
Assume there is no friction.
2.4m
v=1.5m/s
mass of box =12 kg
15m/s
h h
h / 2
A B
C
0 v
D
2
2 2 2
Let's first calculate the change in kinetic energy:
1 (12 )(1.5 / ) 0 13.5
2
And then the (constant) acceleration:
v v (1.5 / ) 0
2( )
f i
f i
f i
K K K kg m s J
a m s
x x
Δ = − = − =
− −
= =
−
2
2
0.469 /
2(2 4 )
This acceleration results from a constant net force given by:
(12 )(0.469 / ) 5.63
From this, the work done on the crate is:
(
m s
m
F ma kg m s N
W F x
=
⋅
= = =
= Δ = 5.63N)(2.4m)=13.5J (same as ΔK= 13.5J !)
5. Now suppose there is somebody standing on the ground, and that the trolley moves at
15 m/sec relative to the ground:
2 2
f i
2 2
Let us repeat the same calculation:
1 v 1 v
2 2
1(12 )(16.5 / ) 1(12 )(15.0 / ) 284
2 2
This example clearly shows that work and
f i K K K m m
kg m s kg m s J
Δ ′= ′ − ′= −
= − =
energy have different values in different frames.
6. The total mechanical energy is: . If there is no friction then is
conserved. This means that the sum does not change with time. For example: a ball
is thrown upwards at
mech mech E =KE+PE E
0
2
2 0
0
speed v . How high will it go before it stops? The loss of potential
energy is equal to the gain of potential energy. Hence, 1v v.
2 2
Now look at the smooth, frictionless motion of
m mgh h
g
= ⇒ =
a car over the hills below:
15m/s
15m/s 16.5m/s
50.4m
48.0m
2 2
Even though the motion is complicated, we can use the fact that the total energy is a
constant to get the speeds at the points B,C,D:
At point A: 1 v 1 v
2 A 2 B m +mgh= m +
2 2 2
C A
2 2 2
D D A
v v
At point C: 1 v 1 v v v
2 2 2
At point D: 1 v 1 v v v 2
2 2
7. Remember that pot
B C
A C
A
mgh
m mgh m mgh gh
m mgh m gh
⇒ =
+ = + ⇒ = +
+ = ⇒ = +
ential energy has meaning only for a force that is conservative. A
conservative force is that for which the work done in going from point A to point B
is independent of the path chosen. Frictio
2
n is an example of a non-conservative force
and a potential energy cannot be defined. For a conservative force, F = . So, for
a spring, 1 and so .
2
8. Derivation of F = :
dV
dx
V kx F kx
dV
dx
−
= =−
−
0
If the particle moves distance in a potential , then
change in PE is where, . From this, . Now let 0.
Hence, F = lim V = .
x
x V
V V F x F V x
x
dV
Δ → x dx
Δ
Δ
Δ Δ = − Δ = − Δ →
Δ
Δ
− −
Δ
Thursday, March 19, 2009
WORK AND ENERGY
1. Definition of work: force applied in direction of displacement displacement. This
means that if the force F acts at an angle with respect to the direction of motion, then
W F d Fd
θ
×
= ⋅ =
cosθ
2 2-2
2. a) Work is a scalar - it has magnitude but no direction.
b) Work has dimensions: ( )
c) Work has units: 1 Newton 1 Metre 1 Joule (J)
3. Suppose you lift a mass of
M× LT− ×L =MLT
× ≡
20 kg through a distance of 2 metres. Then the work you
do is 20 kg 9.8 Newtons 2 metres 39.2 Joules. On the other hand, the force
of gravity is directed opposite to the force you exert
× × =
and the work done by gravity
is - 39.2 Joules.
4. What if the force varies with distance (say, a spring pulls harder as it becomes
longer). In that case, we should break up the distance over which the force acts into
small pieces so that the force is approximately constant over each bit. As we make the
pieces smaller and smaller, we will approach the exact result:
θ
F
d
F
x →
(a,ka)
0
Δx = a / 4
1 2
3
4
a
to . This quantity is the work done by a force, constant or non-constant. So
if the force is known as a function of position, we can always find the work done by
calculating the defini
i f x x
te integral.
5. Just to check what our result looks like for a constant force, let us calculate W if F=b,
0
1( ) 1( ) 1( ) 1( )
4 4 4 4
a
a b + a b + a b + a b =ab ∴∫Fdx=ab
6. Now for a less trivial case: suppose that F=kx, i.e. the force increases linearly with x.
2 2
0
Area of shaded region 1 ( )( )
2 2 2
= a ka =ka ∴ ∫aFdx=ka
7. Energy is the capacity of a physical system to do work:
it comes in many forms – mechanical, electrical, chemical, nuclear, etc
it can be stored
it can be converted into different forms
it can never be created or destroyed
8. Accepting the fact that energy is conserved, let us derive an expression for the kinetic
energy of a body. Suppose a constant force accelerates a mass m from speed 0 to speed
v over a distance d. What is the work done by the force? Obviously the answer is:
2
. But and v2 2 . This gives ( ) v 1 v2. So, we
2 2
conclude that the work done by the force has gone into creating kinetic energy. and that
the amount of kinetic energy possessed by a
W Fd F ma ad W mad m d m
d
= = = = = =
1 2
2 body moving with speed v is mv .
9. The work done by a force is just the force multiplied by the distance – it does not
depend upon time. But suppose that the same amount of work is done in half the time.
F = b
F
0 Δx = a / 4 a x
1 2 3 4
We then say that the power is twice as much. We define:
Power = Work done
Time taken
1
2
If the force does not depend on time: Work v. Therefore, Power = v.
Time t
10.Let's work out an example. A constant force accelerates a bus (mass m) from speed v
to speed v over a dist
F xF F Δ
= =
Δ
ance d. What work is done by the engine?
2 2
2 1 2 1 2
2 2
2 1
2 1 1
Recall that for constant acceleration, v v 2 ( ) where: v = final velocity,
x = final position, v = initial velocity, x = initial position. Hence, v v . Now
2
calculate
a x x
a
d
− = −
−
=
2 2
2 1 2 2
2 1
2
the work done: = v v 1 v 1 v . So the
2 2 2
work done has resulted in an increase in the quantity 1 v , which is kinetic energy.
2
W Fd mad m d m m
d
m
−
= = = −
means that if the force F acts at an angle with respect to the direction of motion, then
W F d Fd
θ
×
= ⋅ =
cosθ
2 2-2
2. a) Work is a scalar - it has magnitude but no direction.
b) Work has dimensions: ( )
c) Work has units: 1 Newton 1 Metre 1 Joule (J)
3. Suppose you lift a mass of
M× LT− ×L =MLT
× ≡
20 kg through a distance of 2 metres. Then the work you
do is 20 kg 9.8 Newtons 2 metres 39.2 Joules. On the other hand, the force
of gravity is directed opposite to the force you exert
× × =
and the work done by gravity
is - 39.2 Joules.
4. What if the force varies with distance (say, a spring pulls harder as it becomes
longer). In that case, we should break up the distance over which the force acts into
small pieces so that the force is approximately constant over each bit. As we make the
pieces smaller and smaller, we will approach the exact result:
θ
F
d
F
x →
(a,ka)
0
Δx = a / 4
1 2
3
4
a
to . This quantity is the work done by a force, constant or non-constant. So
if the force is known as a function of position, we can always find the work done by
calculating the defini
i f x x
te integral.
