It is very difficult or impossible to carry out many phenomena and experiments in an educational institution. In the section BC the car was moving uniformly. The plane is coming out of a dive.

29.11.2020

Option 1.

An airplane flies in a straight line at a constant speed at an altitude of 9 km. The reference frame associated with the Earth is considered inertial. In this case:

1) no forces act on the plane

2) the plane is not affected by gravity

3) the sum of all forces acting on the plane is zero

4) gravity is equal to the Archimedes force acting on the plane

A body weighing 1 kg is acted upon by forces of 6 N and 8 N, directed perpendicular to each other. What is the acceleration of the body?

1) 2 m/s 2 2) 5 m/s 2 3) 10 m/s 2 4) 14 m/s 2

Satellite massT R

1) 2) 3) 4)

A load weighing 2 kg was suspended from a spring 10 cm long with a stiffness coefficient of 500 N/m. What is the length of the spring?

1) 12 cm 2) 13 cm 3) 14 cm 4) 15 cm

A man was carrying a child on a sled along a horizontal road. Then a second child of the same type sat on the sled, but the man continued at the same constant speed. How did the friction force change in this case?

A block slides down an inclined plane. Which vector shown in the figure is redundant or incorrect?

1) 2) 3) 4)

2) on the siteDE

3) in section AB the car moved uniformly

Part B

Three bodies of equal mass, 3 kg each, performed movements. The displacement projection equations are presented in the table. Which graph shows the dependence of the projection of force on time acting on each body?

Solve problems.

A body of mass 10 kg suspended from a cable rises vertically. With what acceleration does the body move if a cable with a stiffness of 59 kN/m is lengthened by 2 mm? What is the elastic force generated in the cable?

The average height of the satellite above the Earth's surface is 1700 km. Determine the speed of its movement.

Option2 .

Part A Choose one correct answer.

The movements of bodies relative to the Earth are listed below. Which frame of reference associated with one of these bodies cannot be considered inertial? The reference frame associated with the Earth is considered inertial.

1) the girl runs at a constant speed

2) the car moves uniformly along a horizontal part of the road

3) the train moves uniformly accelerated

4) the hockey puck slides evenly across smooth ice

1) 2 m/s 2 2) 4 m/s 2 3) 1 m/s 2 4) 8 m/s 2

What expression determines the value of the first escape velocity of the satellite if the radius of the circular orbitR, and the acceleration of free fall at this heightg?

1) 2) 3) 4)

In order for the body in the elevator to experience overload (increase in weight) it is necessary:

1) accelerated upward movement of the elevator

2) slow upward movement of the elevator

3) accelerated movement of the elevator down

4) such a state is impossible

A man was carrying two identical children on a sled along a horizontal road. Then one child got up from the sled, but the man continued moving at the same constant speed. How did the friction force change in this case?

1) did not change 2) increased by 2 times

3) decreased by 2 times 4) increased by 50%

1) 2) 3) 4)

The velocity module of a car weighing 1000 kg changes in accordance with the graph shown in the figure. Which statement is true?

1) in the section BC the car was moving uniformly accelerated

2) on section CD

3) on the siteDEthe car was moving uniformly accelerated, the acceleration vector coincides in direction with the velocity vector.

4) the acceleration module in section AB is less than the acceleration module in sectionDE

Part B

Using the condition of the problem, match the equations from the left column with their graphs in the right column.

Solve problems.

A bus weighing 15 tons starts moving with an acceleration of 0.7 m/s 2 . What friction force acts on the bus if the engine traction force is 15 kN? Express the answer in kN. Why coefficient is equal friction?

The average height of the satellite above the Earth's surface is 900 km. Determine the speed of its movement.

Option 3.

Part A Choose one correct answer.

