Energy of elastic deformation. Energy of elastic deformation Potential energy of an elastically deformed rod

Potential energy is available for a system of interacting bodies. But a separate deformed body also has this type of energy. In this case, the potential energy depends on the relative position of the body parts.

Elastic strain energy

If a load suspended on a wire stretches the suspension and lowers, then gravity is doing work. Due to such work, the energy of the deformed body increases, which has passed from an unstressed state to a stressed one. It turns out that during deformation, the internal energy of the body increases. The growth of the internal energy of the body is to increase the potential energy, which is associated with the relative position of the molecules of the body. If we are dealing with elastic deformation, then after the load is removed, the additional energy disappears, and due to it, the elastic forces do work. During elastic deformation, the temperature of solids does not increase significantly. This is their significant difference from gases, which heat up when compressed. Under plastic deformation, solids can significantly increase their temperature. An increase in temperature, and consequently in the kinetic energy of molecules, reflects an increase in the internal energy of the body during plastic deformation. In this case, an increase in internal energy also occurs due to the work of forces that cause deformation.

In order to stretch or compress the spring, you must perform work () equal to:

where - the value characterizing the change in the length of the spring (elongation of the spring); - coefficient of elasticity of the spring. This work is going to change the potential energy of the spring ():

When writing expression (2), we assume that the potential energy of the spring without deformation is equal to zero.

Potential energy of an elastically deformed rod

The potential energy of an elastically deformed rod during its longitudinal deformation is equal to:

where is Young's modulus; - relative extension; - the volume of the rod. For a homogeneous rod with its uniform deformation, the energy density of elastic deformation can be found as:

If the deformation of the rod is non-uniform, then when using formula (3) to find the energy at the point of the rod, the value for the considered point is substituted into this formula.

The energy density of elastic deformation in shear is found using the expression:

where is the shear modulus; - relative shift.

Examples of problem solving

EXAMPLE 1

Exercise

A stone having a mass when fired from a slingshot began flying at a speed of . What is the coefficient of elasticity of the rubber cord of the slingshot, if the cord received elongation during the shot? Consider that the change in the cross section of the cord can be neglected.

Solution

At the time of the shot, the potential energy of the stretched cord () is converted into the kinetic energy of the stone (). According to the law of conservation of energy, we can write:

We find the potential energy of elastic deformation of a rubber cord as:

where is the coefficient of elasticity of rubber,

kinetic energy of the stone:

hence

We express the rubber stiffness coefficient from (1.4):

Answer

EXAMPLE 2

Exercise	A spring with a stiffness is compressed by a force whose magnitude is equal to . What is the work () of the applied force with additional compression of the same spring for another?
Solution	Let's make a drawing.

A deformed elastic body (for example, a stretched or compressed spring) is capable, returning to an undeformed state, to perform work on the bodies in contact with it. Therefore, an elastically deformed body has potential energy. It depends on the relative position of body parts, such as coils of a spring. The work that a stretched spring can do depends on the initial and final stretches of the spring. Let's find the work that can be done by the stretched spring, returning to the unstretched state, i.e., find the potential energy of the stretched spring.

Let the stretched spring be fixed at one end, and the other end, moving, does work. It should be borne in mind that the force with which the spring acts does not remain constant, but changes in proportion to the stretch. If the initial tension of the spring, counting from the unstretched state, was equal to , then the initial value of the elastic force was , where is the proportionality factor, which is called the spring stiffness. As the spring contracts, this force decreases linearly from a value to zero. So the average value of the force is . It can be shown that the work is equal to this average multiplied by the displacement of the point of application of the force:

Thus, the potential energy of a stretched spring

The same expression is obtained for a compressed spring.