5. Just to check what our result looks like for a constant force, let us calculate W if F=b,
0
1( ) 1( ) 1( ) 1( )
4 4 4 4
a
a b + a b + a b + a b =ab ∴∫Fdx=ab
6. Now for a less trivial case: suppose that F=kx, i.e. the force increases linearly with x.
2 2
0
Area of shaded region 1 ( )( )
2 2 2
= a ka =ka ∴ ∫aFdx=ka
7. Energy is the capacity of a physical system to do work:
it comes in many forms – mechanical, electrical, chemical, nuclear, etc
it can be stored
it can be converted into different forms
it can never be created or destroyed
8. Accepting the fact that energy is conserved, let us derive an expression for the kinetic
energy of a body. Suppose a constant force accelerates a mass m from speed 0 to speed
v over a distance d. What is the work done by the force? Obviously the answer is:
2
. But and v2 2 . This gives ( ) v 1 v2. So, we
2 2
conclude that the work done by the force has gone into creating kinetic energy. and that
the amount of kinetic energy possessed by a
W Fd F ma ad W mad m d m
d
= = = = = =
1 2
2 body moving with speed v is mv .
9. The work done by a force is just the force multiplied by the distance – it does not
depend upon time. But suppose that the same amount of work is done in half the time.
F = b
F
0 Δx = a / 4 a x
1 2 3 4
We then say that the power is twice as much. We define:
Power = Work done
Time taken
1
2
If the force does not depend on time: Work v. Therefore, Power = v.
Time t
10.Let's work out an example. A constant force accelerates a bus (mass m) from speed v
to speed v over a dist
F xF F Δ
= =
Δ
ance d. What work is done by the engine?
2 2
2 1 2 1 2
2 2
2 1
2 1 1
Recall that for constant acceleration, v v 2 ( ) where: v = final velocity,
x = final position, v = initial velocity, x = initial position. Hence, v v . Now
2
calculate
a x x
a
d
− = −
−
=
2 2
2 1 2 2
2 1
2
the work done: = v v 1 v 1 v . So the
2 2 2
work done has resulted in an increase in the quantity 1 v , which is kinetic energy.
2
W Fd mad m d m m
d
m
−
= = = −
APPLICATIONS OF NEWTON’S LAWS – II
1. As a body moves through a body it displaces the fluid. it has to exert a force
on the fluid to push it out of the way. By Newton's third law, the fluid pushes
back on the body with an equal and opposite force. The direction of the fluid
resistance force on a body is always opposite to the direction of the body's velocity
relative to the fluid.
2. The magnitude of the fluid resistance force usually increases with the speed of the
body through the fluid. Typically, v (an empirical law!). Imagine that you
drop a ball bearing into a deep container filled with oil. Af
f =k
final
ter a while the ball bearing
will approach its maximum (terminal) speed when the forces of gravity and friction
balance each other: v from which v / .
3. The above was a simple
mg=k =mg k
example of equilibrium under two forces. In general, while
solving problems you should a)draw a diagram, b)define an origin for a system of
coordinates, c)identify all forces (tension, normal, friction, weight, etc) and their and
components, d)Apply Newton's law separately along the and axes. e) find the
accelerations, then velocities, then displacements. This sounds very coo
x
y xy
k-book, and in
fact it will occur to you naturally how to do this while solving actual problems.
4. Your weight in a lift: suppose you are in a lift that is at rest or moving at constant
velocity. In either case a=0 and the normal force N and the force due to gravity are
exactly equal, N−Mg=0⇒N=Mg.But if the lift is accelerating downwards then
Mg−N=Ma or N=M(g−a) . So now the normal force (i.e. the force with which the
floor of the lift is pushing on you) is decreased. Note that if the lift is accelerating
downwards with acceleration a (which it will if the cable breaks!) then N=0 and you
will experience weightlessness just like astronauts in space do. Finally, if the lift is
accelerating upwards then a is negative and you will feel heavier.
5. Imagine that you are in a railway wagon and want to know how much you are
accelerating. You are not able to look out of the windows. A mass is hung from the
roof. Find the acceleration of the car from the angle made by the mass.
a
F m M
θ
T
mg
We first balance the forces vertically: cos
And then horizontally: sin
From these two equations we find that: tan
Note that the mass doesn't
T mg
T ma
a
g
m
θ
θ
θ
=
=
=
matter - it cancels out!
6. Friction is a funny kind of force. It doe not make up its mind which way to act until
some other force compels it to decide. Imagine a block lying on the floor. If you push
it forward, friction will act backward. And if you push it to the left, friction will act
to the right. In other words, the direction of the frictional force is always in the
opposite direction to the applied force.
7. Let us solve the following problem: a rope of total length L and mass per unit length m
is put on a table with a length l hanging from one edge. What should be l such that the
rope just begins to slip?
To solve this, look at the balance of forces in the diagram below: in the vertical direction,
the normal force balances the weight of that part of the rope that lies on the table:
N=m(L−l)g. In the horizontal direction, the rope exerts a force to the right, which
is counteracted by the friction that acts to the left. Therefore . Substituting
from the first equation we find that
mlg
N mlg N
l L
μ
μ
μ
=
= . Note that if isvery small then even a small
1
piece of string that hangs over the edge will cause the entire string to slip down.
μ
+
9. In this problem, we would like to calculate the minimum force
such that the small block does not slip downwards. Clearly,
since the 2 bodies move together, ( ) . This gives
. W
( )
F
F m Ma
a F
m M
= +
=
+
e want the friction to be at least as large as the downwards force, .
So, we put from which the minimum horizontal force needed to
( )
prevent slippage is ( ) .
N mg
N ma m F
m M
F m M g
μ
μ
⎛ ⎞
= = ⎜⎝ + ⎟⎠
+
=
l
(L−l)
μN
N
m(L−l)g
ml g
0 Δ x x →
1 2 1 2
1
0 1
0
Now add up all the little pieces of work:
To get the exact result let 0 and the number of intervals N : lim
Definition: lim
N
N N n
n
x n n
x n
W W W W F x F x F x F x
x W F x
W F
=
∞
Δ →
=
Δ →
= Δ + Δ + ⋅ ⋅ ⋅ + Δ = Δ + Δ + ⋅ ⋅ ⋅ + Δ ≡ Δ
Δ → → ∞ = Δ
=
Σ
Σ
1
( ) is called the integral of with respect to from
f
i
x
n x
x Fxdx F x
∞
=
Σ Δ ≡ ∫
on the fluid to push it out of the way. By Newton's third law, the fluid pushes
back on the body with an equal and opposite force. The direction of the fluid
resistance force on a body is always opposite to the direction of the body's velocity
relative to the fluid.
2. The magnitude of the fluid resistance force usually increases with the speed of the
body through the fluid. Typically, v (an empirical law!). Imagine that you
drop a ball bearing into a deep container filled with oil. Af
f =k
final
ter a while the ball bearing
will approach its maximum (terminal) speed when the forces of gravity and friction
balance each other: v from which v / .
