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this page, Daily physics 1 - first knowledge
bottomFrench
Units calculation (units, names and values - small calculations with units - (measuresand appareils de mesure)
- Disguised percentages
- Slopes, degrees and trigonometry (clock and sinusoidal curbs, lunar tides and alternative current)
Units :numbers used by convention for measurements and calculations : the meter , the litre , the kilograms (mass) , the
Newton , the Pascal , the kilowatt (power) and kilowatt-hour (carried out work, total consumed energy ).... Some others are more surprising, for
example the light-year (the distance which the light traverses during one year (I let to you calculate at a rate
of 300.000 kilometres a second, that is to say the distance the earth-moon!) or the kilometre/passenger which utilises two units, the distance covered and numbers of people on board (300 people flying on 1000 km = 300.000
km/passengers).
The Mega term (see below), is used without understanding in the trade or the popular speech to say
"much"; Mega bass for a radio set which cannot really deliver the powerful bass ones (very limited by the size of
the loudspeakers, the piles and other electronic cicuits).
Name of very large and very small figures ; thousand (a thousand ); a million = 1000 thousands = a
Mega (1 followed up by 6 zero); a Milliard (GB) or a
billion (US) = thousand millions/Mega (no name ? 1 follow-up by 9 zeros ); one billion (GB) or trillion (US) = thousand milliards (GB) or thousand billion (US) = Tera (1 follow-up with 12 zeros).
And an astronomical one, well known google (1 and 100 zero)
The same ones but into small now (opposite), is: thousandths = 1 divided per 1000 =
1/1000); one millionth = 1/one million = a micro ; a billionth (US) = 1/un billion = a nano (1 followed by 9 zeros); one (name ?) = 1/one billion =
1/thousand billion = a pico (1 divided by 1 follow-up by 12 zeros) ; an Angström, unit of length of wave and distances atomic = 1/1 follow-up by 10 zeros.
These extreme numbers can appear out of the everyday usage, however will know that a printer projects ink drops
calculated in picolitre , that a TGV consumes 5 Megawatts/second and that unit Tera is necessary to measure
the consumption of electricity of Paris over one year (15 Tw/h), equal to that of Eurodif, power station of uranium
enrichment.
Simplification for numbers with a lot of zeros ; example on Angström = 1 divided by ten zeros is also writen 1-10 (1 power -10)
One multiplied by teén zeros would be writen 110 (1 power +10).
said 1 power 10.
Small calculation with the units : a calculation must utilise
units of comparable nature (one multiple step of the monkeys
with hens, but with eggs, yes, if you wish to have a figure
which represents an average output).
Therefore, if you want to know the thickness of stones that
you would obtain by pouring 50 litres of stones on two
square meters (2 meters by 1 meter) it will be necessary to
convert volume into cubic meters or cubic centimetres (and
similar for the surface ). Calculation: one litre = 10 cm *
10 cm * 10 cm = 1000 cubic centimetres. 50 litres make
50.000 cubic centimetre, which you spread out over 2 square
metre is 2 times 100*100 cm = 20.000 square cm (cm2). 50.000
divided by 20.000 = 5/2 (one removes 4 zeros on each side) =
2,5 cm of thickness. Be not thrown into a panic any more by
seeing a ground heap. Once spread, there is nothing any more
left ! and it is packed afterwards.
Note : the official litre of the bottles would make nothing
any more but some 98 centilitres !
Percentages and slopes and degrees:
their definitions can be misleading; one perfectly understands an
increase of 10% : it is the tenth of the basic value. For 100 €, 10%
make 10 € and one finally get 110 €. Beyond the 100%, the brain panics.
Example, the cost has increased by three hundred percent
: one retain the figure of three hundreds, which appears enormous, but
one mentally does not make division per hundred.
In fact, the cost is four times higher. 100% of increase double the value,
200 % triple it.
The slope of the funicular is 80%:
we imagine immediately a quite vertiginous vertical, that the cameraman
don't middto to amplifying while banking its camera. However, it is
simply the definition of the slope, which is the height one
rises when driving or walking divided by the hundred meters base
measured horizontaly. One rises all the
same of 80 meters by 100 meters of horizontal, which forms all the same
an angle of almost 40 degrees (38,7).