A skydiver descends vertically at a constant speed of 2 m/s. The reference frame associated with the Earth is considered inertial. In this case:

1) no forces act on the parachute

2) gravity is balanced by the Archimedes force acting on the parachute

3) the sum of all forces acting on the parachute is zero

4) the sum of all forces is constant and not equal to zero

A body weighing 2 kg is acted upon by forces of 3 N and 4 N, directed perpendicular to each other. What is the acceleration of the body?

1) 3.5 m/s 2 2) 2.5 m/s 2 3) 7 m/s 2 4) 10 m/s 2

Satellite massT moves around the planet in a circular orbit of radiusR. The mass of the planet is M. What expression determines the value of the speed of the satellite?

1) 2) 3) 4)

The elevator has spring scales on which a person stands. How will the scale readings change when the elevator moves up and down at an accelerated rate?

1) up - increase, down - decrease

2) up - decrease, down - increase

3) up - will increase, down - will not change

4) up - will not change, down - will increase

A man was carrying a child on a sled along a horizontal road. Then a second child of the same type sat on the sled, but the man continued at the same constant speed. How did the friction coefficient change?

1) did not change 2) increased by 2 times

3) decreased by 2 times 4) increased by 50%

A block moves upward with uniform acceleration along an inclined plane. Which vector shown in the figure is redundant or incorrect?

1) 2) 3) 4)

The velocity module of a car weighing 1000 kg changes in accordance with the graph shown in the figure. Which statement is true?

1) in the section BC the car moved uniformly

2) on section CDthe car was moving uniformly accelerated, the acceleration vector was directed opposite to the velocity vector

3) on the siteE.F.the car was at rest

4) the acceleration module in section AB is less than the acceleration module in sectionDE

Part B

Using the condition of the problem, match the equations from the left column with their graphs in the right column.

Three bodies of equal mass, 4 kg each, performed movements. The displacement projection equations are presented in the table. Which graph shows the dependence of the projection of force on time acting on each body?

Solve problems.

The elevator descends with an acceleration of 2 m/s 2 . In an elevator, a load weighing 0.7 kg hangs on a spring with a stiffness of 560 N/m. What is the elastic force of the spring? By how many centimeters did the spring lengthen?

The average height of the satellite above the Earth's surface is 600 km. Determine the speed of its movement.

Option4 .

Part A Choose one correct answer.

1) the elevator falls freely

2) the elevator rises evenly

3) the elevator moves slowly upward

4) the elevator is moving rapidly downward

A body of mass 2 kg is acted upon by four forces. What is the acceleration of the body ifF 1 =12 H, F 2 =18 H, F 3 =20 H, F 4 =18 H.

1) 6 m/s 2 2) 16 m/s 2 3) 2 m/s 2 4) 4 m/s 2

The mass of the Moon is approximately 81 times less than the mass of the Earth. What is the force ratio universal gravity F 1 , acting from the Earth on the Moon, to the forceF 2 , acting from the Moon on the Earth?

1)1/81 2) 81 3) 9 4) 1

How can a weight weighing 10 N be made to stretch a dynamometer spring with a force greater than 10 N?

1) move the dynamometer with the weight down with some acceleration

2) move the dynamometer with the weight upward with some acceleration

3) the dynamometer with the weight must fall freely

4) this is impossible to do

A man was carrying two identical children on a sled along a horizontal road. Then one child got up from the sled, but the man continued moving at the same constant speed. How does the friction coefficient change in this case?

1) increased by 2 times 2) decreased by 2 times

3) increased by 50% 4) did not change

A block is moved evenly upward along an inclined plane. Which vector shown in the figure is redundant or incorrect?

1) 2) 3) 4)

The velocity module of a car weighing 1000 kg changes in accordance with the graph shown in the figure. Which statement is true?

1) on section CDthe car was moving uniformly accelerated, the acceleration vector coincides in direction with the velocity vector

2) the acceleration module in section AB is greater than the acceleration module in sectionDE

3) on the siteDEthe car was moving uniformly accelerated, the acceleration vector was directed opposite to the velocity vector.

