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GALILEI Galileo (1564 1642)

can be considered one of the greatest scientists of modern history and author of the scientific method.
His first important discovery was observing the oscillation of a lamp, discovers the law of the pendulum for small oscillations dell'isocronismo: pendulums of equal length make equal time regardless of fluctuations in their amplitude.
The big news is that Galileo introduced precisely to address the telescope (perhaps not invented by him, but it certainly changed and improved) to the sky and begin the first systematic observations of no more than the naked eye. Initially
advocate of the theory Aristotle - Ptolemy, became convinced of the Copernican theory thanks to these sensational discoveries
- spots on the moon are shadows cast by the mountains (which calculates the height);
- the four 'moons' of Jupiter, that shows that not only the earth can be the center of circular motion;
- The Milky Way is made up of countless stars
- the ring of Saturn
- the phases of Venus that show that this planet "could" turn around Sun;
- the planets are naturally dark because they receive light from the Sun;
- sunspots.

His most important and best known is the "Dialogue Concerning the Two Chief World Systems Ptolemaic and Copernican ". Besides being a great work of popular science, laid the foundations of the new physics through the destruction of the old Aristotelian system. It is set as a dialogue, in fact, among three parties: Salviati is the teacher who acts as the bearer of the new, Sagredo is cultured and free-thinker able to change the view, is a dogmatic Aristotelian Simplicio.
course Galileo knows that, from Earth, he could not show that it is spinning around the sun He bypasses the difficulty of moving along two trails: one part the "principle of inertia" and the other the "principle of relativity".
And from here begins to rise to the need for new physics at the expense of the Copernican Aristotle.

Just in defense of the Aristotelian-Ptolemaic tradition, Galileo was condemned by the church inquisitor of the time and is forced to recant, that the public renunciation and repudiation of his ideas. This painful episode would have created the legend of Galileo, who once stood up after the recantation, hit the ground and murmured: "And yet it moves!"

Towards the end of his life, when she was completely blind, published another of his important wrote: "Discourses and mathematical demonstrations concerning two new sciences"; it is the laws of motion and structure of matter.

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NEWTON (1642-1727)
physicist and mathematician of the greatest of all time.
His most important are the "Philosophiae Naturalis Principia Mathematica," which lists the results of its mechanical and astronomical surveys, as well as lay the foundations of calculus. Among other works include "Optik", a study in which he argued the famous corpuscular theory of light, "Arithmetica universalis and Methodus fluxionum et serierum infinitarum" published posthumously.

The Newton's laws of motion (the one most commonly known as "three laws of motion") are still the basis of classical mechanics. The first law is the principle of inertia states that a body perseveres in its state of rest or uniform rectilinear motion, unless it is compelled to change that state by forces outside the second law, stating that the acceleration of a body is directly proportional to the applied force, allowing the one hand, moment by moment to calculate the position and velocity of the body are known when the initial conditions of motion, on the other hand the definition of one of the most important concepts of physics: the inertial mass . The third law states that for every action there is always an equal and opposite reaction.

's more specific contribution to the description of Newton the forces of nature came from law of universal gravitation: it states that two bodies attract each other with a force directly proportional to the product of their masses and inversely proportional to the square of their distance, this law has vast implications: it introduces the concept of mass gravity, explained the motion of planets around the Sun and the objects inside the Earth's gravitational field, but it is also responsible for the phenomenon of gravitational collapse, leading to the understanding of the phenomenon of blacks holes. The legend wants that the idea of \u200b\u200buniversal gravitation by the fall of an apple suggested to among other things, it would seem authentic.

Among his numerous studies include recognition white light as a result of the superposition of all the colors of the spectrum, the theory of light propagation and the introduction of differential and integral calculus, he was also responsible for understanding the phenomenon of the tides and the precession of the equinoxes. The
Kepler's laws of planetary motion and the theory of Galileo on falling bodies were both confirmed and recognized as consequences of Newton's Second Law of Newton and his law of universal gravitation.

Trivia: In her tomb in Westminster Abbey is this epitaph: "Sibi gratulentur mortales that humani generis decus tantumque exstitisse (mortals rejoice that there has been a such and such great honor of mankind).