In formula (98.1), the potential energy is expressed in terms of the stiffness of the spring and in terms of its extension. Replacing with , where is the elastic force corresponding to the tension (or compression) of the spring, we obtain the expression

which determines the potential energy of the spring, stretched (or compressed) force. It can be seen from this formula that, by stretching different springs with the same force, we will give them a different supply of potential energy: the stiffer the spring, i.e. the greater its elasticity, the less potential energy; and vice versa: the softer the spring, the more energy it will store for a given tensile force. This can be clearly understood if we take into account that, with the same acting forces, the extension of a soft spring is greater than that of a rigid one, and therefore the product of the force and the displacement of the point of application of the force, i.e. work, is also greater.

This pattern is of great importance, for example, when constructing various springs and shock absorbers: when landing on the ground, the landing gear shock absorber, compressing, must do a lot of work, damping the vertical speed of the aircraft. In a shock absorber with a low rigidity, the compression will be greater, but the resulting elastic forces will be less and the aircraft will be better protected from damage. For the same reason, road shocks are felt more sharply when the bicycle tires are heavily inflated than when they are lightly inflated.

In Laos, where the Mekong, the "father of the rivers", smoothly carries its waters, there is the Mountain of Wonders. 328 steps lead to the top of Mount Phousi. Climbing the Mountain of Wonders under the scorching rays of the sun is a serious test. But at the same time, a miracle happens: the pilgrim gets rid of the burden of worldly worries and gains complete self-confidence. The pagoda standing on top was erected, according to legend, on the personal instructions of the Buddha at the place where the passage to the center of the Earth began. When rising under the rays of the scorching sun, the worldly worries of a layman decrease. What does it increase?

10th c. Potential energy of an elastically deformed body

	An undeformed spring with a stiffness of 30 N/m is stretched by 4 cm. What is the potential energy of the stretched spring?


	How will the potential energy of an elastically deformed body change with an increase in its deformation by 3 times?
	1) increase by 9 times	2) will increase by 3 times
	3) decrease by 3 times	4) decrease by 9 times

When a spring is stretched by 0.1 m, an elastic force equal to 2.5 N arises in it. Determine the potential energy of this spring when stretched by 0.08 m.

1) 25 J 2) 0.16 J

3) 0.08 J 4) 0.04 J

The student investigated the dependence of the modulus of elasticity
springs from stretching and got the following results:

Determine the potential energy of the spring when stretched by 0.08 m

1) 0.04 J 2) 0.16 J

3) 25 J 4) 0.08 J

A weight of 0.4 kg was suspended vertically from the dynamometer. The dynamometer spring was stretched by 0.1 m, and the load was at a height of 1 m from the table. What is the potential energy of the spring?

1) 0.1 J 2) 0.2 J

3) 4 J 4) 4.2 J

11. Kinetic energy theorem

	The work of the resultant of all forces acting on a material point, when the modulus of its velocity changes from before is equal to
	1)	2)
	3)	4)
	The speed of a car weighing 1 ton increased from 10 m/s to 20 m/s. The work of the resultant force is


	To communicate a given speed to a fixed body required to do work . What work must be done to increase the speed of this body from value to value 2?


	Ball mass moves at speed. After an elastic collision with the wall, it began to move in the opposite direction, but with the same speed in modulus. What is the work of the elastic force acting on the ball from the side of the wall?
	1) 2)	3) 4) 0

A load with a mass of 1 kg under the action of a force of 50 N directed vertically upwards rises to a height of 3 m. The change in the kinetic energy of the load is equal to

12. The work of gravity and the change in potential energy

	A ball of mass 100 g rolls down a hill 2 m long, making an angle of 30 o with the horizontal. Determine the work done by gravity.
		2) J

	The student lifted a ruler 0.5 m long lying on the table by one end so that it was in a vertical position. What is the minimum work done by the student if the mass of the ruler is 40 g?


	The student lifted a ruler 1 m long lying on the table at one end so that it turned out to be tilted to the table at an angle of 30 o. What is the minimum work done by the student if the mass of the ruler is 40 g?


	The student lifted a ruler 0.5 m long lying on the table at one end so that it turned out to be inclined to the table at an angle of 30 o. What is the minimum work done by the student if the mass of the ruler is 40 g?


