Rules for the addition of forces. Addition of forces

Addition of forces

operation of determining a vector quantity R, equal to geom the metric sum of vectors representing the forces of a given system and is called the main vector of this system of forces. S. s. is carried out according to the rule of vector addition, in particular by constructing a polygon of forces (See Polygon of forces). Mechanical meaning of quantity R is determined by theorems of statics (See Statics) and dynamics (See Dynamics). So, if a system of forces acting on a rigid body has a resultant, then it is equal to the main vector of these forces. When moving any mechanical system its center of mass moves in the same way as a material point would move if it has a mass equal to the mass of the entire system and is under the influence of a force equal to the main vector of all external forces acting on the system.

Great Soviet Encyclopedia. - M.: Soviet Encyclopedia. 1969-1978 .

See what “Addition of forces” is in other dictionaries:

Addition of forces- Addition of forces: and forces F1, F2, F3.., Fn, application to the body; b addition of forces according to the polygon rule, a b c d..n force polygon; R is the resultant of forces. ADDITION OF FORCES, finding the geometric sum (the so-called main vector) of a given... ... Illustrated Encyclopedic Dictionary

The operation of determining a vector quantity R equal to geom. the sum of vectors depicting the forces of a given system and is called. the main vector of this system of forces. S. s. is carried out according to the rule of vector addition, in particular by constructing a parallelogram of forces or... ... Physical encyclopedia

Finding the geometric sum (the so-called main vector) of a given system of forces by consistent application rules for parallelogram of forces or construction of force polygon. For forces applied at one point, when adding forces, it is determined... ... Big encyclopedic Dictionary

Finding the geometric sum (the so-called principal vector) of a given system of forces by sequentially applying the force parallelogram rule or constructing a force polygon. For forces applied at one point, with the addition of forces... ... encyclopedic Dictionary

addition of forces- jėgų sudėtis statusas T sritis fizika atitikmenys: engl. addition of forces; composition of forces vok. Zusammensetzung von Kräften, f rus. addition of forces, n pranc. composition des forces, f … Fizikos terminų žodynas

Finding geom. sums (the so-called main vector) of a given system of forces through successive applying the force parallelogram rule or constructing a force polygon. For forces, app. at one point, at S. s. their resultant is determined... Big Encyclopedic Polytechnic Dictionary

Finding geom. sums (the so-called main vector) of a given system of forces through successive applying the force parallelogram rule or constructing a force polygon. For forces applied at one point, at S. s. their resultant is determined... Natural science. encyclopedic Dictionary

ADDITION, addition, cf. 1. units only Action under Ch. add 2, 5 and 7 digits. fold fold. Addition of forces (replacement of several forces with one that produces an equivalent effect; physical). Addition of quantities. Resignation of duties. 2. only units. One... ... Dictionary Ushakova

1) speeds and accelerations, 2) forces, 3) moments of forces and momentum. C. speeds and accelerations. When expanding the motion of a point or solid into the components of a movement and when combining several movements (see Connecting movements) is... ... Encyclopedic Dictionary F.A. Brockhaus and I.A. Efron

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When several forces act simultaneously on one body, the body moves with acceleration, which is the vector sum of the accelerations that would arise under the action of each force separately. The forces acting on a body and applied to one point are added according to the rule of vector addition.

The vector sum of all forces simultaneously acting on a body is called the resultant force and is determined by the rule of vector addition of forces: $\overrightarrow(R)=(\overrightarrow(F))_1+(\overrightarrow(F))_2+(\overrightarrow(F)) _3+\dots +(\overrightarrow(F))_n=\sum^n_(i=1)((\overrightarrow(F))_i)$.

The resultant force has the same effect on a body as the sum of all forces applied to it.

To add two forces, the parallelogram rule is used (Fig. 1):

Figure 1. Addition of two forces according to the parallelogram rule

In this case, we find the modulus of the sum of two forces using the cosine theorem:

If you need to add more than two forces applied at one point, then use the polygon rule: ~ from the end of the first force draw a vector equal and parallel to the second force; from the end of the second force - a vector equal and parallel to the third force, and so on.

Figure 2. Addition of forces according to the polygon rule

The closing vector drawn from the point of application of forces to the end of the last force is equal in magnitude and direction to the resultant. In Fig. 2 this rule is illustrated by the example of finding the resultant of four forces $(\overrightarrow(F))_1,\ (\overrightarrow(F))_2,(\overrightarrow(F))_3,(\overrightarrow(F) )_4$. Note that the vectors being added do not necessarily belong to the same plane.

The result of a force acting on a material point depends only on its modulus and direction. A solid body has certain dimensions. Therefore, forces of equal magnitude and direction cause different movements of a rigid body depending on the point of application. The straight line passing through the force vector is called the line of action of the force.