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Also I did some concept maps!
you can enlarge or simply give it a try!
laws of dynamics
motions
Galilean relativity

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.. to find in you tube video of Sarah, use this gadget!

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... come to the wiki!

Okay guys! I saw that you worked so hard and I'm glad that you are passionate.
I beg you, put the things we talked about in class on the wiki .. and do not forget to tag (see the tags) for each page.
Remember also that if, for example, Sarah has created a page of the laboratory tagging workshop and some of you think it is more appropriate to another tag, well're ready to add the tags differently.
E 'prorpio their purpose, and do so without fear of making mistakes! So do I!
Vivian, the beautiful logo that you and your group have done and you sent me. As you have seen and I've uploaded my opinion is very comfortable. If someone does not like, however, say that we will try to change it to please everyone! Look
comments!

Great job guys!

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Experiment on the parabolic motion

Material: a rigid plastic tube (which would be blowgun), an electromagnet, a power supply DC power from 0 to 20 V, a ball of iron, a glass marble, electrical cables for connecting two support rods, aluminum foil, two wires terminal, a switch;

Purpose: show that in a parabolic motion of a severe horizontal and vertical motions are independent and that the time of vertical fall is the time of horizontal displacement;

Procedure: mount the tube horizontally on one of the two supports, attaching the electromagnet to the other support, adjusting the height and direction of the blowgun to aim at position to deal with the ball hooked all'elettrocalamita. Secure with scotch tape the wires with terminal ends of the tube, they attach to a strip of aluminum foil, so that it covers the exit hole of the blowpipe.

The structure of the equipment is summarized in the following figure:

all'elettrocalamita Hook the metal ball and use the other as "bullet" in the blowpipe.

Before proceeding with the experience itself must be "calibrated" the pole of the blowgun horizontally and vertically to achieve alignment with the metal ball.

When the ball breaks the foil projectile breaks the circuit and determines the fall of the ball is supported by the electromagnet. The two balls then start at the same time their motion vertical drop. The difference between the two is that the ball projectile, having also a horizontal initial velocity, describes a parabolic motion.

balls collide in a point located at the vertical of the electromagnet. This shows that the downward shift of the metal ball is the same as that of the ball projectile, at the same time interval. In addition, the time taken by the metal ball to fall along the vertical is the same ball used by the projectile along the horizontal line that corresponds to the distance between the electromagnet and exit point from the blowpipe.

A confirmation of impact occurred, in many cases the glass ball breaks.

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Uniform circular motion

a) uniform circular motion

DEF: The motion of a body that is a circle (a circle) with speed (in form) is said constant uniform circular motion. When we refer only to the intensity of the speed we are talking about speed climb.

ATTENTION: The speed is a vector, it is characterized by intensity, direction and orientation.
in uniform circular motion is the intensity of speed to be constant, the direction and to change the time!
NOTE: For each type of trajectory, the velocity vector is always tangent to the trajectory.
Since the form of speed is constant, one might be tempted to consider a motion is not accelerated. But we must remember the definition of acceleration (it is also a carrier!) And note that the difference of two vectors with the same form is not 0. The fact that the speed changes of direction, even if it does not change in intensity, uniform circular motion is therefore an accelerated motion.
For the second principle of dynamics, if the motion is accelerated, then this is a force.

Some important parameters relating to the uniform circular motion are:

1)

PERIOD The period is the time it takes to make a full circle. It is measured in SI (International System) in seconds. It is usually indicated by a capital letter T.
We observe that the concept of time also applies to any motion that they be periodic but the characteristic of, or to "wipe" to the same point after a certain time.

2) FREQUENCY

The frequency indicates the number of revolutions made per unit time. In SI, the frequency is measured in hertz (Hz) and the number of revolutions per second. It is usually denoted by the lowercase Greek letter f or ν. The frequency features in general a periodic phenomenon qualunque.Fra the period and frequency there is a mathematical relationship important:

f = 1 / T;

ie the frequency is the inverse of the period.