3. The above was a simple
mg=k =mg k
example of equilibrium under two forces. In general, while
solving problems you should a)draw a diagram, b)define an origin for a system of
coordinates, c)identify all forces (tension, normal, friction, weight, etc) and their and
components, d)Apply Newton's law separately along the and axes. e) find the
accelerations, then velocities, then displacements. This sounds very coo
x
y xy
k-book, and in
fact it will occur to you naturally how to do this while solving actual problems.
4. Your weight in a lift: suppose you are in a lift that is at rest or moving at constant
velocity. In either case a=0 and the normal force N and the force due to gravity are
exactly equal, N−Mg=0⇒N=Mg.But if the lift is accelerating downwards then
Mg−N=Ma or N=M(g−a) . So now the normal force (i.e. the force with which the
floor of the lift is pushing on you) is decreased. Note that if the lift is accelerating
downwards with acceleration a (which it will if the cable breaks!) then N=0 and you
will experience weightlessness just like astronauts in space do. Finally, if the lift is
accelerating upwards then a is negative and you will feel heavier.
5. Imagine that you are in a railway wagon and want to know how much you are
accelerating. You are not able to look out of the windows. A mass is hung from the
roof. Find the acceleration of the car from the angle made by the mass.
a
F m M
θ
T
mg
We first balance the forces vertically: cos
And then horizontally: sin
From these two equations we find that: tan
Note that the mass doesn't
T mg
T ma
a
g
m
θ
θ
θ
=
=
=
matter - it cancels out!
6. Friction is a funny kind of force. It doe not make up its mind which way to act until
some other force compels it to decide. Imagine a block lying on the floor. If you push
it forward, friction will act backward. And if you push it to the left, friction will act
to the right. In other words, the direction of the frictional force is always in the
opposite direction to the applied force.
7. Let us solve the following problem: a rope of total length L and mass per unit length m
is put on a table with a length l hanging from one edge. What should be l such that the
rope just begins to slip?
To solve this, look at the balance of forces in the diagram below: in the vertical direction,
the normal force balances the weight of that part of the rope that lies on the table:
N=m(L−l)g. In the horizontal direction, the rope exerts a force to the right, which
is counteracted by the friction that acts to the left. Therefore . Substituting
from the first equation we find that
mlg
N mlg N
l L
μ
μ
μ
=
= . Note that if isvery small then even a small
1
piece of string that hangs over the edge will cause the entire string to slip down.
μ
+
9. In this problem, we would like to calculate the minimum force
such that the small block does not slip downwards. Clearly,
since the 2 bodies move together, ( ) . This gives
. W
( )
F
F m Ma
a F
m M
= +
=
+
e want the friction to be at least as large as the downwards force, .
So, we put from which the minimum horizontal force needed to
( )
prevent slippage is ( ) .
N mg
N ma m F
m M
F m M g
μ
μ
⎛ ⎞
= = ⎜⎝ + ⎟⎠
+
=
l
(L−l)
μN
N
m(L−l)g
ml g
0 Δ x x →
1 2 1 2
1
0 1
0
Now add up all the little pieces of work:
To get the exact result let 0 and the number of intervals N : lim
Definition: lim
N
N N n
n
x n n
x n
W W W W F x F x F x F x
x W F x
W F
=
∞
Δ →
=
Δ →
= Δ + Δ + ⋅ ⋅ ⋅ + Δ = Δ + Δ + ⋅ ⋅ ⋅ + Δ ≡ Δ
Δ → → ∞ = Δ
=
Σ
Σ
1
( ) is called the integral of with respect to from
f
i
x
n x
x Fxdx F x
∞
=
Σ Δ ≡ ∫
APPLICATIONS OF NEWTON’S LAWS – I
1. An obvious conclusion from is that if 0 then 0 ! How simple, yet
how powerful ! This says that for any body that is not accelerating the
must va
F ma F a
sum of all
the forces acting upon it
= = =
nish.
2. Examples of systems in equilibrium: a stone resting on the ground; a pencil balanced
on your finger; a ladder placed against the wall, an aircraft flying at a constant speed
and constant height.
3. Examples of systems out of equilibrium: a stone thrown upwards that is at its highest
point; a plane diving downwards; a car at rest whose driver has just stepped on the
car's accelerator.
4. If you know the acceleration of a body, it is easy to find the force that causes it to
accelerate. Example: An aircraft of mass m has position vector,
r 3 2 4
2 2
2 2
2
( )ˆ ( )ˆ
What force is acting upon it?
SOLUTION: ˆ ˆ
6 ˆ (2 12 )ˆ
5. The other way around is
at bt i ct dt j
F md xi md y j
dt dt
bmt i m c d t j
= + + +
= +
= + +
2
2
not so simple: suppose that you know and you want to
find . For this you must solve the equation,
This may or may not be easy, depending upon
F
x
d x F
dt m
=
(which may depend upon both as
well as if the force is not constant).
6. Ropes are useful because you can pull from a distance to change the direction of a
force. The tension, often denote
F x
t
d by , is the force you would feel if you cut the
rope and grabbed the ends. For a massless rope (which may be a very good
approximation in many situations) the tension is the same at every p
T
oint along the
rope. Why? Because if you take any small slice of the rope it weighs nothing (or
very little). So if the force on one side of the slice was any different from the force
force on the other side, it would be accelerating hugely. All this was for the "ideal
rope" which has no mass and never breaks. But this idealization if often good enough.
7. We are all familiar with frictional force. When two bodies rub against each other,
the frictional force acts upon each body separately opposite to its direction of motion
(i.e it acts to slow down the motion). The harder you press two bodies against each
other, the greater the friction. Mathematically, , where is the force with which
you press the two bodies against ea
F= μN N
ch other (normal force). The quantity is called the
coefficient of friction (obviously!). It is large for rough surfaces, and small for smooth
ones. Remember that F N is an empirical re
μ
= μ
lation and holds only approximately.
This is obviously true: if you put a large enough mass on a table, the table will start to
bend and will eventually break.
8. Friction is caused by roughness at a microscopic level
- if you look at any surface with a powerful microscope
you will see unevenness and jaggedness. If these big bumps
are levelled somehow, friction will still not disappear because
there will still be little bumps due to atoms. More precisely,
atoms from the two bodies will interact each other because of the electrostatic interaction
between their charges. Even if an atom is neutral, it can still exchange electrons and there
will be a force because of surrounding atoms.
9. Consider the two blocks below on a frictionless surface:
1 2
2
1
We want to find the tension and acceleration: The total force on the first mass is
and so . The force on the second mass is simply and so . Solving the
above, we get:
F T
F T ma T T ma
T m F
m m
−
− = =
=
+ 2 1 2
and a F .
m m
=
+
10. There is a general principle by which you solve equilibrium problems. For equilibrium,
the sum of forces in every direction must vanish. So 0. You may always
choose the , ,
x y z F F F
x y z
= = =
directions according to your convenience. So, for example, as in the
lecture problem dealing with a body sliding down an inclined plane, you can choose the
directions to be along and perpendicular to the surface of the plane.
1 m 2 F T T m
how powerful ! This says that for any body that is not accelerating the
must va
F ma F a
sum of all
the forces acting upon it
= = =
nish.