4) in section AB the car moved uniformly

Part B

Using the condition of the problem, match the equations from the left column with their graphs in the right column.

Three bodies of equal mass, 2 kg each, performed movements. The displacement projection equations are presented in the table. Which graph shows the dependence of the projection of force on time acting on each body?

Solve problems.

A car weighing 1 ton moves with an acceleration of 0.8 m/s 2 . Is there a force of 2 kN acting on the car? Determine the thrust force of the engine (express the answer in kN) and the coefficient of friction.

The average height of the satellite above the Earth's surface is 300 km. Determine the speed of its movement.

In section DE the car was moving uniformly accelerated, the acceleration vector was directed opposite to the velocity vector

In section AB the car moved uniformly

The acceleration module in section AB is less than the acceleration module in section DE.

Solve problems.

9. A body of mass 10 kg suspended from a cable rises vertically. With what acceleration does the body move if a cable with a stiffness of 59 kN/m is lengthened by 2 mm? What is the elastic force generated in the cable?

Given: SI: Solution:

10. The average height of the satellite above the Earth’s surface is 1700 km. Determine the speed of its movement.

Given: SI: Solution:

Solve the problem.

A cart with a mass of 5 kg moves under the action of a weight with a mass of 2 kg. Determine the thread tension if the friction coefficient is 0.1.

Given: Solution:

OPTION 2

1. The movements of bodies relative to the Earth are listed below. Which frame of reference associated with one of these bodies cannot be considered inertial? The reference frame associated with the Earth is considered inertial.

1) the girl runs at a constant speed

2) the car moves uniformly along a horizontal part of the road

3) the train moves uniformly accelerated

4) a hockey puck glides evenly on smooth ice

2. A body weighing 2 kg is acted upon by four forces. What is the acceleration of the body if

F 1 = 20 N, F 2 = 18 N, F 3 = 20 N, F 4 = 16 N.

1) 2 m/s 2 2) 4 m/s 2 3) 1 m/s 2 4) 8 m/s 2

3. What expression determines the value of the satellite’s first escape velocity if the radius of its circular orbit is R and the acceleration of free fall at this altitude is g?

4. In order for the body in the elevator to experience overload (increase in weight) it is necessary:

1) accelerated upward movement of the elevator 2) slow upward movement of the elevator 3) accelerated downward movement of the elevator 4) this state is impossible

5. A man was carrying two identical children on a sled along a horizontal road. Then one child got up from the sled, but the man continued moving at the same constant speed. How did the friction force change in this case?

1) did not change 2) increased by 2 times 3) decreased by 2 times 4) increased by 50%

6. The block moves uniformly upward along the inclined plane. Which vector shown in the figure is redundant or incorrect?

7. The velocity module of a car weighing 1000 kg changes in accordance with the graph shown in the figure. Which statement is true?

2) in section CD the car was moving uniformly accelerated, the acceleration vector coincides in direction with the velocity vector

3) in section DE the car was moving uniformly accelerated, the acceleration vector coincides in direction with the velocity vector

4) the acceleration module in section AB is less than the acceleration module in section DE

7. Using the condition of the problem, match the equations from the left column of the table with their graphs in the right column.

Solve problems.

8. A bus weighing 15 tons starts from rest with an acceleration of 0.7 m/s 2 . What friction force acts on the bus if the engine traction force is 15 kN? Express the answer in kN. What is the coefficient of friction?

Given: SI: Solution:

9. The average height of the satellite above the Earth’s surface is 900 km. Determine the speed of its movement.

Given: SI: Solution:

Solve the problem.

10. Two weights of masses 200 g and 300 g are connected by a thread. Determine the acceleration of the loads and the tension force of the thread between them if a force of 10 N directed horizontally to the right is applied to a body of mass m 1.

Given: SI: Solution:

Rating _____ teacher signature ________________/L.S. Tishkina/

OPTION 3

PART A Choose one correct answer.

