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The action of force on a material point can be characterized not only by changing the speed of the body, but by using
the amount of displacement that the body under consideration makes under the action of a force
($\bar{F}$).

Elementary work

Elementary work $(\delta A)$ of some force
$\bar{F}$ is defined as a dot product:

$$\delta A=\bar{F} \cdot d \bar{r}=F \cdot d s \cdot \cos \alpha(2)$$

$\bar{r}$ radius is the vector of the point to which the force is applied,
$\bar{r}$ –
elementary movement of a point along a trajectory,
$\alpha$ – angle between vectors
$d s=|d \bar{r}|$ and $d \bar{r}$. If a
$\alpha$ is an obtuse angle work less than zero if the angle
$\alpha$ is sharp, then the work is positive, for
$\alpha=\frac{\pi}{2} \delta A=0$

In Cartesian coordinates, formula (2) has the form:

$$\delta A=F_{x} d x+F_{y} d y+F_{z} d z(3)$$

where F _x ,F _y ,F _z are vector projections
$\bar{F}$ to Cartesian axes.

When considering the work of a force applied to a material point, you can use the formula:

$$\delta A=\bar{F} \bar{v} d t=\bar{v} d \bar{p}(4)$$

where $\bar{v}$ is the velocity of the material point,
$\bar{p}$ is the momentum of the material point. 9{n} \bar{F}_{i} \bar{v}_{i} d t(5)$$

where the summation of elementary work of all forces is carried out, dt is a small period of time during which elementary work is performed
$\delta$ over the system.

The resulting work of internal forces, even if the rigid body is moving, is zero.

Let a rigid body rotate around a fixed point – the origin of coordinates (or a fixed axis that passes through this point).
In this case, the elementary work of all external forces (let’s assume that their number is n) that act on the body is: 9{s} \bar{F} \cdot d \bar{r}(7)$$

In the event that the force vector is a constant value on the entire segment of the movement, then:

$$A=F_{\tau} \cdot s$$

where $F_{\tau}=F \cos \alpha$ is the force projection on the tangent to the trajectory.

Units of measure for work

The base unit of moment of work in the SI system is: [A]=J=N•m

In CGS: [A]=erg=dyn•cm

1J=10 ⁷ erg

Examples of problem solving

9{n}$ . What is the value of n?

Solution. As a basis for solving the problem, we use the formula:

$$\delta A=\bar{F} \bar{v} d t=m\left(\bar{a}_{n}+\bar{a}_{\tau}\right) \bar{v} d t=m \bar{a}_{n} \bar{v} d t+m \bar{a}_{\tau} \bar{v} d t(2.1)$$

Knowing the dependence of speed on time, we find the relationship between the tangential component of acceleration and time:

$$a_{\tau}=\frac{d v}{d t} \sim t(2.2)$$

The normal component of acceleration will be: 9{4}$$

Answer. n=4

Read more: Ampère force formula.

All physics formulas for grade 7 with explanations – table and cheat sheets

Physics cheat sheets for grade 7

It is difficult to cover the entire physics course in one article, but we have covered the main topics for grade 7 and this is enough to refresh knowledge in mind. Download and print both cheat sheets – one of them (detailed) will come in handy for thoughtful preparation for the OGE and the Unified State Examination, and the second (short) will serve to solve problems.

Download a cheat sheet with all the formulas and definitions in physics for grade 7 (small on one page) .

For those who are homeschooled or are forced to study the material on their own due to absences due to illness, we also recommend A.V. Peryshkin’s textbook on physics with formulas for grade 7 and easy, accessible explanations on all topics. It was written several decades ago, but is still very popular and in demand.

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Measurement of physical quantities

In the 7th grade physics course, they learn the rules for measuring using instruments with a scale. If the value of the scale interval is unknown, you can find it out using the following formula:

CSD = (max − min) / n, where CSD is the value of the division, max is the maximum value of the scale, min is the minimum value of the scale, n is the number of divisions between them .

Instead of the maximum and minimum, you can take any other values ​​of the scale, the numerical expression of which we know.

A distinction is made between direct and indirect measurements:

• with direct measurement, the result can be seen directly on the scale of the instrument;

• In an indirect measurement, the value of a quantity is calculated using another quantity (for example, the average speed is determined based on several speed measurements).

For convenience and standardization of measurements, the International System of Units (SI) was adopted in 1963. It regulates which units of measurement are considered basic and used for formulas. The designations of these units are also taught in the 7th grade physics curriculum.

Mechanical movement: formulas for class 7

In order to describe motion, you need a body of reference, a coordinate system, and a tool for measuring time. These are the components of the reference system.

The study of mechanical motion in the 7th grade physics course includes the following terms:

• Body displacement is the minimum distance that connects two selected points of the motion trajectory.

• Motion trajectory is a mental line along which the body moves.

• Path is the length of the body path from the start to the end point.

• Speed ​​ – the speed of movement of the body or the ratio of the distance traveled by it to the time of passage.

• Acceleration – the rate of change in the speed with which the body moves.

The formula for the speed of uniform rectilinear motion:

V = S / t, where S is the path of the body, t is the time it took to travel this path.

The formula for the speed of uniform curvilinear motion:

SI unit of speed: meter per second (m/s).

Uniform speed formula:

V = V ₀ + at, where V ₀ is the initial speed and a is the acceleration.

SI unit of acceleration: m/s ² .

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Gravity, weight, mass, density

Formulas, concepts and definitions describing these physical characteristics are studied in the 7th grade within the framework of such a section of physics as dynamics.

Please note: body weight is measured in newtons, body weight in grams and kilograms.