2. Examples of systems in equilibrium: a stone resting on the ground; a pencil balanced
on your finger; a ladder placed against the wall, an aircraft flying at a constant speed
and constant height.
3. Examples of systems out of equilibrium: a stone thrown upwards that is at its highest
point; a plane diving downwards; a car at rest whose driver has just stepped on the
car's accelerator.
4. If you know the acceleration of a body, it is easy to find the force that causes it to
accelerate. Example: An aircraft of mass m has position vector,
r 3 2 4
2 2
2 2
2
( )ˆ ( )ˆ
What force is acting upon it?
SOLUTION: ˆ ˆ
6 ˆ (2 12 )ˆ
5. The other way around is
at bt i ct dt j
F md xi md y j
dt dt
bmt i m c d t j
= + + +
= +
= + +
2
2
not so simple: suppose that you know and you want to
find . For this you must solve the equation,
This may or may not be easy, depending upon
F
x
d x F
dt m
=
(which may depend upon both as
well as if the force is not constant).
6. Ropes are useful because you can pull from a distance to change the direction of a
force. The tension, often denote
F x
t
d by , is the force you would feel if you cut the
rope and grabbed the ends. For a massless rope (which may be a very good
approximation in many situations) the tension is the same at every p
T
oint along the
rope. Why? Because if you take any small slice of the rope it weighs nothing (or
very little). So if the force on one side of the slice was any different from the force
force on the other side, it would be accelerating hugely. All this was for the "ideal
rope" which has no mass and never breaks. But this idealization if often good enough.
7. We are all familiar with frictional force. When two bodies rub against each other,
the frictional force acts upon each body separately opposite to its direction of motion
(i.e it acts to slow down the motion). The harder you press two bodies against each
other, the greater the friction. Mathematically, , where is the force with which
you press the two bodies against ea
F= μN N
ch other (normal force). The quantity is called the
coefficient of friction (obviously!). It is large for rough surfaces, and small for smooth
ones. Remember that F N is an empirical re
μ
= μ
lation and holds only approximately.
This is obviously true: if you put a large enough mass on a table, the table will start to
bend and will eventually break.
8. Friction is caused by roughness at a microscopic level
- if you look at any surface with a powerful microscope
you will see unevenness and jaggedness. If these big bumps
are levelled somehow, friction will still not disappear because
there will still be little bumps due to atoms. More precisely,
atoms from the two bodies will interact each other because of the electrostatic interaction
between their charges. Even if an atom is neutral, it can still exchange electrons and there
will be a force because of surrounding atoms.
9. Consider the two blocks below on a frictionless surface:
1 2
2
1
We want to find the tension and acceleration: The total force on the first mass is
and so . The force on the second mass is simply and so . Solving the
above, we get:
F T
F T ma T T ma
T m F
m m
−
− = =
=
+ 2 1 2
and a F .
m m
=
+
10. There is a general principle by which you solve equilibrium problems. For equilibrium,
the sum of forces in every direction must vanish. So 0. You may always
choose the , ,
x y z F F F
x y z
= = =
directions according to your convenience. So, for example, as in the
lecture problem dealing with a body sliding down an inclined plane, you can choose the
directions to be along and perpendicular to the surface of the plane.
1 m 2 F T T m
FORCE AND NEWTON’S LAWS
1. Ancient view: objects tend to stop if they are in motion; force is required to keep
something moving. This was a natural thing to believe in because we see objects
stop moving after some time; frictionless motion is possible to see only in rather
special circumstances.
2. Modern view: objects tend to remain in their initial state; force is required to change
motion. Resistance to changes in motion is called inertia. More inertia
means it is harder to make a body accelerate or decelerate.
3. Newton’s First Law: An object will remain at rest or move with constant velocity unless
acted upon by a net external force. (A non-accelerating reference frame is called an
inertial frame; Newton’s First Law holds only in inertial frames.)
4. More force leads to more acceleration:
5. The greater the mass of a body, the harder it is to change its state of motion. More
mass means more inertia. In other words, more mass le
⇒ a∝F
ads to less acceleration:
1
Combine both the above observations to conclude that:
6. Newton's Second Law: (or, if you pref
a
m
a F
m
a F
m
⇒ ∝
∝
= er, write as ).
7. is one relation between three independent quantities ( , , ). For it to be
useful, we must have separate ways of measuring mass, acceleration, and force.
Accelerati
F ma
F ma maF
=
=
on is measured from observing the rate of change of velocity; mass is a
measure of the amount of matter in a body (e.g. two identical cars have twice
the mass of a single one). Forces (due to g
-2
ravity, a stretched spring, repulsion of
two like charges, etc) will be discussed later.
8. Force has dimensions of [mass] [acceleration] . In the MKS system
the unit of force is the
× =MLT
2
Newton. It has the symbol N where:
1 Newton = 1 kilogram.metre/second .
9. Forces can be internal or external. For example the mutual attraction of atoms
within a block of wood are called internal forces. Something pushing the wood
is an external force. In the application of , remember that stands for the
total external force upon the body.
10. Forces are vectors, and so they must be added vectorially:
F=ma F
1 2 3
This means that the components in the ˆ direction must be added separately, those in
the ˆ direction separately, etc.
11. Gravity acts directly on the
F F F F
x
y
= + + + ⋅ ⋅ ⋅ ⋅
1 1 1 2
mass of a body - this is a very important experimental
observation due to Newton and does not follow from . So a body of mass
experiences a force while a body of mass exper
F ma
m F m g m
=
=
2 2
iences a force
, where is the acceleration with which any body (big or small) falls under
the influence of gravity. (Galileo had established this important fact when he dropped
F =mg g
different masses from the famous leaning tower of Pisa!)
12. The weight of a body is the force which gravity exerts upon it, . Mass and
weight are two completely different quantities. So, f
W W= mg
or example, if you used a spring
balance to weigh a kilo of grapes on earth, the same grapes would weigh only 1/7 kilo
on the moon.
13. Newton's Third Law: for every action there is an equal and opposite reaction. More
precisely, , where is the force exerted by body upon whereas
is the force exerted by body upon . Ask yourself what would happen if this wa
AB BA AB BA F F F B A F
A B
= −
s not
true. In that case, a system of two bodies, even if it is completely isolated from the
surroundings, would have a net force acting upon it because the net force acting upon
both bodies would be 0.
14. If action and reaction are always equal, then why does a body accelerate at all? Students
are often confused by this. The answer: in considering the acceleration o
AB BA F +F ≠
f a body you must
consider only the (net) force acting upon that body. So, for example, the earth pulls a stone
towards it and causes it to accelerate because there is a net force acting upon the stone. On
the other hand, by the Third Law, the stone also pulls the earth towards it and this causes the
earth to accelerate towards the stone. However, because the mass of the earth is so large, we
are only able to see the acceleration of the stone and not that of the earth.
something moving. This was a natural thing to believe in because we see objects
stop moving after some time; frictionless motion is possible to see only in rather
special circumstances.
2. Modern view: objects tend to remain in their initial state; force is required to change
motion. Resistance to changes in motion is called inertia. More inertia
means it is harder to make a body accelerate or decelerate.