3) SPEED 'SCALAR

The velocity scale of uniform circular motion is, as with all speed, measured by the ratio space / Time. If the radius of the circle is R, whereas the entire circumference measure 2 π R and that the total time to tour is the period T, then you will have:
v = s / t = 2 π R / T.
This is the formula of the scalar speed of rectilinear motion. It can also be expressed as a function of frequency taking into account that f = 1 / T. Then you get: v = 2 π R
f.
speed climb, of course, is measured in SI in m / s.

b) centripetal acceleration

The rectilinear motion with uniform acceleration because the direction of its velocity changes point by point. Let's see how this acceleration is calculated and its characteristics.
consider velocity vectors at points A and B respectively, and call them v1 and v2:
means for accelerating the change in velocity per unit time. Dv call with the change in velocity between points A and B for which we have:

v2 = v1 + dv

since the speed at point B is the speed at point A plus the change in speed (all three are vectors!).
For convenience, we report the carrier at point A by a parallel shift. We get :

Remember that the intensity of v1 and v2 are the same and to make the sum of two vectors, you must use the rule of the parallelogram.
We have obtained the vector change in velocity dv that is directed toward the center of the circle along which the motion takes place.
If we divide this vector for the time Dt in which the point is from A to B, we finally obtain the sought acceleration which is itself a carrier who has the same direction and orientation (since the time that we share is a positive number ) of the vector change in velocity dv.
The acceleration is then:

a = dv / dt

. . Please note that we have indicated the acceleration with the "subscript" c. This means that the acceleration "point" toward the center, and this is called centripetal acceleration .
NOTE: This acceleration, at a given point on the circumference, is exactly pointing to the center though, looking at the graph, this would seem true only approximately. In the chart, we took two points (A and B) "somewhat" distant for reasons of simplicity. If we take them "very close" (infinitely close), you would see that dv is directed exactly toward the center and there would then the instantaneous change in speed.

How much is the intensity of centripetal acceleration? Need to derive some basic knowledge of differential calculus, for which we give directly the result. The strength of the centripetal acceleration is: a

c = v ^ 2 / R

where v is the velocity scale of the motion and R the radius of the circle. Also note that here, speed and acceleration are staggered arrangements.
Note that the centripetal acceleration is directly proportional to the square of the velocity and inversely proportional to the radius. This means that if the speed is doubled, the acceleration quadruples and so on. If the radius doubles, the acceleration halved, if the radius by half, the acceleration doubles etc..

c) centripetal force

If a body moves with accelerated motion, it is because it suffers the action of a force (resultant). For the second law of dynamics, the relationship between force and acceleration is given by the formula: F = ma

m is the mass of a scalar, the force and acceleration vectors.
in uniform circular motion, then a force acts, the so-called centripetal force, which is due to the fact that the body along a circular path. If your body does not act force (resultant), the body moves in rectilinear motion (first law of motion ).
The centripetal force is then: F

c = ma c

and will be targeted as the centripetal acceleration, m is the mass of a positive number (multiplying a vector by a positive number, direction and orientation the carrier that you get do not change).

The intensity of the centripetal force will be:

the centripetal force for the same considerations of direct and inverse proportionality that we have done for the centripetal acceleration.

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About the motion of projectiles ... here are two interesting applet:
and a two !

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the motion of a projectile

Galileo was the first in a scientific way to study the motion of a projectile showing that its trajectory is a parabola. The results are published in the work "Discourses and mathematical demonstrations concerning two new sciences."

Obtain the results of Galileo by the equations of motion, taking into account only the gravitational forces acting on the projectile, considered as a material point, and neglecting air friction.

We choose a reference system with the y-axis positive upward, so that the origin of the axes is the point (0 x, y 0) = (0,0) of departure of the projectile; The components will be x = 0, y = - g.

Using the law of fall of a serious, we draw the trajectory of a bullet, making sure it is a parable and then showing some more features.

The velocity vector v at the initial instant t = 0 has form v 0 and is tilted at an angle θ with respect to the positive direction of x, its components are:

v 0x = v 0 cos θ

_{0Y v = v 0} senθ

The law of motion, which expresses the speed is a function of time t (v (t) = v 0 + at).
Since there are no horizontal components of acceleration, the horizontal component of velocity v x remains constant, the vertical component v y change over time because there is a constant downward acceleration (a y = - g):

v x = v 0x

v y = v 0Y - gt

The velocity vector is tangent to the trajectory at each point, its form is not constant and can be obtained by applying the Pythagorean theorem.