Figure 3. Addition of forces applied to different points of the body

If forces are applied to different points of the body and do not act parallel to each other, then the resultant is applied to the point of intersection of the lines of action of the forces (Fig. 3).

A point is in equilibrium if the vector sum of all forces acting on it is equal to zero: $\sum^n_(i=1)((\overrightarrow(F))_i)=\overrightarrow(0)$. In this case, the sum of the projections of these forces onto any coordinate axis is also zero.

The replacement of one force by two, applied at the same point and producing the same effect on the body as this one force, is called the decomposition of forces. The decomposition of forces is carried out, as is their addition, according to the parallelogram rule.

The problem of decomposing one force (the modulus and direction of which are known) into two, applied at one point and acting at an angle to each other, has a unique solution in following cases, if known:

directions of both components of forces;
module and direction of one of the component forces;
modules of both components of forces.

Let, for example, we want to decompose the force $F$ into two components lying in the same plane with F and directed along straight lines a and b (Fig. 4). To do this, it is enough to draw two lines parallel to a and b from the end of the vector representing F. The segments $F_A$ and $F_B$ will depict the required forces.

Figure 4. Decomposition of the force vector by directions

Another version of this problem is to find one of the projections of the force vector given the force vectors and the second projection. (Fig. 5 a).

Figure 5. Finding the projection of the force vector using given vectors

The problem comes down to constructing a parallelogram along the diagonal and one of the sides, known from planimetry. In Fig. 5b such a parallelogram is constructed and the required component $(\overrightarrow(F))_2$ of the force $(\overrightarrow(F))$ is indicated.

The second solution is to add to the force a force equal to - $(\overrightarrow(F))_1$ (Fig. 5c). As a result, we obtain the desired force $(\overrightarrow(F))_2$.

Three forces~$(\overrightarrow(F))_1=1\ N;;\ (\overrightarrow(F))_2=2\ N;;\ (\overrightarrow(F))_3=3\ N$ applied to one point, lie in the same plane (Fig. 6 a) and make angles~ with the horizontal $\alpha =0()^\circ ;;\beta =60()^\circ ;;\gamma =30()^\ circ $respectively. Find the resultant of these forces.

Let us draw two mutually perpendicular axes OX and OY so that the OX axis coincides with the horizontal along which the force $(\overrightarrow(F))_1$ is directed. Let's project these forces onto the coordinate axes (Fig. 6 b). The projections $F_(2y)$ and $F_(2x)$ are negative. The sum of the projections of forces onto the OX axis is equal to the projection onto this axis of the resultant: $F_1+F_2(cos \beta \ )-F_3(cos \gamma \ )=F_x=\frac(4-3\sqrt(3))(2)\ approx -0.6\ H$. Similarly, for projections onto the OY axis: $-F_2(sin \beta \ )+F_3(sin \gamma =F_y=\ )\frac(3-2\sqrt(3))(2)\approx -0.2\ H$ . The modulus of the resultant is determined by the Pythagorean theorem: $F=\sqrt(F^2_x+F^2_y)=\sqrt(0.36+0.04)\approx 0.64\ Н$. The direction of the resultant is determined using the angle between the resultant and the axis (Fig. 6 c): $tg\varphi =\frac(F_y)(F_x)=\ \frac(3-2\sqrt(3))(4-3\sqrt (3))\approx 0.4$

The force $F = 1kH$ is applied at point B of the bracket and is directed vertically downwards (Fig. 7a). Find the components of this force in the directions of the bracket rods. The required data is shown in the figure.

F = 1 kN = 1000N

$(\mathbf \beta )$ = $30^(\circ)$

$(\overrightarrow(F))_1,\ (\overrightarrow(F))_2$ - ?

Let the rods be attached to the wall at points A and C. The decomposition of the force $(\overrightarrow(F))$ into components along the directions AB and BC is shown in Fig. 7b. This shows that $\left|(\overrightarrow(F))_1\right|=Ftg\beta \approx 577\ H;\ \ $

\[\left|(\overrightarrow(F))_2\right|=F(cos \beta \ )\approx 1155\ H. \]

Answer: $\left|(\overrightarrow(F))_1\right|$=577 N; $\left|(\overrightarrow(F))_2\right|=1155\ Н$

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Lesson type: formation of new knowledge.

Lesson methods: research method.

Lesson objectives:

Educational: show the connection between the material being studied and real life with examples; familiarize students with the concept of resultant force;
Developmental: developing skills in working with instruments; improve group work skills;
Educational: cultivate diligence, accuracy and clarity when answering, the ability to see physics around you.

Equipment: dynamometer (spring, demonstration), body different weights, cart, spring, ruler, multi-media projector. Self-work card.

