Force is a vector quantity, it is denoted by the letter F. Force is a vector. Force units

Coriolis force The peculiarity of the world of rotating systems is not limited to the existence of radial gravity forces. Let's get acquainted with another interesting effect, the theory of which was given in 1835 by the Frenchman Coriolis.

Force and potential energy during oscillation With any oscillation around the equilibrium position, a force acts on the body, "desiring" to return the body to the equilibrium position. As the point moves away from the equilibrium position, the force slows down as the point approaches

Torque as a vector So far, we have been talking about the magnitude of the torque. But the rotational moment has the properties of a vector quantity. Consider the rotation of a point with respect to some "center". On fig. 62 shows two close positions of the point.

2. Centrifugal force Open the umbrella, rest it with its end on the floor, spin it around and throw inside a ball, crumpled paper, a handkerchief - in general, some light and unbreakable object. You will see that the umbrella does not seem to want to accept a gift: a ball or a paper lump themselves

Chapter 3 Gravity - The First Fundamental Force From Heaven to Earth and Back B modern physics talk about four fundamental forces. The force of gravity was discovered first. The law of universal gravitation known to schoolchildren determines the force of attraction F between any masses

73 Strength in centimeters, or Clearly Hooke's law For the experiment we need: a balloon, a felt-tip pen. Hooke's law is passed at school. There lived such a famous scientist who studied the compressibility of objects and substances and deduced his own law. This law is very simple: the stronger we

Force = geometry Despite constant illnesses, Riemann eventually changed the prevailing ideas about the meaning of force. Since the time of Newton, scientists have considered force to be the instantaneous interaction of bodies distant from each other. Physicists called it "long-range action", which meant

First, the distinction between "gravity" and "gravity" used in geophysics. "Gravity" refers to Newton's law of gravity. (No one uses general theory relativity to modeling gravity for small, lumpy masses such as the Earth, Mars, or the Moon.) "Gravity" refers to how things appear to fall from the point of view of an observer fixed relative to the rotating Earth. Thus, gravity includes gravitational acceleration (inward, more or less towards the center of the Earth) and centrifugal acceleration (outward, away from the Earth's axis of rotation). This question asks about gravity, not about gravity.

As I understand it, to calculate the gravity vector does not allow us to calculate the normal to the ellipsoid, but we need to calculate the normal to the geoid (by definition, a geoid is a surface to which gravity is everywhere perpendicular).

It's the other way around. Geoid - calculated surface. Before the satellite era, one of the key inputs to the geoid calculation were observations of local gravity deviations, in particular the vertical deviation. In which direction gravity pointed to several places, a clue was given as to the local shape of the geoid.

Observation of satellite orbits provides a global measure of the Earth's gravitational field. Satellites have been specifically built for this job, most recently by GRACE and GOCE. The Earth's gravitational field is published in terms of spherical harmonic coefficients. The gravity vector for a point in space on or above the Earth's surface can be computed directly from these coefficients. The vector addition in centrifugal acceleration due to the Earth's rotation results in a gravitational vector. The position also gives a nominal gravity vector assuming an ellipsoidal Earth.

So I have some questions:

1. How to compute normal to geoid?

As noted above, the geoid is not needed. Modern geoid models are calculated from the same spherical harmonic coefficients (plus the Earth's rotation) used to calculate gravitational acceleration and gravity.

The technical term is "vertical deviation" (with variations). Per Hirt et al., this is up to 100 arcseconds, about 10 kilometers south of the summit of Annapurna II. This is a calculated value based on various satellite models (which are a bit rough) combined with digital terrain maps combined with some hairier math to create fine scale models.

We don’t know how things were in your school with physics and how much you liked this subject, but after today’s post, your attitude towards it will definitely change. Because if you look inside all the exercises, you can find a curious thing - they are all based on the principles of Newtonian mechanics! And it is the mechanics that determines how effective this or that exercise will be for a particular muscle group.

power itself on her shoulder. The shoulder in this case is understood as the shortest distance from the line along which the force passes to the axis of rotation.

Consider this using the example of push-ups from the floor with a standard setting of the hands:

It can be seen that the force of gravity that affects the athlete passes through three joints - the shoulder, elbow and wrist. In this case, the load decreases with the passage of force through each subsequent joint. That is, the main load goes to the shoulder joint (and, accordingly, the pectoral muscles), and the triceps receive less load, since the load on flexion in the elbow joint is minimal.