The distance covered on the slope is then close to 130 meters. The 45 °
slope is particular because the horizontal distance equalizes with the
rise, i.e 100 meters for both. The distance
covered (diagonal of the triangle called then “right-angled”), is
approximately 140 meters (141,5).
Slopes and distance to the meter.
On the road, a slope of 12% means that one rises (or goes down) of 12
meters by 100 meters gone on the horizontal line. The real distance
rode on the slope (the road) is hardly larger (100,72) because the
angle is still small. The angle corresponding is almost 7 degrees. A
descent known as “standard” a plane follows is 3 degrees slope, that is
to say roughly a 5% slope. Less than in a car ? yes, because the plane
flies much more quickly and thus goes down more quickly despite a
smaller slope. Moreover, on the basis of 3.000 or 10.000 meters, it
will cross a height much more important
(pressure..). How
to calculate the distance covered on the slope?
one knows the horizontal one, 100 meters, the vertical, 80 meters: the
distance covered “read on the meter” by the funicular is given by a
formula known as “theorem of Pythagore", I.e. that the distance meter
measured on the slope “P” is equal to the root square
(*)
of the square the horizontal distance (100 meters), i.e 10.000, plus
the square of uneven (80 meters), i.e 6400. We thus have to calculate
the square root of the total of both, i.e 16400, which gives 128 m
(128,06).
(*)
the square root of a number is the opposite operation of the square: if
2 times 2 make 4, square root of 4 is 2.
By multiplying 128,06 by
128,06, one finds 16400
Slopes, degrees and trigonometry.(sine, tangent, cosine of angles). If the length of the slope is 130
meters and the uneven one “gone up” is half,
i.e 65 meters, the angle of the
slope is 30 degrees. The report/ratio
(division) between the side “height of uneven”
of a right-angled triangle and the side “distances on
the slope”, is called sine. If the uneven height
is equal to the horizontal distance, our right-angled triangle
becomes also equilateral. The ratio (division) of these two equal
numbers gives 1, which will be the value of another trigonometrical
definition, the tangent. In this case, the sine would be 0,70 as well
as the cosine because we have two angles of 45°. Sines and cosine vary
in opposite direction. An angle of 30° has a sine of 0,5 and one cosine
of 0,866. An angle of 60° has a sine of 0,866 and one cosine of 0,30.
An angle of 45° has a sine and a cosine of 0,707. Our two angles of the
right-angled triangle (the third is 90°), can
finally be measured by the sine, the tangent or the cosine. Do not
only forget these numbers, in spite of their strange names, are only
divisions on two sides of a right-angled triangle. In fact the
selected sides determine if the number is a sine, a cosine or a
tangent. For each value of these numbers
corresponds a precise angle which one finds in books
or with a scientific calculator.
Practically speaking :
one can measure the height of hillock, a building
or a mountain if, by knowing his distance (OH), one measures the
angle under which one sees the top of it.
This has been used for long
1 /
On can measure the angle that makes the direction OP targeting to the summit, compared to the horizontal
base (OH), which is the length of the shade ; one can calculate the height PH using trigonométry as seen before.
2 /One does not know how to measure the angle. In our environment
vicinity, le rays of the sun come from the same direction
everywhere, at any hour of the day. On this spot, the lenght
of any shade has an identical ratio comparing to it's height.
Plowing a vertical stick, one can find the ratio by dividing the
length of the stick by its height (PH).
The
height of the building is egal to the lenght of its shade,
divided by the lengfht of the stick shade, then multiplied by the
stick height (identical ratio).
Ultra
short waves (GPS),
the laser and satellites allow very precise measures.
Alarm clock
and sine waves. Warying our
angle of slope since 7° (slope of 12%), with 30° (sine 0,5 - slope of
44%), then 38,7 degrees (sine 0,625 - slope of 80%), finally of 45° (sines
0,70 - slope of 100%), one can observe that the slope turns like the
reverse of the needles of an alarm clock. Let us observe as comparison
the big hand of an alarm clock: the vertical
distance traversed by its point is small when
nearby the top (both sides of
the 12) or nearby the bas (both sides
from the 6), and large close to the horizontal line.