1. A parachutist descends vertically at a constant speed of 2 m/s. The reference frame associated with the Earth is considered inertial. In this case:

1) no forces act on the parachute

2) gravity is balanced by the Archimedes force acting on the parachute

3) the sum of all forces acting on the parachute is zero

4) the sum of all forces is constant and not equal to zero

2. A body weighing 2 kg is acted upon by forces of 3 N and 4 N, directed perpendicular to each other. What is the acceleration of the body?

1) 3.5 m/s 2 2) 2.5 m/s 2 3) 7 m/s 2 4) 10 m/s 2

3. A satellite of mass m moves around a planet in a circular orbit of radius R. The mass of the planet is M. What expression determines the acceleration value of the satellite?

4. The elevator has spring scales on which a person stands. How will the scale readings change when the elevator moves up and down at an accelerated rate?

1) up - increase, down - decrease

2) up - decrease, down - increase

3) up - will increase, down - will not change

4) up - will not change, down - will increase

5. A man was carrying a child on a sled along a horizontal road. Then a second child of the same type sat on the sled, but the man continued moving at the same constant speed. How did the friction coefficient change in this case?

1) did not change 2) increased by 2 times 3) decreased by 2 times 4) increased by 50%

6. A block moves upward with uniform acceleration along an inclined plane. Which vector shown in the figure is redundant or incorrect?

7. The modulus of velocity of a car weighing 1000 kg changes in accordance with the graph shown in the figure. Which statement is true?

1) in the section BC the car was moving uniformly accelerated

2) in section CD the car was moving uniformly accelerated, the acceleration vector was directed opposite to the velocity vector.

3) in section EF the car was at rest

4) the acceleration module in section AB is less than the acceleration module in section DE

8. Using the condition of the problem, match the equations from the left column of the table with their graphs in the right column.

Solve problems.

9. The elevator descends with an acceleration of 2 m/s 2 . In an elevator, a load weighing 0.7 kg hangs on a spring with a stiffness of 560 N/m. What is the elastic force of the spring? How many centimeters did the spring lengthen?

Given: Solution:

10. The average height of the satellite above the Earth’s surface is 600 km. Determine the speed of its movement.

Given: SI: Solution:

Solve the problem.

11. A block weighing 400 g comes into motion with an acceleration of 0.4 m/s 2 under the action of a load weighing 100 g. Find the friction force and the coefficient of friction of the block on the surface.

Given: SI: Solution:

Rating _____ teacher signature ________________/L.S. Tishkina/

OPTION 4

PART A Choose one correct answer

1) the elevator falls freely 2) the elevator rises uniformly

3) the elevator moves slowly up 4) the elevator moves quickly down

2. A body of mass 2 kg is acted upon by four forces. What is the acceleration of the body if F 1 = 12 N, F 2 = 18 N, F 3 = 20 N, F 4 = 18 N.

1) 6 m/s 2 2) 16 m/s 2 3) 2 m/s 2 4) 4 m/s 2

3. The mass of the Moon is approximately 81 times less than the mass of the Earth. What is the ratio of the force of universal gravity F 1 acting from the Earth on the Moon to the force F 2 acting from the Moon on the Earth?

1) 1/81 2) 81 3) 9 4) 1

4. How can a weight weighing 10N be made to stretch a dynamometer spring with a force greater than 10N?

1) move the dynamometer with the weight down with some acceleration

2) move the dynamometer with the weight upward with some acceleration

3) the dynamometer with the weight must fall freely

4) this is impossible to do

5. A man was carrying two identical children on a sled along a horizontal road. Then one child got up from the sled, but the man continued moving at the same constant speed. How has it changed?
coefficient of friction?

1) increased by 2 times 2) decreased by 2 times 3) increased by 50% 4) did not change

6. A block lies motionless on an inclined plane. Which vector shown in the figure is redundant or incorrect?

1) 2) 3) 4)

7. The modulus of velocity of a car weighing 1000 kg changes in accordance with the graph shown in the figure. Which statement is true?