3. Newton’s First Law: An object will remain at rest or move with constant velocity unless
acted upon by a net external force. (A non-accelerating reference frame is called an
inertial frame; Newton’s First Law holds only in inertial frames.)
4. More force leads to more acceleration:
5. The greater the mass of a body, the harder it is to change its state of motion. More
mass means more inertia. In other words, more mass le
⇒ a∝F
ads to less acceleration:
1
Combine both the above observations to conclude that:
6. Newton's Second Law: (or, if you pref
a
m
a F
m
a F
m
⇒ ∝
∝
= er, write as ).
7. is one relation between three independent quantities ( , , ). For it to be
useful, we must have separate ways of measuring mass, acceleration, and force.
Accelerati
F ma
F ma maF
=
=
on is measured from observing the rate of change of velocity; mass is a
measure of the amount of matter in a body (e.g. two identical cars have twice
the mass of a single one). Forces (due to g
-2
ravity, a stretched spring, repulsion of
two like charges, etc) will be discussed later.
8. Force has dimensions of [mass] [acceleration] . In the MKS system
the unit of force is the
× =MLT
2
Newton. It has the symbol N where:
1 Newton = 1 kilogram.metre/second .
9. Forces can be internal or external. For example the mutual attraction of atoms
within a block of wood are called internal forces. Something pushing the wood
is an external force. In the application of , remember that stands for the
total external force upon the body.
10. Forces are vectors, and so they must be added vectorially:
F=ma F
1 2 3
This means that the components in the ˆ direction must be added separately, those in
the ˆ direction separately, etc.
11. Gravity acts directly on the
F F F F
x
y
= + + + ⋅ ⋅ ⋅ ⋅
1 1 1 2
mass of a body - this is a very important experimental
observation due to Newton and does not follow from . So a body of mass
experiences a force while a body of mass exper
F ma
m F m g m
=
=
2 2
iences a force
, where is the acceleration with which any body (big or small) falls under
the influence of gravity. (Galileo had established this important fact when he dropped
F =mg g
different masses from the famous leaning tower of Pisa!)
12. The weight of a body is the force which gravity exerts upon it, . Mass and
weight are two completely different quantities. So, f
W W= mg
or example, if you used a spring
balance to weigh a kilo of grapes on earth, the same grapes would weigh only 1/7 kilo
on the moon.
13. Newton's Third Law: for every action there is an equal and opposite reaction. More
precisely, , where is the force exerted by body upon whereas
is the force exerted by body upon . Ask yourself what would happen if this wa
AB BA AB BA F F F B A F
A B
= −
s not
true. In that case, a system of two bodies, even if it is completely isolated from the
surroundings, would have a net force acting upon it because the net force acting upon
both bodies would be 0.
14. If action and reaction are always equal, then why does a body accelerate at all? Students
are often confused by this. The answer: in considering the acceleration o
AB BA F +F ≠
f a body you must
consider only the (net) force acting upon that body. So, for example, the earth pulls a stone
towards it and causes it to accelerate because there is a net force acting upon the stone. On
the other hand, by the Third Law, the stone also pulls the earth towards it and this causes the
earth to accelerate towards the stone. However, because the mass of the earth is so large, we
are only able to see the acceleration of the stone and not that of the earth.
Sunday, March 15, 2009
KINEMATICS information
1. x(t) is called displacement and it denotes the position of a body at time. If the
displacement is positive then that body is to the right of the chosen origin and if
negative, then it is to the left.
2. If a body is moving with average speed v then in time t it will cover a distance d=vt.
But, in fact, the speed of a car changes from time to time and so one should limit the
use of this formula to small time differences only. So, more accurately, one defines an
average speed over the small time interval Δt as:
average speed distance travelled in time t
t
Δ
=
Δ
3. We define instantaneous velocity at any time t as:
2 1
2 1
v x(t ) x(t ) x
t t t
− Δ
= ≡
− Δ
.
Here and are both very small quantities that tend to zero but their
ratio v does not.
Δx Δt
4. Just as we have defined velocity as the rate of change of distance, similarly we can
define instantaneous acceleration at any time t as:
2 1
2 1
a v(t) v(t) v
t t t
− Δ
= ≡
− Δ
.
Here v and are both very small quantities that tend to zero but their
ratio is not zero, in general. Negative acceleration is called deceleration.
The speed of a decelerating body decreases with
t
a
Δ Δ
time.
5. Some students are puzzled by the fact that a body can have a very large acceleration
but can be standing still at a given time. In fact, it can be moving in the opposite
direction to its acceleration. There is actually nothing strange here because position,
velocity, and acceleration are independent quantities. This means that specifying one
does not specify the other.
13. Two vectors can be added together geometrically. We take any one vector, move
it without changing its direction so that both vectors start from the same point, and
then make a parallelogram. The diagonal of the parallelogram is the resultant.
6. For constant speed and a body that is at x=0 at time t=0, x increases linearly with
time, x∝t (or x=vt). 0 If the body is at position x at time t= 0, then at
0 time t, x =x +vt.
7. For constant acceleration and a body that starts from rest at t = 0, v increases
0
0
linearly with time, v (or v ). If the body has speed v at 0, then at
time , v v .
t at t
t at
∝ = =
= +
8. We know in (6) above how far a body moving at constant speed moves in time t. But
what if the body is changing its speed? If the speed is increasing linearly (i.e. constant
acceleration), then the answer is particularly simple: just use the same formula as in
(6) but use the average speed: 0 0 (v + v + at) / 2. So we get
1 2
0 0 0 0 0 2 x =x+(v +v +at)t / 2= x +v t+ at . This formula tells you how far a body
moves in time t if it moves with constant acceleration a, and if started at position x0 at
t=0 with speed v0 .
9. We can eliminate the time using (7), and arrive at another useful formula that tells us
what the final speed will be after the body has traveled a distance equal to
2 2
0 0 0 x−x after time t, v =v + 2a(x − x ).
10. Vectors: a quantity that has a size as well as direction is called a vector. So, for
example, the wind blows with some speed and in some direction. So the wind velocity
is a vector.
11. If we choose axes, then a vector is fixed by its components along those axes. In one
dimension, a vector has only one component (call it the x-component). In two
dimensions, a vector has both x and y components. In three dimensions, the
components are along the x,y,z axes.
12. If we denote a vector ( , ) then, cos , and sin . x y r= xy r =x=r θ r =y=r θ
Note that x2+y2=r2. Also, that tanθ =y/x.
14. Two vectors can also be added algebraically. In this case, we simply add the
components of the two vectors along each axis separately. So, for example,
Two vectors can be put together as (1.5,2.4)+(1,−1) = (2.5,1.4).
displacement is positive then that body is to the right of the chosen origin and if
negative, then it is to the left.
2. If a body is moving with average speed v then in time t it will cover a distance d=vt.
But, in fact, the speed of a car changes from time to time and so one should limit the
use of this formula to small time differences only. So, more accurately, one defines an
average speed over the small time interval Δt as:
average speed distance travelled in time t
t
Δ
=
Δ
3. We define instantaneous velocity at any time t as:
2 1
2 1
v x(t ) x(t ) x
t t t
− Δ
= ≡
− Δ
.