The laws of motion describing the motion of the projectile in space are those of a rectilinear motion along x and y uniformly accelerated along, independent of each other. Then the coordinates of the projectile in parametric form (the parameter is the time t) at a generic instant t are:

x (t) = v 0x

t y (t) = v 0Y t - 1 / 2GT ^ 2

From this equation it is possible to obtain the equation of the trajectory in Cartesian form, obtaining t from the first equation and substituting in the second. You get the equation of the trajectory of the bullet:

as you can see that is a downward parabola through the origin of the axes. A drawn representation of motion with the velocity components is shown below.

The vertex of the parabola can be found mathematically by the known relationship V = (-b/2a; -Δ/4a). Arguing from a physical point of view, the vertex of the parabola is obtained by requiring that the velocity along y is 0. It is then the point:

M x represents the abscissa of the point maximum height, y M the maximum height reached by the projectile.

To calculate the range, that is the point at which the bullet falls on the axis of x, y sufficient to impose (x) = 0, ie to the intersection of the parabolic trajectory of the bullet with the x-axis You get two solutions:

The first is obviously the source, the second is the range sought.

The time taken to travel x G is called time of flight (t Flight ) and coincides with twice the time necessary to reach the maximum height y M and return to the soil

t Flight G = x / v = 2x 0x M / v 0x .

Note that the location where the bullet touches the x-axis, the speed is the same in the form at the start but it is symmetrical with respect to x.

The launch angle for maximum range is where you can get as follows:

sen2θ = 1 → 2θ = 90 ° → θ = 45 °.

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Video

Hi everyone!
I allowed to put on a wiki (in the laboratory on the page number 4) the video playback experiment. I hope you enjoy it. I have not reported the discursive part of the experience, but it is already on the blog. Waiting for the final go-ahead for prof ....
good work!

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Exercises on falling bodies and parabolic motion

EXERCISE

A body is launched, with a velocity 'initial horizontal 10 m / sec from a tall building h = 35 m. Determine:
a) the distance d, measured from the base of the building, the point of impact with the ground of the body.
b) The flight time.

SOLUTION

During the motion of fall speed 'remains constant while the horizontal and vertical (at all) varies according to the law:

establish a baseline that, starting from the base of the building, the x-axis is horizontal and the vertical z axis. The projections of the motion along the x-axis and the z-axis are the following:

From (3) by putting z = 0 we get the flight time:

Correspondingly, the projection along the x-axis has traversed a distance:

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link? Concept map on Newton

Good evening everyone!
I write about the experience of laboratory No. 4. Make a link to the theoretical treatment of the system "more passenger lift," you agree with me?
if we do so directly on the wiki?
soon and good work (though perhaps no longer the time)! Sara

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I created a concept map on Newton, there's link here.
I realized that I do concept maps is useful to summarize the fundamental concepts of a topic to study!

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Publishing on the wiki!

Ok guys! I have read your work and I think it is time to publish. Maddalena and Paul, Luke and Sara, you must put your work on the Wiki?
As for the story to wait a moment, lavoriamoci a little 'because there are new suggestions, ok?

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Prof. Buongiorno!
I usually use Flickr and I delel uploaded photos can be useful, in particular may serve to Patricia and Ross. There are two photos: one of Newton and Galileo. Here they are

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laboratory experience

Construction of a dynamometer

Need: a helical spring, a support of wood, a piece of graph paper, pencil, some bodies sample mass note.
Design: We hung a
'end of the spring support, on which we glued a strip of graph paper vertically.
· Calibration of the instrument :
we have indicated with the pencil in zero reference index of the spring discharge. Our laboratory is equipped with a mass of 0.1 Kg, 0.5 Kg, 1 Kg, we hung on the spring weight and we have drawn a smaller mark on the paper at the index and indicates the value of the force hanging from the spring (assuming g = 9.80 m / s ^ 2, we scored 0,980 N). We have different masses hung by suitable combinations of those available and scoring scala.Il corresponding weights on dynamometer is constructed: we can now proceed to the measure of an unknown weight.
· Measurement of an unknown weight : we hung the body of which we measure the weight and the value we read on the scale at the index, the reading is the weight of the body. In the calibration of the instrument we used the bodies of known mass, then multiplied by the acceleration of gravity to find the weight. For this reason, the reliability of the instrument ceases to be valid if taken to a point on the Earth's surface other than calibration, where g has a slightly different value. Here in the picture the image of a dynamometer.