1) in section CD the car was moving uniformly accelerated, the acceleration vector coincides in direction with the velocity vector

2) the acceleration module in section AD is greater than the acceleration module in section DE

3) in section DE the car was moving uniformly accelerated, the acceleration vector was directed opposite to the velocity vector

4) in section AB the car moved uniformly

8. Using the condition of the problem, match the equations from the left column of the table with their graphs in the right column.

Solve problems.

9. A car weighing 1 ton moves with an acceleration of 0.8 m/s 2 . A friction force of 2 kN acts on a car. Determine the thrust force of the engine (express the answer in kN) and the coefficient of friction.

Given: SI: Solution:

10. The average height of the satellite above the Earth’s surface is 300 km. Determine the speed of its movement.

Given: SI: Solution:

Solve the problem.

11. Two weights of masses 200 g and 300 g are suspended on a cord thrown over a stationary block. With what acceleration do the weights move? What is the tension in the thread?

Given: SI: Solution:

Rating _____ teacher signature ________________/L.S. Tishkina/

Date “___” _________20____

Task 12 on the topic

"Application of the law of conservation of momentum of a body"

Solve problems:

1. Find the momentum of a truck weighing 10 tons moving at a speed of 36 km/h and a passenger car weighing 1 ton moving at a speed of 25 m/s.

Given: SI: Solution:

2. A train weighing 2000 tons, moving in a straight line, accelerated from 36 to 72 km/h. Find the change in momentum.

Given: SI: Solution: Given: SI: Solution:

Given: SI: Solution:

Rating _____ teacher signature ________________/L.S. Tishkina/

Date “___” _________20____

Task 15 on the topic

“Formation and propagation of waves.

Task No. 6

Question:

Two forces are applied to the body, the modules of which are equal to 10 N and 20 N. It is known that the forces are directed in one straight line and in opposite directions. What will be the resultant force (in N)?

Write down the number:

________10 ________________

Task No. 7

Question:

A body weighing 100 kg is acted upon by a resultant force equal to 20 N. What is the module of acceleration of the body (in m/s 2)?

Write down the number:

_________0,2 _______________

Task No. 8

Question:

A body of mass 5 kg rests on a horizontal table surface. Determine with what force (in N) the table will act on this body?

Write down the number:

__________49 _______________

Task No. 9

Question:

The figure shows two forces acting on a body. Find the force modulus F 2(in N) if the body moves to the right with a constant speed of 2 m/s.

Image:

Write down the number:

________17,3 ________________

Task No. 10

Question:

A body of mass m moves with an acceleration of 3 m/s 2 . How many times must the resultant force increase for the body to begin to move with an acceleration of 9 m/s 2?

Write down the number:

______3_________________

The law of universal gravitation. Cosmic speeds

Task No. 1

Question:

The proportionality coefficient in the formula describing the law of universal gravitation is numerically equal to...

1) About 10 9

2) About 10 5

3) About 10 -19

4) About 10 -11

Task No. 2

Question:

Select the quantities on which the first two escape velocities of this planet depend

Select several of 5 answer options:

Weight

2) Albedo

Radius

4) Period of revolution around its axis

5) The period of revolution around its star

Task No. 3

Question:

Choose the correct statements

__ Gravitational interaction between bodies always manifests itself in the form of mutual attraction

__ The force of gravity is proportional to the masses of bodies

The force of gravity is inversely proportional to the distance between bodies

The law of universal gravitation is universal and can be applied with high accuracy to any pair of bodies

Task No. 4

Question:

The speed with which a body must move to leave the orbit of a given celestial body is...

Choose one of 4 answer options:

1) The first escape velocity of a given body

2) Second escape velocity of a given body

The third escape velocity of a given body

4) The fourth escape velocity of a given body

Task No. 5

Question:

The pencil is resting on the table. What interaction is this due to?