Here and are both very small quantities that tend to zero but their
ratio v does not.
Δx Δt
4. Just as we have defined velocity as the rate of change of distance, similarly we can
define instantaneous acceleration at any time t as:
2 1
2 1
a v(t) v(t) v
t t t
− Δ
= ≡
− Δ
.
Here v and are both very small quantities that tend to zero but their
ratio is not zero, in general. Negative acceleration is called deceleration.
The speed of a decelerating body decreases with
t
a
Δ Δ
time.
5. Some students are puzzled by the fact that a body can have a very large acceleration
but can be standing still at a given time. In fact, it can be moving in the opposite
direction to its acceleration. There is actually nothing strange here because position,
velocity, and acceleration are independent quantities. This means that specifying one
does not specify the other.
13. Two vectors can be added together geometrically. We take any one vector, move
it without changing its direction so that both vectors start from the same point, and
then make a parallelogram. The diagonal of the parallelogram is the resultant.
6. For constant speed and a body that is at x=0 at time t=0, x increases linearly with
time, x∝t (or x=vt). 0 If the body is at position x at time t= 0, then at
0 time t, x =x +vt.
7. For constant acceleration and a body that starts from rest at t = 0, v increases
0
0
linearly with time, v (or v ). If the body has speed v at 0, then at
time , v v .
t at t
t at
∝ = =
= +
8. We know in (6) above how far a body moving at constant speed moves in time t. But
what if the body is changing its speed? If the speed is increasing linearly (i.e. constant
acceleration), then the answer is particularly simple: just use the same formula as in
(6) but use the average speed: 0 0 (v + v + at) / 2. So we get
1 2
0 0 0 0 0 2 x =x+(v +v +at)t / 2= x +v t+ at . This formula tells you how far a body
moves in time t if it moves with constant acceleration a, and if started at position x0 at
t=0 with speed v0 .
9. We can eliminate the time using (7), and arrive at another useful formula that tells us
what the final speed will be after the body has traveled a distance equal to
2 2
0 0 0 x−x after time t, v =v + 2a(x − x ).
10. Vectors: a quantity that has a size as well as direction is called a vector. So, for
example, the wind blows with some speed and in some direction. So the wind velocity
is a vector.
11. If we choose axes, then a vector is fixed by its components along those axes. In one
dimension, a vector has only one component (call it the x-component). In two
dimensions, a vector has both x and y components. In three dimensions, the
components are along the x,y,z axes.
12. If we denote a vector ( , ) then, cos , and sin . x y r= xy r =x=r θ r =y=r θ
Note that x2+y2=r2. Also, that tanθ =y/x.
14. Two vectors can also be added algebraically. In this case, we simply add the
components of the two vectors along each axis separately. So, for example,
Two vectors can be put together as (1.5,2.4)+(1,−1) = (2.5,1.4).
Saturday, March 7, 2009
Electronics History
Introduction
People have known about static electricity for thousands of years. (Microsoft Corp) Biblical references to lighting were a reflection of God’s wrath. (Canby) Science did not make concern itself until the 1700s. (Microsoft Corp)
Early ideas
The Greeks, as early a 600 BC, rubbed amber and thought it had properties, also lodestone was thought to hold some type of attraction. (Canby) But, for almost 2000 years very little was done until the 1600s, Wm Gillbert discusses magnetism and amber’s attraction. (Canby) In 1745 Dutch person, Prof Musschenbroek, invents the Leyden jar, a crude capacitor. (Dummer) Ben Franklin discusses his theory electricity and in 1752 Franklin is credited with the first lighting rod. In 1772 iron dust filings reveal the magnetic lines of force, which lead to inductors or a beginning of a solenoid. (Dummer and Canby) In 1774, Lesage installs a primitive telegraph at Geneva, using 24 wires and glass tubes. (Canby). In 1775 Volta, invents electrophorus, and later the voltmeter. (Canby). In 1785, Colomb proves the inverse sq. law. (Canby). In 1786, Galvani electrifies frog legs. Again, Volta in 1796 invents the first battery. (Canby) Oersted, in 1820 discovers that a current can create a magnetic field. Also in 1820 Ampere develops terminology for electric current. In 1821 Faraday establishes the fact that a charge on the outside of a conductor produces
55
no electric field. (Canby) In 1827 Ohm’s law is published. (Microsoft) All these great ideas, inventions, and more can be put on to graphic organizers by chronology, brainstorming, logical connections or just connections with no logic. See the attached graphic organizers (Appendix B) and pick the one that suits the situation(s).
The Start of Electronics
As mention in the beginning of this abstract Electricity and Electronic have a shared beginning. The two-shared phenomena are static electricity and magnetism. To physicists before the 19th century, electricity, magnetism and light seemed like entirely distinct phenomena. By the early 1800’s, work by Galvani, Oersted, and Faraday on galvanism, electromagnetism, and electromagnetic induction opened up a new field of experimental work which ultimately paved the way to present day electronic. (Dummer) In 1865 James Clark Maxwell publishes his paper "A Dynamical Theory of Electromagnetic Field." These two great ideas were put together (Canby).