Weight formula:

P = mg, where m is the mass of the body, g is the acceleration due to gravity.

Free fall acceleration occurs under the action of gravity, which affects all bodies on our planet.

g = 9.806 65 m/s ² or 9.8 N/kg

If a body is at rest or in uniform motion in a straight line, its weight is equal to gravity.

F _heavy = mg

But these concepts cannot be identified: the force of gravity acts on the body due to the presence of gravity, while weight is the force with which the body itself acts on the surface.

Density formula:

ρ = m / V, where m is the mass of the body or substance, V is the volume occupied.

Density unit in SI: kg/m ³ .

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Mechanical lever, moment of force

Archimedes spoke about the mechanical lever when he promised to turn the Earth over if only a suitable fulcrum was found. This is a simple mechanism that helps lift weights attached to one end of it by applying force to the other end. In this case, the weight of the load far exceeds the applied force. In grade 7, physical formulas describing this process are studied in the same section of dynamics.

The lever is in equilibrium if the product of the force on the arm on one side is equal to the product of the force on the arm on the other side.

Equation of equilibrium of the lever:

F ₁ × l ₁ = F ₂ × l ₂

It follows that the lever is balanced when the moduli of the forces applied to its ends are inversely proportional.

Moment formula:

M = F × l, where F is the modulus of force, l is the arm length.

SI unit of torque: newton meter (Nm).

This formula is true if the force is applied perpendicular to the axis of the lever. If it is applied at an angle, such a case is beyond the scope of the 7th grade physics course and is studied in detail in the 9th grade.

In other words: a lever is in equilibrium if the sum of the moments of all forces applied to it about any axis is equal to zero.

М ₁ + М ₂ + М _n + … = 0

Pressure, pressure force

area this force is distributed. This phenomenon is explained in the 7th grade program by the physical terms “pressure” and “pressure force”.

Pressure formula:

p = F / S, where F is the modulus of force, S is the surface area.

SI unit of pressure: pascal (Pa).

1 Pa = 1 N/m ²

It is clear that with the same impact force, a surface with a smaller area will experience a higher pressure.

The formula for calculating the pressure force is easy to derive:

F = p × S

In physics problems for grade 7, the pressure force is usually equal to the weight of the body.

Pressure of gases and liquids

Liquids and gases filling a vessel exert pressure in all directions: on the walls and bottom of the vessel. This pressure depends on the height of the column of a given substance and on its density.

Hydrostatic pressure formula:

р = ρ × g × h, where ρ is the density of the substance, g is the gravitational acceleration, h is the height of the column.

g = 9. 8 m/s ²

SI unit of pressure for a liquid or gas: pascal (Pa).

A homogeneous liquid or gas presses uniformly on the vessel walls, since this pressure is created by randomly moving molecules. And the external pressure exerted on the substance is also evenly distributed throughout its volume.

The external pressure exerted on a liquid or gas is calculated by the formula:

p = F / S, where F is the modulus of force, S is the surface area.

Communicating vessels

If ρ ₁ = ρ ₂ , then h ₁ = h ₂ and ρ ₁ gh ₁ = ρ ₂ gh ₂ , where:

p – where:

p – where:

liquid density,

h is the height of the liquid column,

g = 9.8 m/s ² .

If the liquid in the communicating vessels is not homogeneous, i.e. has different densities, the height of the column in the vessel with the denser liquid will be proportionately smaller.

The heights of the columns of liquids with different densities are inversely proportional to the densities.

If pressure p ₁ = f ₁ /s ₁ is formed under piston 1, and pressure p ₂ = f ₂ /s is formed under piston 2, then according to law 2 90.1 Pascal, p ₁ = p ₂

, therefore,

Forces acting on the pistons of the hydraulic press F ₁ and F ₂ , are directly proportional to the areas of these pistons S ₁ and S and S and S and S and S and S and S and s ₂ .

In other words, the force of piston 1 is greater than the force of piston 2 as many times as its area is greater than the area of ​​piston 2. This makes it possible to balance the many times greater force in a hydraulic machine with a small force.

Archimedes’ Law

Formula of the Archimedean force:

F _a = ρ × g × V, where ρ is the density of the liquid, V is the volume of the submerged part of the body, g is the acceleration 9.8 m/s ² .

Archimedes’ law helps to calculate how a body will behave when immersed in media of different density. The following statements are true:

• if the density of the body is higher than the density of the medium, it will sink to the bottom;

• if the density of the body is lower, it will float to the surface.

In other words, the body will rise to the surface if the Archimedean force is greater than the force of gravity.

Work, energy, power

The formula for work in the course of physics for grade 7:

A = F × S, where F is the acting force, S is the path traveled by the body.

SI unit of work: joule (J).

Power refers to the rate at which mechanical work is performed. It tells how much work was done in a unit of time.

Power formula:

N = A / t, where A is the work, t is the time it takes to complete it.

Power can also be calculated knowing the force acting on the body and the average speed of movement of this body.

N = F × v, where F is the force, v is the average speed of the body.

SI unit of power: watt (W).

A body can do some work if it has energy – kinetic and/or potential.

• Kinetic is the energy of body movement. She talks about how much work needs to be done to give the body a certain speed.

• Potential is the energy of interaction of a body with other bodies or interaction between parts of one whole. The potential energy of a body raised above the Earth characterizes what work the force of gravity must do in order to lower this body again to the zero level.

Table with formulas in physics for grade 7 for calculating kinetic and potential energy:

In order to understand how much of the work done was useful, calculate the efficiency or efficiency. It is used to determine the effectiveness of various mechanisms, tools, etc.