Choose one of 4 answer options:

Gravitational

2) Electromagnetic

3) Strong

Task No. 6

Question:

Find the force (in mN) with which two asteroids weighing 10,000 tons each are attracted in outer space if the distance between them is 1 km.

Write down the number:

_______6,67 _________________

Task No. 7

Question:

To make an aircraft artificial satellite some planet, this aircraft, departing from this planet you need to reach a speed of 2 km/s. If the mass of this planet is 10 23 kg, then what is its radius (in km)?

Write down the number:

______1667,5 _________________

Task No. 8

Question:

Find the second escape velocity of the Moon in km/s. The mass of the Moon is 7.3 x 10 22 kg, and the radius is 1737 km.

Write down the number:

______1,67 _________________

Task No. 9

Question:

Find the force (in TN) with which the Sun acts on Pluto. The mass of the Sun is 2x10 30 kg, the mass of Pluto is 1.3x10 22 kg. The average distance between the Sun and Pluto is taken to be 5913 million km.

Write down the number:

_____49600 _________________

Task No. 10

Question:

Find the radius of the planet (in km) whose first escape velocity is 12 km/s and whose gravitational acceleration is 15 m/s 2 .

Write down the number:9600

Gravity. Weight, weightlessness, overload

Task No. 1

Question:

Choose the correct statements

Indicate true or false answer options:

YES) The force of gravity acting on a body is equal to the product of the mass of the body and the acceleration of gravity

NO)Body weight equal to the product body mass and gravitational acceleration

NO) Weight is a scalar quantity

YES) Weight is the force acting on a support or suspension

Task No. 2

Question:

A person experiences overload while in an elevator if...

Choose one of 4 answer options:

1) The elevator is at rest

The elevator goes up

3) The elevator goes down

4) If a person stands on his hands

Task No. 3

Question:

Astronauts on low earth orbit experience a state of weightlessness because...

1) They are far enough from the Earth that gravity ceases to act on them

They are in free fall, falling around the Earth

3) They begin to be attracted to others celestial bodies, and the total action of these bodies balances the force of gravity acting from the Earth

Task No. 4

Question:

Compare the situation with the consequence of this situation

Please select a match for all 4 answer options:

The pilot experiences overload

2) The force of gravity acting on the pilot is not equal to his weight

3) The force of gravity acting on the pilot is equal to his weight

4) The pilot experiences weightlessness

4) The plane goes into a tailspin

The plane comes out of a dive

3) The plane flies with horizontal acceleration

2) The plane flies with vertical acceleration

Task No. 5

Question:

Is the Earth in a state of weightlessness?

Choose one of 3 answer options:

3) Depending on the choice of reference system

Task No. 6

Question:

The waiter lifts the tray vertically upward with an acceleration of 3 m/s 2 . The mass of the dishes lying on the tray is 2 kg. Determine the force (in N) with which the dish acts on the tray.

Write down the number:

____________26 _______________

Task No. 7

Question:

A block with a mass of 400 g rests on a board. The board is lifted together with the block and released. Find the force (in N) with which the block will act on the board during flight.

Write down the number:

_______0 ________________

Task No. 8

Question:

A person weighing 50 kg swings on a swing, which is attached using two identical ropes. The length of each rope is 2 m. The weight of a person at the moment when he passes the lowest point of the trajectory of his movement is 1.2 kN. Find the maximum linear speed(in m/s) with which a person swings.

Write down the number:

_______5,29 ___________________

Task No. 9

Question:

The car goes over the bridge. At the same time, its weight decreases. Then this bridge...

Choose one of 4 answer options:

2) Curved down

Curved upward

4) There is not enough information to draw any conclusions

Task No. 10

Question:

The elevator moves up at a speed of 1 m/s. An elevator contains a load weighing 100 kg. What force (in N) does this load exert on the elevator during such a movement?

Write down the number: 981

Test No. 2

Dynamics.