Conclusion: For an identical angle of rotation, that is
to say an equal time, the traversed vertical distance is much more
important close to horizontal than of the vertical. If one
accelerated the movement of the alarm clock by removing the regulator
and that one can see the needle by its profile and not
by its face, one would
see only the vertical movement of its big
hand and one would see there is
a stop at the top and bas, then acceleration, then maximum
speed close to horizontal and so on. A
curb could be obtained making
sliding a band of paper,
while putting down the different positions of the needle. This curve is a
sinusoid (see below).
translation
: faibles variations (small variations).
Lunar tides and alternating electrical
current. The moon turns
around the ground and makes a full rotation in 28 days (roughly). The
moon exerts a variable force of attraction on all that lives on
our earth, and acts on
the reproduction of the species, mammals mainly
(tides for all the liquids, human include) or
the growing of plants. Like
the point of the needle, it describes its circle
around the ground and its force of attraction make vary
the tide relating to the same rules. There is a phase or the
tide is low, then it starts to go up slowly,
accelerates goes up (or goes down) very quickly, then slows down to
stop again at high tide. To simplify, the sailors
divide a cycle into three periods
of equal duration.
First period, it starts to go up slowly. Second period, it goes up
quickly. Third period, it slows down before immobilizing
to set out again in opposite direction. It also follows a movement
progressive of acceleration, deceleration and
passage at null speed of sinusoidal type.
The alternating electrical current is a kind of electric
tide. With the same sinusoidal law, it starts by arriving
slowly of a terminal of the socket, increases
its force very quickly, then slows down to stop and to set out again
again, this time by the other terminal. Like the
tide, it changes direction. It arrives and it
from goes away. Not in
6 hours or a bit less for the tide, but in a
fiftieth of second (sixtieth
in USA), that is to say fifty times a second.
Physics 3 "electricity" (bas of page).
Chart of the sinusoidal variation.
Looking again at the preceding clock, divided by half hour period, and
pointing each time the different heightsof the needle (thin horizontal
lines), one obtains the right hand curve. One can observe there the
periods of change with one almost "'immobilization" (both at the top
and bas), followed by acceleration, then maximum speed (with the
passage of the thick horizontal line), then deceleration etc.
Between the
points A and B, there is a complete cycle of the variation which is
said a “period”. For the tide, it is a little less than 6 hours, for
the alternating electrical current, 50 times a second in general, 60 in
USA.
Translation : heures = hours ; défilement du temps pointage par 1/2 heure = running time by period of
half an hour.
The curves
: there is of course the circle, but we will speak here about names which make sometimes fear or too
scientist, they are in fact related to the life of our planet: the ellipse, the parabola, the chain, the "curve of the dog".
The ellipse is the curve all planets and stars follow in the their race around another
one larger, whose retains them by his enormous gravity (attraction due to its mass); like the moon around
the earth, earth around the sun and so on.
An ellipsecan be drawn by planting two drawing pins or points on two points (called focus) and by
fixing on each one the tip of a thin thread.
This thread will be cut definitely longer than the space reserved between the points. One tightens then the
thread by pushing a pencil against it while having it run along (one cannot make so only half of the ellipse and it
is necessary to take again on the other side). The shape and the size of the ellipse will thus depend on the spacing
between the points and the length of the thread, which summarizes a mathematical formula.
Let us return to the thread: its length is always the same one (constant)
wherever is the pencil which tightens it. Conclusion, in any point of an ellipse, the addition of
the two distances towards the two points is constant.
The parabola
is the curve that any stone launched in the air in direction of a target makes.
Even the ball of a rifle follows such a curve and it is necessary to regulate the sight (the rise) according to the distance. If the
way is very short, one can't see the curb and one believe, wrongly, that it is a straight line. In fact it is impossible because gravity inevitably draws the
stone or the ball downwards; it thus goes up by the power of the throw, then falls down more and more vertically. It is difficult
building a parabola with a thread because it is necessary that this thread be fixed at a point (the
focus) but slide at the other end along a straight line called director.
In any point of a parabola, the distances between the focus (the point) and a line called director, remain equal.