Is it possible to change the technique of push-ups in such a way as to increase the load on the triceps? Of course, since we now know that we need to create a rotational moment directed to flexion in the elbow joint. Then the triceps will join in the work, counteracting such an effort. To achieve this effect, it is necessary to make sure that gravity has a shoulder relative to the elbow joint. This can be achieved, for example, by moving the hands closer friend to friend.

It would seem that we only slightly changed the position of the hands, but at the same time we were able to significantly increase the load on the triceps and make the exercise more targeted! And there are a lot of such moments! Therefore, if you want your workouts to be effective, you need to always think about what, how and why you are doing, trying to get the most out of each repetition in each set!

http://website/uploads/userfiles/5540.jpg We don’t know how things were in your school with physics and how much you liked this subject, but after today’s post, your attitude towards it will definitely change. Because if you look inside all the exercises, you can find a curious thing - they are all based on the principles of Newtonian mechanics! And it is the mechanics that determines how effective this or that exercise will be for a particular muscle group. Let's start by looking at a schematic representation of a person. The main joints are marked in red, because all movements occur in them. As you know, muscles are attached to bones (with the help of tendons), while our body is so wonderfully arranged that for each joint there are two muscle groups (antagonists) that allow rotation in opposite directions..jpg The rotational load that sets everything in motion is called the moment of force and is equal to the product power itself on her shoulder. In this case, the shoulder is understood as the shortest distance from the line along which the force passes to the axis of rotation..jpg It can be seen that the force of gravity that affects the athlete passes through three joints - the shoulder, elbow and wrist. In this case, the load decreases with the passage of force through each subsequent joint. That is, the main load goes to the shoulder joint (and, accordingly, the pectoral muscles), and the triceps receive less load, since the load on flexion in the elbow joint is minimal. Is it possible to change the technique of push-ups in such a way as to increase the load on the triceps? Of course, since we now know that we need to create a rotational moment directed to flexion in the elbow joint. Then the triceps will join in the work, counteracting such an effort. To achieve this effect, it is necessary to make sure that gravity has a shoulder relative to the elbow joint. This can be achieved, for example, by moving the hands closer to each other..jpg It would seem that we only slightly changed the position of the hands, but at the same time we were able to significantly increase the load on the triceps and make the exercise more targeted! And there are a lot of such moments! Therefore, if you want your workouts to be effective, you need to always think about what, how and why you are doing, trying to get the most out of each repetition in each set! 100 day workout - Table of contents

In mechanics, the concept is introduced strength, which is extremely widely used in other sciences. The physical essence of this concept is clear to every person directly from experience.

Fig. 1. Deformation of bodies under the action of force:

A- deformations of compression - stretching;

b- bending deformation.

Let us dwell on the definition of force for absolutely rigid bodies. These bodies can interact, as a result of which the nature of their movement changes. Force is a measure of the interaction of bodies. For example, the interaction of the planets and the Sun is determined by the forces of gravity, the interaction of the Earth and various bodies on its surface is determined by the forces of gravity, etc.

It should be emphasized that during the interaction of real, and not absolutely rigid bodies, the emerging forces can not only lead to a change in the nature of their motion, but also cause a change in the shape or size of these bodies. In other words, in real physical bodies forces cause deformation.

Mechanics considers and studies not the nature of acting forces, but the effect produced by them. The effect of the force is determined by three factors that completely determine it:

2. Numerical value (modulus);

3. Application point.

In other words, strength is vector quantity.

In addition to forces, other vector quantities are often found in mechanics - in particular, speed, acceleration.

A quantity that has no direction is called scalar, or scalar value, Scalar quantities include, for example, time, temperature, volume, etc.

A vector is represented by a segment, at the end of which an arrow is placed. The direction of the arrow indicates the direction of the vector, the length of the segment - the magnitude of the vector, plotted on the selected scale.

Rice. 2. The image of force vectors in the drawings.

Vector originating at a point IN and end at a point WITH(Fig. 2, A), can be denoted by the same letters, but with a dash at the top: , and in the first place put the letter at the beginning of the vector, and then the letter at the end of the vector. Sometimes a vector is denoted by a letter: , , etc. (Fig. 2, b).

The line of action of a force is the straight line on which the force vector lies.(Fig. 2, V).

If it is necessary to show the size of the eyelids in the drawing
torus, it is depicted by an arrow, next to which is written
value, or module. The magnitude of the vector is indicated by the same letter as the vector itself, but without a dash at the top (Fig. 2, G).