The early 1800s was a time of great progress in theories and inventions. (Dummer) Infrared and ultra-violet radiation was discovered. Dalton’s atomic theory is put forward in 1808. Thermoelectricity, electrolysis, and the photovoltaic effect were all discovered before 1840. Work on low-pressure discharge tubes, glow discharges, new types of battery and the early microphone took place in the 20 years. (Dummer) So, between 1800 and 1875 basic physical phenomena were discovered, culminating in the practical applications of the telephone, phonograph, microphones and loudspeakers. Towards the end of the 1800s, wireless telegraphy, magnetic recording, and the cathode-ray oscillograph were all developed. (Dummer)
As corporations started to develop, one can see a shift from the individual to the industrial organization of the development of electronics. (Antebi) The great individuals such a George Westinghouse, Nikola Tesla, and Thomas Edison, to mention these few, begin to submerge to the collective of corporate organization. (Antebi)
As the 20th century begins we see Marconi’s wireless transatlantic radio signal. (Canby) Rutherford’s atomic model in 1911 and Bohr’s 1913 electron orbital theory corresponded to various permissible energy levels. (Dummer)
The early 1900s also saw the beginnings of the present-day electronic technologies. The 3-electrode valve opened the way to radio broadcasting and the Campbell-Swinton theory of television. But, it is WW1 that accelerates the pace for the development of electronics. (Dummer)
56
• WW1 marked the impetus to develop radio communications with components such as resistors and capacitors. (Dummer) In 1920, Pittsburgh’s KDKA broadcast the 1st scheduled radio program for Westinghouse Corp. In 1925, Bell Telephone Lab invents a mechanism for recording sound electrically. (Canby) But, it is WW2 that had tremendously effect on components since the War was to be fought in climates all around the world. WW2 requirements were of the following nature:
• 1.Standardization-for faster production
• 2. Miniaturization-for aircraft, submarines, etc
• 3. Reliability-no component failures
• 4. Maintainability-quick replacement
• 5. Transport hazards-an ability to handle shocks
• 6. Mechanical shocks-impact of shells and parachute landing
• 7. Storage-long periods of use
• 8. Hot and cold temperatures
• 9. Humidity-tropics
• 10. High Altitude-high flying aircraft
• 11. Combined environments-8, 9, and 10 above
• 12. High Powers- increase range radio and radar
• 13. Radiation resistance- to withstand nuclear environment (Dummer)
Perhaps one of most important developments of the WW2 started before the War that is RADAR. It had tremendous effect on the War and should not be overlooked. (Dummer) Using radar the "Battle of Britain 1940" was won. Moreover, with the British using radar in its night bombing it hastens the end to the War. (Dummer)
After the WW2, many Europeans came to the USA bringing their ideas. This brain drain led to increased inventions in the USA that would continue until the 1960s. Furthermore, in 1946 printed circuit began to be used with miniature tubes. But, again in 1948, Bell Labs invented the transistor, which replaced the vacuum tube. (Dummer)
Integrated circuits appeared in the early 1950s. (Dummer) Resistors such as nickel chromium film is developed in 1957. (Dummer) The solid electric capacitor was developed in 1956. (Dummer)
Recent Developments
The development of the integrated circuits has revolutionized communication, information handling, warfare, and computing. Integrated circuits reduce the size of devices and lower manufacturing costs, while providing speed and reliability. Digitalization even further reduces size, increases speed, and lower costs. (Microsoft)
57
Electronics improves medicine with use of MRI and the CAT. (Microsoft)
Magnetic Resonance Imaging (MRI), medical diagnostic technique that creates images of the body using the principles of nuclear magnetic resonance. A versatile, powerful, and sensitive tool, MRI can generate thin-section images of any part of the body—including organs such as the heart, lungs, arteries and veins for any angle and direction, without surgical invasion and in a cross section of the human body. These maps give basic biomedical and anatomical information that provides great help in diagnosis. (Microsoft)
MCI is possible in the human body because the body is filled with small biological "magnet," the most abundant and responsive of which is the proton, the nucleus of the hydrogen atom. The principles of MRI take advantage of the random distribution of protons, which possess fundamental magnetic properties. Once the patient is placed in the cylindrical magnet, the diagnostic process follows 3 basic steps. First, MRI creates a steady state within the body by placing the body in a steady magnetic field that’s 30,000 times stronger than Earth’s magnetic field. Then MRI stimulates the body with radio waves to change the steady-state orientation of protons. It then stops the radio waves and "listens" to the body’s electromagnetic transmissions at a selected frequency. The transmitted signal is used to construct internal images of the body. (Microsoft)
The CAT scan, or computed axial tomography, is medical technology that uses X- rays and computers to produce three-dimensional images of the human body. (Microsoft)
The CT scanner contains an X-ray source, which emits beams of X-ray; an X-ray detector, which monitors the number of X rays that strikes various parts of its surface; and a computer. The source and detector face each other on the inside of the scanner ring and are mounted so they rotate around the rim of the scanner. Beans from the X-ray source pass through the human and are recorded on the other side by the detector. As the source and detector rotate in a three hundred sixty degree circle around the patient, X-ray emissions are recorded from many angles. The resulting data are sent to the computer, which interprets the information and translates it into images that appear as cross-sections on a television monitor. (Microsoft)
Both, the CT and MRI are used to create diagnostic images for better treatment of internal problems. (Microsoft)
Today’s research is used to increase speed, reduce size, and improve reliability. Very-large-scale integrated (VLSI) circuits that contain several hundred thousand components on a single chip have been developed. Superconducting circuits using
58
Josephson junctions that operate at temperature near absolute zero will replace very-high-speed computers. (Microsoft)
Strategies
One can use any history or scientific ideas, even all the abovementioned and put them on graphic organizers. The attached graphic organizers are provided to do so. Moreover, lesson and activities can be designed to fit the National Teaching and Learning Standards that were adapted for the state of Pa. (See Appendix A)
Classroom Activities
One can choose any of the graphic organizers provided (See Appendix B) and do various sections of this "Brief History of Electronics." Or, one may choose only certain time period(s) or specific invention(s) for a chapter, unit, or a constant practice of integrating graphic organizers in all lessons.
59
Bibliography
1. Standards- Based SCIENCE Graphic Organizers, Rubrics, and Writing Prompts for Middle Students. By Incentive Publisher, Inc. Nashville, TN. 2001.
2. Novak, J.D. and Gowin, B.D. Learning How to Learn. Cambridge, England: Cambridge University Press. 1984.
3. Bueche, Frederick J. Principles of Physics: Copyright 1988, McGraw-Hill Book Company, New York, NY.
4. Dobson, Ken. Science Spectrum: New York: Holt, Rhinehart, and Winston, 2001.
5. Canby, Edward Tatnall. A History of Electricity: New York: Hawthorn Books Inc., 1963.
6. Antebi, Elizabeth. The Electronic Epoch: New York: Van Nostrand Reinhold
Company, 1982.
7. Dummer, G.W.A. Electronic Inventions and Discovers: New Yor: Pergamon
Press, 1983
8. Landis, Fred. Microsoft Encarta Reference Library 2002: Microsoft Corp. 1993-2001.
60
People have known about static electricity for thousands of years. (Microsoft Corp) Biblical references to lighting were a reflection of God’s wrath. (Canby) Science did not make concern itself until the 1700s. (Microsoft Corp)
Early ideas
The Greeks, as early a 600 BC, rubbed amber and thought it had properties, also lodestone was thought to hold some type of attraction. (Canby) But, for almost 2000 years very little was done until the 1600s, Wm Gillbert discusses magnetism and amber’s attraction. (Canby) In 1745 Dutch person, Prof Musschenbroek, invents the Leyden jar, a crude capacitor. (Dummer) Ben Franklin discusses his theory electricity and in 1752 Franklin is credited with the first lighting rod. In 1772 iron dust filings reveal the magnetic lines of force, which lead to inductors or a beginning of a solenoid. (Dummer and Canby) In 1774, Lesage installs a primitive telegraph at Geneva, using 24 wires and glass tubes. (Canby). In 1775 Volta, invents electrophorus, and later the voltmeter. (Canby). In 1785, Colomb proves the inverse sq. law. (Canby). In 1786, Galvani electrifies frog legs. Again, Volta in 1796 invents the first battery. (Canby) Oersted, in 1820 discovers that a current can create a magnetic field. Also in 1820 Ampere develops terminology for electric current. In 1821 Faraday establishes the fact that a charge on the outside of a conductor produces
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no electric field. (Canby) In 1827 Ohm’s law is published. (Microsoft) All these great ideas, inventions, and more can be put on to graphic organizers by chronology, brainstorming, logical connections or just connections with no logic. See the attached graphic organizers (Appendix B) and pick the one that suits the situation(s).
The Start of Electronics
As mention in the beginning of this abstract Electricity and Electronic have a shared beginning. The two-shared phenomena are static electricity and magnetism. To physicists before the 19th century, electricity, magnetism and light seemed like entirely distinct phenomena. By the early 1800’s, work by Galvani, Oersted, and Faraday on galvanism, electromagnetism, and electromagnetic induction opened up a new field of experimental work which ultimately paved the way to present day electronic. (Dummer) In 1865 James Clark Maxwell publishes his paper "A Dynamical Theory of Electromagnetic Field." These two great ideas were put together (Canby).