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n 3 Concept map on Galileo

Prof, Ross and I have prepared this concept map on the observations of Galileo. How do you think? the link is here
To all: if you want to change something in our map go to the folder "mechanical" in cmap as we did in the lab on Wednesday!

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Let the WIKI? Laboratory experiments

Great Guys, you're doing a great job everyone!
The work done in the group are a bit 'to be corrected, but are well written and I see with pleasure that a cast that is much collaborate via the web. The next time we meet we discuss in class well in voice and decide which posts will be "promoted" to go to the wiki.

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n 2

The second law of dynamics

We have combined with a mass of 1 kg of a spring and we have a spurt of 2 m / s ^ 2. To measure the acceleration of the body we used a motion sensor connected via a USB interface Pasporta-supplied PC program DataStudio.
We have carefully measured the elongation Δl of the spring associated with the force that the spring exerts on the block. We then replaced with another body of mass m 1 and applied to that body the same force, that which produces the same stretch of the spring measured in the previous case (we have assumed that the force of the spring is proportional to elongation thereof). In this case we measured an acceleration other than 2 m / s ^ 2, ie 0.5 m / s ^ 2. Is defined as the ratio of mass of the two bodies of the mutual relationship of the two acceleration impressed on them by the same force: 1 m / m = a 0 0 / a 1.
The second body, which undergoes an acceleration equal to one fourth that of the first body with the same force acting, has a mass four times greater.
Finally, we verified that the relationship between the two masses is independent of the applied force, if this is the same for both: so we repeated the experience with a force that acts different, and we found: m 1 / m = a 0 0 / a 1 = a 0 '/ a 1'.

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inertial mass and gravitational mass

The concept of mass is one of the concepts of physics more "complicated" to be defined.
mass, like every physical quantity must be measurable. Then need to define the laws expressed in mathematical formulas that invoke it.

There are therefore two types of mass

1) the inertial mass , one that appears in the formula 2 'principle of dynamics:

F = ma

2) the gravitational mass , one that appears in the formula of the law of gravitation:

F = Gm 1 m 2 / R.

These are two different types of mass, as defined in the phenomena of a different nature and therefore different mathematical formulas. But then we see to give a more precise definition of the two types of mass.

1) The inertial mass indicates the "resistance" that a body opposed to a change in its state of motion .

In fact, if we apply the same force to two different bodies, we get different accelerations.
If, for example, a force of 100 N to a body of 10,000 kg inertial mass we get an acceleration equal to:

a = F / m = 100/10000 = 0, 01 m / s ^ 2

If we apply the same force to a body's inertial mass 5 kg, we get the acceleration:

a = F / m = 100 / 5 = 20 m / s ^ 2.

A higher body mass inertia opposes a greater "resistance" to change its state of motion that, with the same force, you get a lower acceleration. A body mass inertia opposes child less "resistance" to change its state of motion that, with the same force, you get a greater acceleration.

We can then define the inertial mass as the ratio:

m = F / a.

To calculate the inertial mass of a body then simply divide the force acting on it by the acceleration it undergoes. At equal strength, lower inertia mass means faster acceleration, greater inertial mass means less acceleration (acceleration and inertial mass are inversely proportional).

2) The gravitational mass indicates the "capacity" that the bodies of attract gravitationally.

The gravitational force that occurs between two bodies is directly proportional to the masses
bodies and inversely proportional to the square of their distance (calculated with respect to their centers of mass).

What is the relationship between the two types of mass?

Experience has shown that inertial mass and gravitational mass are linked with each other (
for this reason that justifies the use of the term "mass").

In fact, thanks to sophisticated experiments, occurs inertial mass and gravitational mass
coincide (with great precision), this fact is not obvious, so as to represent a new
law of nature, which he called Einstein equivalence principle . The equivalence between the two types of mass is the basic logic underlying the theory of general relativity .