Module, or magnitude of force is a quantitative characteristic of the measure of the interaction of bodies. The amount of force in international system units (SI) is measured in newtons (H). Larger units of measurement are also used: 1 kilonewton (1 kN= 10 3 H), 1 meganewton (1 MH = 10 6 N).

The content of the article

STATICS, branch of mechanics, the subject of which are material bodies that are at rest when acted upon external forces. In the broad sense of the word, statics is the theory of equilibrium of any bodies - solid, liquid or gaseous. In a narrower sense, this term refers to the study of the equilibrium of rigid bodies, as well as non-stretching flexible bodies - cables, belts and chains. The equilibrium of deforming solids is considered in the theory of elasticity, and the equilibrium of liquids and gases - in hydroaeromechanics.
Cm. HYDROAEROMECHANICS.

Historical reference.

Statics is the oldest branch of mechanics; some of its principles were already known to the ancient Egyptians and Babylonians, as evidenced by the pyramids and temples they built. Among the first creators of theoretical statics was Archimedes (c. 287–212 BC), who developed the theory of leverage and formulated the basic law of hydrostatics. The ancestor of modern statics was the Dutchman S. Stevin (1548–1620), who in 1586 formulated the law of addition of forces, or the parallelogram rule, and applied it in solving a number of problems.

Basic laws.

The laws of statics follow from the general laws of dynamics as special case when the velocities of rigid bodies tend to zero, but historical reasons and pedagogical considerations, statics is often stated independently of dynamics, building it on the following postulated laws and principles: a) the law of addition of forces, b) the principle of equilibrium, and c) the principle of action and reaction. In the case of rigid bodies (more precisely, ideally rigid bodies that do not deform under the action of forces), another principle is introduced based on the definition of a rigid body. This is the principle of force transferability: the state of a rigid body does not change when the point of application of the force moves along the line of its action.

Force as a vector.

In statics, a force can be considered as a pulling or pushing force that has a certain direction, magnitude, and point of application. From a mathematical point of view, this is a vector, and therefore it can be represented as a directed straight line segment, the length of which is proportional to the magnitude of the force. (Vector quantities, unlike other quantities that have no direction, are denoted in bold letters.)

Parallelogram of forces.

Consider the body (Fig. 1, A) on which the forces act F 1 and F 2 applied at the point O and represented in the figure by directed segments OA And OB. As experience shows, the action of forces F 1 and F 2 is equivalent to one strength R, represented by a segment OC. The magnitude of the force R is equal to the length of the diagonal of the parallelogram built on the vectors OA And OB how its sides; its direction is shown in Fig. 1, A. Force R called the resultant force F 1 and F 2. Mathematically, this is written as R = F 1 + F 2 , where addition is understood in geometric sense the words above. This is the first law of statics, called the rule of the parallelogram of forces.

Balanced force.

Instead of building a parallelogram OACB, to determine the direction and magnitude of the resultant R one can construct the triangle OAC by translating the vector F 2 parallel to itself until its starting point (former point O) coincides with the end point (point A) of the vector OA. The trailing side of the triangle OAC will obviously have the same magnitude and the same direction as the vector R(Fig. 1, b). This method of finding the resultant can be generalized to a system of many forces F 1 , F 2 ,..., F n applied at the same point O of the considered body. So, if the system consists of four forces (Fig. 1, V), then you can find the resultant of forces F 1 and F 2, fold it with force F 3 , then add the new resultant with the force F 4 and, as a result, obtain the total resultant R. Resultant R, found by such a graphical construction, is represented by the closing side of the OABCD force polygon (Fig. 1, G).

The definition of the resultant given above can be generalized to the system of forces F 1 , F 2 ,..., F n applied at points O 1 , O 2 ,..., O n of the rigid body. A point O is chosen, called the reduction point, and a system of parallel transferred forces is built in it, equal in magnitude and direction to the forces F 1 , F 2 ,..., F n. Resultant R these parallel transferred vectors, i.e. the vector represented by the closing side of the polygon of forces is called the resultant of the forces acting on the body (Fig. 2). It is clear that the vector R does not depend on the chosen reduction point. If the magnitude of the vector R(segment ON) is not equal to zero, then the body cannot be at rest: in accordance with Newton's law, any body on which a force acts must move with acceleration. Thus, a body can be in equilibrium only if the resultant of all forces applied to it is zero. However, this necessary condition cannot be considered sufficient - the body can move when the resultant of all forces applied to it is equal to zero.