The early 1800s was a time of great progress in theories and inventions. (Dummer) Infrared and ultra-violet radiation was discovered. Dalton’s atomic theory is put forward in 1808. Thermoelectricity, electrolysis, and the photovoltaic effect were all discovered before 1840. Work on low-pressure discharge tubes, glow discharges, new types of battery and the early microphone took place in the 20 years. (Dummer) So, between 1800 and 1875 basic physical phenomena were discovered, culminating in the practical applications of the telephone, phonograph, microphones and loudspeakers. Towards the end of the 1800s, wireless telegraphy, magnetic recording, and the cathode-ray oscillograph were all developed. (Dummer)
As corporations started to develop, one can see a shift from the individual to the industrial organization of the development of electronics. (Antebi) The great individuals such a George Westinghouse, Nikola Tesla, and Thomas Edison, to mention these few, begin to submerge to the collective of corporate organization. (Antebi)
As the 20th century begins we see Marconi’s wireless transatlantic radio signal. (Canby) Rutherford’s atomic model in 1911 and Bohr’s 1913 electron orbital theory corresponded to various permissible energy levels. (Dummer)
The early 1900s also saw the beginnings of the present-day electronic technologies. The 3-electrode valve opened the way to radio broadcasting and the Campbell-Swinton theory of television. But, it is WW1 that accelerates the pace for the development of electronics. (Dummer)
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• WW1 marked the impetus to develop radio communications with components such as resistors and capacitors. (Dummer) In 1920, Pittsburgh’s KDKA broadcast the 1st scheduled radio program for Westinghouse Corp. In 1925, Bell Telephone Lab invents a mechanism for recording sound electrically. (Canby) But, it is WW2 that had tremendously effect on components since the War was to be fought in climates all around the world. WW2 requirements were of the following nature:
• 1.Standardization-for faster production
• 2. Miniaturization-for aircraft, submarines, etc
• 3. Reliability-no component failures
• 4. Maintainability-quick replacement
• 5. Transport hazards-an ability to handle shocks
• 6. Mechanical shocks-impact of shells and parachute landing
• 7. Storage-long periods of use
• 8. Hot and cold temperatures
• 9. Humidity-tropics
• 10. High Altitude-high flying aircraft
• 11. Combined environments-8, 9, and 10 above
• 12. High Powers- increase range radio and radar
• 13. Radiation resistance- to withstand nuclear environment (Dummer)
Perhaps one of most important developments of the WW2 started before the War that is RADAR. It had tremendous effect on the War and should not be overlooked. (Dummer) Using radar the "Battle of Britain 1940" was won. Moreover, with the British using radar in its night bombing it hastens the end to the War. (Dummer)
After the WW2, many Europeans came to the USA bringing their ideas. This brain drain led to increased inventions in the USA that would continue until the 1960s. Furthermore, in 1946 printed circuit began to be used with miniature tubes. But, again in 1948, Bell Labs invented the transistor, which replaced the vacuum tube. (Dummer)
Integrated circuits appeared in the early 1950s. (Dummer) Resistors such as nickel chromium film is developed in 1957. (Dummer) The solid electric capacitor was developed in 1956. (Dummer)
Recent Developments
The development of the integrated circuits has revolutionized communication, information handling, warfare, and computing. Integrated circuits reduce the size of devices and lower manufacturing costs, while providing speed and reliability. Digitalization even further reduces size, increases speed, and lower costs. (Microsoft)
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Electronics improves medicine with use of MRI and the CAT. (Microsoft)
Magnetic Resonance Imaging (MRI), medical diagnostic technique that creates images of the body using the principles of nuclear magnetic resonance. A versatile, powerful, and sensitive tool, MRI can generate thin-section images of any part of the body—including organs such as the heart, lungs, arteries and veins for any angle and direction, without surgical invasion and in a cross section of the human body. These maps give basic biomedical and anatomical information that provides great help in diagnosis. (Microsoft)
MCI is possible in the human body because the body is filled with small biological "magnet," the most abundant and responsive of which is the proton, the nucleus of the hydrogen atom. The principles of MRI take advantage of the random distribution of protons, which possess fundamental magnetic properties. Once the patient is placed in the cylindrical magnet, the diagnostic process follows 3 basic steps. First, MRI creates a steady state within the body by placing the body in a steady magnetic field that’s 30,000 times stronger than Earth’s magnetic field. Then MRI stimulates the body with radio waves to change the steady-state orientation of protons. It then stops the radio waves and "listens" to the body’s electromagnetic transmissions at a selected frequency. The transmitted signal is used to construct internal images of the body. (Microsoft)
The CAT scan, or computed axial tomography, is medical technology that uses X- rays and computers to produce three-dimensional images of the human body. (Microsoft)
The CT scanner contains an X-ray source, which emits beams of X-ray; an X-ray detector, which monitors the number of X rays that strikes various parts of its surface; and a computer. The source and detector face each other on the inside of the scanner ring and are mounted so they rotate around the rim of the scanner. Beans from the X-ray source pass through the human and are recorded on the other side by the detector. As the source and detector rotate in a three hundred sixty degree circle around the patient, X-ray emissions are recorded from many angles. The resulting data are sent to the computer, which interprets the information and translates it into images that appear as cross-sections on a television monitor. (Microsoft)
Both, the CT and MRI are used to create diagnostic images for better treatment of internal problems. (Microsoft)
Today’s research is used to increase speed, reduce size, and improve reliability. Very-large-scale integrated (VLSI) circuits that contain several hundred thousand components on a single chip have been developed. Superconducting circuits using
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Josephson junctions that operate at temperature near absolute zero will replace very-high-speed computers. (Microsoft)
Strategies
One can use any history or scientific ideas, even all the abovementioned and put them on graphic organizers. The attached graphic organizers are provided to do so. Moreover, lesson and activities can be designed to fit the National Teaching and Learning Standards that were adapted for the state of Pa. (See Appendix A)
Classroom Activities
One can choose any of the graphic organizers provided (See Appendix B) and do various sections of this "Brief History of Electronics." Or, one may choose only certain time period(s) or specific invention(s) for a chapter, unit, or a constant practice of integrating graphic organizers in all lessons.
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Bibliography
1. Standards- Based SCIENCE Graphic Organizers, Rubrics, and Writing Prompts for Middle Students. By Incentive Publisher, Inc. Nashville, TN. 2001.
2. Novak, J.D. and Gowin, B.D. Learning How to Learn. Cambridge, England: Cambridge University Press. 1984.
3. Bueche, Frederick J. Principles of Physics: Copyright 1988, McGraw-Hill Book Company, New York, NY.
4. Dobson, Ken. Science Spectrum: New York: Holt, Rhinehart, and Winston, 2001.
5. Canby, Edward Tatnall. A History of Electricity: New York: Hawthorn Books Inc., 1963.
6. Antebi, Elizabeth. The Electronic Epoch: New York: Van Nostrand Reinhold
Company, 1982.
7. Dummer, G.W.A. Electronic Inventions and Discovers: New Yor: Pergamon
Press, 1983
8. Landis, Fred. Microsoft Encarta Reference Library 2002: Microsoft Corp. 1993-2001.
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