This curve has a characteristic; The parabolic shape of reflectors of flashlight, headlight, TV/telephone antenna (parabolic) or radar, allows the light emitted at what we called the
focus, to return all these radiations in a parallel beam. Conversely, the parabola concentrates the
received rays, presumably parallel, at the point called focus; this is why you will observe that the parabolic aerials one a whole a kind of arm in the medium
; it is at the tip of that arm that is the point called focus and it is there the light, radio wave or sound are emitted or caught).
The sound can be thus listened by far while directing a parabola towards the source (people,
animal). The microphone is placed at the focus (at the end of a stem).
The chain curves
is the curve which any thread tended between two points makes under the effect of gravity ; washing line or
powerline, nothing escapes from it.
One cannot plot this curve of which the mathematical resolution is complex and inaccurate because one makes in fact
numerous estimations.
Thus do not think the sag the cable makes to cross the river or to cross the valley could be reduced by tightening it more,
either those of the bridges, whose weight for each meter is enormeous.
They are already under a very strong tension and with the cold and the weight of snow, ready to break in spite of
appearances. You will thus tend "in straight line" and only seemingly, a resistant and light thread on a short
distance. It is what the masons practise for tracing a horizontal line on a wall: one coats the wire with a
coloured powder, one tightens it well and one pinch/release it on the wall so that it deposits its color onto.
The curve of the dog is so called by reference to four dogs which would keep chasing
while leaving each one the corner of a square. At every moment, the race of the one of the dogs is perpendicular to that of the
pursued dog because it is the shortest way to reach it. As the dogs run themselves all after, the direction of each dog
changes without stop. Each curve describes a kind of spiral. Without studies, without calculation, the dog follows this complex curve which is the best to
catch up with the other which must also avoid the other.
This curve is only interesting to underline our aptitude (like the dogs considered), to correct our
trajectory automatically in order to maintain a distances minimum (because that corresponds to the minimum effort). This
concept of minimum effort and thus of distance minimum always pushes us to take the direct straight line at any moment to reach a
spot. of which the pressed lawns whereas a path skakes aside, the reversed fences, angers to have to make a great
loop where one passed before straight
(motorways, properties), conflicts which go to wounds or dead of man if paths
were vital (seen in New Caledonia). Without speaking about the toads one collects to make them
cross the motorway at the season of love, of crabs crushed everywhere in the Pacific Islands and besides. All the life is conditioned by
that : lots of current roads were old ways of passage, coming from the paths of the bas of the ages, not only
from the men but also of the animals. One says in Corsica that to trace the path in the mountain, one follows the goat
(which combines shortest with easiest). In the car, you often have two routes, shortest and fastest.
Hectic curved of the tennis ball, the balloon or golf ball.
When a force of propulsion is applied, a shot, a kick, whatever, the
projectile starts in the direction the force is applied, in straight line,
excepted influence of a good cross-wind. How devil can manifest so that the
ball, as animated by an interior force, deviates gradually towards the left
or the right-hand side ? answer: by giving it an effect, i.e. by
striking the ball on the right or left side, so that it spins around a
vertical axle. The forces of air braking becoming unequal on a side and
other of the ball, it deviates gradually on a side, giving this twisted pace
of the trajectory. .
A vertical effect can be added, striking also both on a side and a bit under or above. That alter the
height of the curb, but mainly the bouncing on the ground at the arrival
(the ball tend to run back or at the contrary slip flat.
To better controlling the flow of air around a ball, one can try to break turbulences by putting to
it facets, for example (golf ball)
How
to calculate the distance covered on the slope?
For an identical angle of rotation, that is
to say an equal time, the traversed vertical distance is much more
important close to horizontal than of the vertical. If one
accelerated the movement of the alarm clock by removing the regulator
and that one can see the needle by its profile and not
by its face, one would
see only the vertical movement of its big
hand and one would see there is
a stop at the top and bas, then acceleration, then maximum
speed close to horizontal and so on. A
curb could be obtained making
sliding a band of paper,
while putting down the different positions of the needle. This curve is a
sinusoid (see below).
translation
: faibles variations (small variations).