As a simple but important example, explaining what has been said, consider a thin rigid rod of length l, the weight of which is negligible compared to the magnitude of the forces applied to it. Let two forces act on the rod F And -F applied to its ends, equal in magnitude but oppositely directed, as shown in Fig. 3, A. In this case, the resultant R is equal to F – F= 0, but the rod will not be in equilibrium; obviously, it will rotate around its midpoint O. The system of two equal, but oppositely directed forces, acting not in one straight line, is a “pair of forces”, which can be characterized by the product of the magnitude of the force F on the shoulder" l. The significance of such a product can be shown by the following reasoning, which illustrates the lever rule derived by Archimedes and leads to the conclusion about the condition of rotational equilibrium. Consider a lightweight homogeneous rigid rod that can rotate around an axis at point O, on which the force acts F 1 applied at a distance l 1 from the axis, as shown in fig. 3, b. Under the force F 1 the rod will rotate around the point O. As you can easily see from experience, the rotation of such a rod can be prevented by applying some force F 2 at that distance l 2 to satisfy the equality F 2 l 2 = F 1 l 1 .

Thus rotation can be prevented in countless ways. It is only important to choose the force and the point of its application so that the product of the force on the shoulder is equal to F 1 l 1 . This is the rule of leverage.

It is not difficult to derive the equilibrium conditions for the system. Action of forces F 1 and F 2 per axis causes a reaction in the form of a reaction force R, applied at the point O and directed opposite to the forces F 1 and F 2. According to the law of mechanics about action and reaction, the magnitude of the reaction R equal to the sum of forces F 1 + F 2. Therefore, the resultant of all forces acting on the system is equal to F 1 + F 2 + R= 0, so that the above necessary equilibrium condition is satisfied. Force F 1 creates a clockwise torque, i.e. moment of power F 1 l 1 about point O, which is balanced by a counterclockwise moment F 2 l 2 strength F 2. Obviously, the equilibrium condition of the body is the equality to zero of the algebraic sum of the moments, which excludes the possibility of rotation. If strength F acts on the rod at an angle q, as shown in fig. 4, A, then this force can be represented as the sum of two components, one of which ( F p), value F cos q, acts parallel to the rod and is balanced by the reaction of the support - F p , and the other ( F n) F sin q directed at right angles to the lever. In this case, the torque is Fl sin q; it can be balanced by any force that creates an equal moment acting counterclockwise.

To make it easier to take into account the signs of the moments in cases where a lot of forces act on the body, the moment of force F relative to any point O of the body (Fig. 4, b) can be considered as a vector L equal to the vector product r ґ F position vector r for strength F. Thus, L = rґ F. It is easy to show that if a system of forces applied at the points O 1 , O 2 ,..., O n (Fig. 5) acts on a rigid body, then this system can be replaced by the resultant R forces F 1 , F 2 ,..., F n applied at any point Oў of the body, and a pair of forces L, the moment of which is equal to the sum [r 1 ґ F 1 ] + [r 2 ґ F 2 ] +... + [r n ґ F n]. To verify this, it is enough to mentally apply at the point Oў a system of pairs of equal but oppositely directed forces F 1 and - F 1 ; F 2 and - F 2 ;...; F n and - F n , which obviously does not change the state of the rigid body.

Carried F 1 applied at the point O 1 , and the force - F 1 , applied at the point Oў, form a pair of forces, the moment of which relative to the point Oў is equal to r 1 ґ F 1 . Just the same strength F 2 and - F 2 applied at the points O 2 and Oў, respectively, form a pair with moment r 2 ґ F 2 , etc. Total moment L of all such pairs with respect to the point Oў is given by the vector equality L = [r 1 ґ F 1 ] + [r 2 ґ F 2 ] +... + [r n ґ F n]. Remaining forces F 1 , F 2 ,..., F n , applied at the point Oў, in total give the resultant R. But the system cannot be in equilibrium if the quantities R And L are different from zero. Consequently, the condition of equality to zero at the same time of the quantities R And L is necessary condition balance. It can be shown that it is also sufficient if the body is initially at rest. Thus, the equilibrium problem is reduced to two analytical conditions: R= 0 and L= 0. These two equations represent the mathematical notation of the equilibrium principle.

Theoretical provisions of statics are widely used in the analysis of forces acting on structures and structures. In the case of a continuous distribution of forces, the sums that give the resulting moment L and resultant R, are replaced by integrals and in accordance with the usual methods of integral calculus.