During the classes

1. Goal setting

– What concept have we been studying for several lessons?

– Would you like to know more about power? What exactly?

2. Repetition

Tell me what you know about strength?
What significance does it have in life? What is it intended for?
What forces exist in nature?

– Let’s show the effect of forces on a car. Not one, but several forces can act on a body.

– Give examples in which several forces act on a body.

3. Formation of new knowledge

Let's conduct an experiment:

We hang two weights (a) from the spring, one under the other, and note the length to which the spring stretches. Let's remove these weights and replace them with one weight (b), which stretches the spring to the same length. Let us conclude that there is a force that produces the same effect as several at the same time active forces, called resultant.

The designation of this force is R, units - 1 N.

Fill the table.

4. Consolidation of the studied material

– Solving problems involving the resultant. ( In the presentation)

– Independent work to find different forces.

Independent work “Strength. Resultant"

5. Homework: paragraph 29, rep. to questions, ex. 11 (1, 2, 3 letters).

Force. Addition of forces

Any changes in nature occur as a result of interaction between bodies. The ball lies on the ground and will not begin to move unless you push it with your foot; the spring will not stretch if you attach a weight to it, etc. When a body interacts with other bodies, the speed of its movement changes. In physics, they often do not indicate which body and how it acts on a given body, but say that “a force acts on the body.”

Strength is physical quantity, which quantitatively characterizes the action of one body on another, as a result of which the body changes its speed. Force is a vector quantity. That is, except numerical value, force direction. Force is designated by the letter F and in the International System is measured in newtons. 1 newton is the force that a body weighing 1 kg at rest produces in 1 second at a speed of 1 meter per second in the absence of friction. You can measure strength using a special device - a dynamometer.

Depending on the nature of the interaction in mechanics, three types of forces are distinguished:

gravity,
elastic force,
friction force.

As a rule, not one, but several forces act on the body. In this case, the resultant of forces is considered. A resultant force is a force that acts in the same way as several forces simultaneously acting on a body. Using the results of the experiments, we can conclude: the resultant of forces directed along one straight line in one direction is directed in the same direction, and its value is equal to the sum of the values of these forces. The resultant of two forces directed along one straight line in opposite directions is directed towards greater strength and is equal to the difference between the values of these forces.

Physics. 7th grade

Topic: Interaction of bodies

Lesson 21. Addition of forces

Yudina N.A., physics teacher of the highest category, Central Educational Center No. 1409, finalist of the city competition “Teacher of the Year” (Moscow, 2008)

October 27, 2010

Addition of forces - resultant force, resultant force

Good afternoon.

Today is the twenty-first lesson.

Section "Interaction of bodies". And today we will get acquainted with the method of adding forces, when a body is acted upon not by one, but by several forces at once, a resultant force or a resultant force.

Let's take an example. We will hang two weights from the spring, the mass of each of which is 100 g. So, the total mass of the resulting body is 200 g.

This means that the force of gravity that acts on this resulting body is 2 N. Let's try to depict this force of gravity graphically to scale.

Drawing

The scale chosen is 1H - this is a single segment. Then the force of gravity acting on the body =.

Now we will try to attach another weight weighing 100 g.

As we can see, the spring has stretched. The dynamometer shows us overall strength 3N.

Let us again depict the force acting on the first two loads.

Then we add the force of gravity acting on the additional load, .

Please note that both forces are directed along the same straight line in the same direction. The resultant force, let’s find it, for this we need to add the modules of these forces R=F1+F2.

The direction of the resultant will be in the same direction where both forces were directed.

Now let’s turn to an example that will allow us to analyze the situation when forces are directed towards different sides.

So, the two teams are in a tug of war. The total force of one team is =500 N. The total force of the second team is =700 N.

Scale: 100 N.

I chose the scale - a single segment corresponds to 100 N.

And then the figure clearly shows: 5 single segments - the force of the first team is 500 N; 7 unit segments - the force of the second command is 700 N. The figure shows that these two forces are directed in different directions along the same straight line. In order to find the resultant of these two forces, it is necessary to subtract the smaller force R = F2-F1 from the larger force in magnitude, and the direction of the resulting force will be in the direction of the larger force.

On the drawing we can indicate the name: – resultant or resultant force.

In the case when not one, but several forces act on a body at once, it is necessary to find their resultant.

It must also be remembered that if several forces act on a body, but, as in this case, these forces are equal in magnitude and opposite in direction, the force of gravity acting on these loads towards the ground, downward, and the elastic force acting upward are these the forces are equal in magnitude and opposite in direction.

In this case, the body will either be at rest, or it can move uniformly and rectilinearly.

Thank you. Goodbye.