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Newton's laws

Newton was able to sum up the description of the phenomena of mechanics and gravitation in three laws of motion and law of universal gravitation. This is the first and perhaps biggest, unification of scientific knowledge. In a few laws expressed in mathematical form, describes a large number of natural phenomena.

1) a 'principle of dynamic or principle of inertia (already discovered by Galileo) Means a body not subject to forces moves with constant velocity (in intensity, direction and orientation) with respect to a inertial reference system.

2) 2 ' principle of dynamics: a force acting on a body gives him an acceleration (change in velocity) proportional to the force itself (the coefficient of proportionality is called the mass). The principle is expressed mathematically by the formula F = m · to.

3) principle of action and reaction : for every force is an opposing force ( equal in intensity and direction, but in opposite direction).

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remember all the settings that we chose to include this material in our blog and wiki are:
character: Times
font size: 12
Good job everyone!

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laboratory experience n + 5

The candle in freefall
Need:
a candle, a match, a transparent and robust.
Design:
a 'further review of the' absence of serious effects in a free fall can be done using a candle, placed in a transparent and robust.
We lit the candle with the match. The flame of a candle is fed by the oxygen of the air: stops in environments (such as municipalities) that is continuously replenished by the convective motions of 'air around the candle flame, which in turn generated by the buoyant force, a consequence of gravity opposed by the container firm. We place the candle in the container and dropped freely container system + candle flame is extinguished, according to forecasts.

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passenger elevator system

Consider a man of 70 kg mass is traveling on an elevator. The motion of the lift is directed vertically and is uniformly accelerated with acceleration a (write all scalar quantities in the game as being directed along the z axis of an orthonormal reference system).
In the scheme of the problem is indicated by the weight of the passenger W (W = 70 kg * 9.80 m / s ^ 2 = 686 N) with R and the force exerted on it from the floor. Note that the third law of motion for R is always equal in magnitude and opposite in direction to the force exerted by the passenger on the floor. The quantities involved are considered positive if it agrees to the z axis drawn in the figure, negative otherwise. Applying the second law of dynamics is written
F = ma, or

R - W = ma, where a is the acceleration
system + passenger lift.
So if for example a = 0.5 m / s ^ 2 (positive, ie upward), we get
R = 70 kg * 9.80 m / s ^ 2 + 70 kg * 0.5 m / s ^ 2 = 721 N,
The passenger, still in the frame of the lift, the feeling of more weight than usual. The 'apparent weight' of the passenger (in the form of the force he exerts on the floor and vice versa) is in fact higher than it would if the elevator was at rest or of uniform motion moved, was that a reference system INS. This could occur by placing the passenger on a dynamometer attached to the floor of the elevator. Where a = -0.5 m / s ^ 2, is
R = 70 kg * 9.80 m / s ^ 2 - 70 kg * 0.5 m / s ^ 2 = 651 N,
The passenger exerts less force on the floor if the direction of acceleration is opposite to the axis z. The example on display is very easy for example reflected in daily life: we can easily realize on the floor to exercise a power greater than our normal weight every time we are in an accelerated upward (lift or games of amusement parks) , the lower when the environment in question is accelerated towards the low.
An interesting case is that of free fall if the lift cable was cut, the system + passenger elevator would fall freely toward the Earth with acceleration a =-g. Then R would be nothing, the passenger and the floor is not exerting any force on each other and the apparent weight of the passenger (possibly indicated by the dynamometer) would be zero.

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laboratory experience n 4:

free fall of bodies
We verified the absence of apparent weight of a falling body through the law of Stevin. This law states that the difference between the pressures at two points of a fluid in equilibrium in the presence of gravity is given by the pressure exerted at the base by a fluid column height equal to the difference between the two points. We can therefore write: AP = ρgh.
We took a plastic bottle and made a hole a few inches from the bottom. We filled the water bottle so that h is the depth of the hole from the surface of the water and we adjourned to a 'considerable height (eg standing on a table or a chair). The water pressure is p = ρgh, where ρ is its density. We observed a gush of liquid out of the hole, perpendicular to the surface of bottle. We then dropped the bottle freely: the system is the same water bottle + of + passenger elevator system studied in theory. The apparent weight of the water bottle in the frame in free fall is zero, so it's nothing the pressure p calculated according to the law of Stevin. According to forecasts, the gush of water ceases to flow.