DEMO VERSION

A1. An airplane flies in a straight line at a constant speed at an altitude of 9 km. The reference frame associated with the Earth is considered inertial. In this case:

1. no forces act on the plane

2. the plane is not affected by gravity

3. the sum of all forces acting on the plane is zero

4. gravity is equal to the Archimedes force acting on the plane

A2. A body of mass 2 kg is acted upon by four forces. What is the acceleration of the body if

F 1 =20 H, F 2 =18 H, F 3 =20 H, F 4 =16 H

A3. A satellite of mass m moves around the planet in a circular orbit of radius R. The mass of the planet is M. What expression determines the value of the speed of the satellite?

A4. In order for the body in the elevator to experience overload (increase in weight) it is necessary:

accelerated upward movement of the elevator

elevator moving up slowly

accelerated movement of the elevator down

such a state is impossible

A5. A man was carrying a child on a sled along a horizontal road, then a second child of the same type sat on the sled, but the man continued to move at the same constant speed, how did the friction force change?

hasn't changed

increased by 2 times

decreased by 2 times

increased by 50%

A6. A block moves uniformly upward along an inclined plane. Which vector shown in the figure is redundant or incorrect?

A7. The velocity module of a car weighing 1000 kg changes in accordance with the graph shown in the figure. Which statement is true?

1. in the section BC the car moved uniformly

2. in section DE the car was moving uniformly accelerated, the acceleration vector was directed opposite to the velocity vector

3. in section AB the car moved uniformly

4. the acceleration module in section AB is less than the acceleration module in section DE

IN 1. Three bodies of equal mass, 2 kg each, performed movements. The displacement projection equations are presented in the table. Which graph shows the dependence of the projection of force on time acting on each body?

AT 2. A body of mass 10 kg suspended from a cable rises vertically. With what acceleration does the body move if a cable with a stiffness of 59 kN/m is lengthened by 2 mm?

AT 3. The average height of the satellite above the earth's surface is 900 km. Determine the speed of its movement. (Give your answer in km/s)

1. As you already know, the force with which a body, due to its attraction to the Earth, acts on a support or suspension is called body weight P.

Body weight is applied to a support or suspension; in contrast, the force of gravity is applied to the body. Weight and gravity have not only different points applications, but also of different nature: gravity - gravitational force, and weight is the elastic force.

From the 7th grade physics course, you also know that if a body suspended on a thread or placed on a support is at rest or moves uniformly and rectilinearly, then its weight modulo equal to force gravity:

P = mg.

2. Let us now assume that the body, together with the support or suspension, moves relative to the Earth with acceleration. Will the weight of the body and the force of gravity be equal in this case?

Consider the movement of a person in an elevator. Let the elevator have an acceleration a, directed downwards (Fig. 52). In the inertial frame of reference associated with the Earth, a person is acted upon by: the force of gravity directed downwards and the elastic force from the floor of the elevator directed upwards. The elastic force in this case is called ground reaction force and denoted by the letter N. The resultant of these forces imparts acceleration to a person.

Using Newton's second law, we can write in vector form:

F = ma,
F cord + N = ma.

Let's direct the axis Y vertically down and write this equation in projections onto this axis, taking into account that F cord = mg, projections of acceleration and gravity onto the axis Y are positive, and the projection of the ground reaction force is negative. We get:

mg – N = ma.

From here:

N = mg – ma = m(g – a).

According to Newton's third law, the absolute weight of a body is equal to the support reaction force:

P = N.

Then

P = m(g – a).

From the resulting formula it is clear that the weight of the body is less than the force of gravity. Thus, if a body, together with a support or suspension, moves downward with an acceleration that is directed in the same direction as the acceleration of free fall, then its weight is less than the force of gravity, i.e. less than the weight of a body at rest.

You experience a decrease in weight while in the elevator, at the moment it begins to move down.

If the acceleration of the body is equal to the acceleration of gravity a = g, then body weight P= 0. This state is called the state weightlessness. Astronauts are in a state of weightlessness spaceship during flight, as they move around the Earth with a centripetal acceleration equal to the acceleration of gravity.

But not only astronauts experience weightlessness. A runner may be in this state for short periods of time when both feet are off the ground; ski jumper during flight.

3. Consider again the movement of the elevator and the person standing in it. But only now the elevator has acceleration a, directed upward (Fig. 53).

Using Newton's second law, we can write:

F = ma,
F cord + N= ma.

Directing the axis Y vertically down, we write this equation in projections onto this axis:

mg – N = –ma; N = mg + ma; N = m(g + a).

Because the P = N, That

P = m(g + a).

From the formula it is clear that the weight in this case is greater than the force of gravity. Thus, if a body, together with a support or suspension, moves with acceleration directed opposite to the acceleration of free fall, then its weight is greater than the force of gravity, i.e., greater than the weight of the body at rest.

An increase in body weight caused by accelerated movement is called overload.

You experience overload in the elevator at the moment it begins to move upward. Cosmonauts and jet pilots experience enormous overloads during takeoff and landing; pilots performing an aerobatics maneuver called a “loop” at its lowest point. In order to reduce the pressure on the astronauts' skeleton during takeoff, special chairs are made in which the astronauts are in a reclining position. In this case, the pressure force that acts on the astronaut is distributed over a larger area, and the pressure on the skeleton becomes less than when the astronaut is in a sitting position.

4. Example of problem solution

What is the weight of a pilot weighing 70 kg performing a “loop” at the lower and upper points of the trajectory if the radius of the loop is 200 m and the speed of the aircraft during the loop is 100 m/s?

Given:

Solution

m= 70 kg

R= 200 m

v= 100 m/s

g= 10 m/s 2

The pilot is affected by gravity at the lower and upper points of the trajectory F tension and reaction force from the chair N(Fig. 54). The ground reaction force is equal in magnitude to the weight of the pilot: P = N.

In accordance with Newton's second law, we can write:

N + F cord =ma.

P 1?

P 2?

For the bottom point of the trajectory, this equation is in projections onto the axis Y(Fig. 54, A) will look like:

–N 1 + F cord = – ma, or N 1 – mg= ma.

Hence,

P 1 = N 1 = ma+ mg= m(a + g).

For the top point of the trajectory (Fig. 54, b) can be written:

N 1 + F cord = ma.

From here

N 1 = ma – mg.

Hence,

P 2 = N 1 = m(a – g).

Because the a= , then

P 1 = m + g; P 2 =– g.

P 1 = 70 kg + 10 m/s 2 = 4200 N;

P 2 = 70 kg – 10 m/s 2 = 2800 N.

If the force of gravity acting on the pilot F heavy = 70 kg 10 m/s 2 = 700 N, then its weight at the bottom point of the trajectory is 6 times greater than the force of gravity: == 6. They say that the pilot experiences a sixfold overload.

At the top point of the trajectory, the pilot experiences a fourfold overload: == 4.

Answer: P 1 = 4200 N; P 2 = 2800 N.

Self-test questions

1. What is body weight called? What is the nature of body weight?

2. In what case is the weight of a body equal in magnitude to the force of gravity?

3. How does the weight of a body change when it moves with acceleration directed upward; down?

4. What state is called the state of weightlessness? When does it come?

5. What condition is called overload? When do you experience overload?

Task 15

1. The elevator begins to move downward with an acceleration of 2 m/s 2 . What is the weight of a 60 kg person standing in this elevator?

2. With what force does a car weighing 1 ton press on the middle of a convex bridge having a radius of curvature of 30 m? The car speed is 72 km/h.

3. A stone weighing 400 g is rotated uniformly in a vertical plane on a rope 1 m long at a speed of 2 m/s (Fig. 55). What is the tension force in the rope when the stone passes the upper and lower points of the trajectory?

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