	A man took hold of the end of a homogeneous log of mass 80 kg and a length of 2 m lying on the ground and lifted this end so that the log was in a vertical position. What work did the person do?
	1) 160 J 2) 800 J	3) 16000 J 4) 8000 J
	A man took hold of the end of a homogeneous log of mass 80 kg and a length of 2 m lying on the ground and lifted this end so that the log turned out to be tilted to the ground at an angle of 45°. What work did the person do?
	1) 50 J 2) 120 J	3) 250 J 4) 566 J

13. Simple mechanisms.

14. efficiency

	Determine the useful power of the engine if its efficiency is 40%, and the power according to the technical data sheet is 100 kW


	With the help of a fixed block fixed on the ceiling, a load of 20 kg is lifted to a height of 1.5 m. What work is done if the efficiency of the block is 90%?


	With the help of a system of blocks, a load of 10 kg is evenly lifted, applying a force of 55 N (Fig.) The efficiency of such a mechanism is equal to
	1) 5,5 % 2) 45 %	3) 55 % 4) 91 %
	The load is moved uniformly along an inclined plane 2 m long. Under the action of a force of 2.5 N directed along the plane, the load was lifted to a height of 0.4 m. If we consider the part of the work that went to increase the potential energy of the load to be useful, then the efficiency of the inclined plane in this process is 40%. What is the weight of the cargo?

	The angle of inclination of the plane to the horizon is 30 o. A box with a mass of 90 kg is dragged up this plane, applying a force directed parallel to the plane and equal to 600 N. The efficiency of the inclined plane is


	The efficiency of the inclined plane is 80%. The angle of inclination of the plane to the horizon is 30 o. To drag a box of mass 120 kg up this plane, a force must be applied to it, directed parallel to the plane and equal to


	A plane inclined to the horizon at an angle , are used to uniformly retract the load to a certain height. Force is applied along a plane. The coefficient of friction of the load on the plane is equal to . The efficiency of such a mechanism

	The cannon, fixed at a height of 5 m, shoots in a horizontal direction with projectiles with a mass of 10 kg. Due to the recoil, its barrel, which has a mass of 1000 kg, compresses the spring by 1 m, reloading the gun. At the same time, the relative share The recoil energy is used to compress the spring. What is the stiffness of the spring if the range of the projectile is 600 m?
	The cannon, fixed at a height of 5 m, shoots in a horizontal direction with projectiles with a mass of 10 kg. Due to recoil, its barrel, which has a mass of 1000 kg, compresses a spring with a stiffness of 6000 N / m, reloading the gun. In this case, the relative share of the recoil energy goes to compress this spring. What is the maximum amount of spring deformation if the range of the projectile is 600 m?
	A cannon fixed at a certain height fires projectiles with a mass of 10 kg in a horizontal direction. Due to recoil, its barrel, which has a mass of 1000 kg, compresses a spring of stiffness 6000 N / m by 1 m, reloading the gun. Wherein The recoil energy is used to compress the spring. What is the flight time of the projectile if the range of the projectile is 600 m?
	The cannon, fixed at a height of 5 m, shoots in a horizontal direction with projectiles with a mass of 10 kg. Due to recoil, its barrel, which has a mass of 1000 kg, compresses a spring of stiffness 6000 N / m by 1 m, reloading the gun. What proportion of the recoil energy is used to compress the spring if the range of the projectile is 600 m?

15. The law of conservation of mechanical energy

The car moves uniformly along the bridge thrown over the river. The mechanical energy of the car is determined

only its speed and mass

only the height of the bridge above the water level in the river

only its speed, mass, height of the bridge above the water level in the river

its speed, mass, potential energy reference level and height above this level

The law of conservation of mechanical energy is applicable for

1) any system of bodies in any frame of reference

2) any system of bodies with interactions by any forces in inertial frames of reference

3) a closed system of bodies interacting only with the forces of elasticity and the forces of universal gravitation, in inertial frames of reference

4) a closed system of bodies interacting by any forces in inertial reference systems

	The ball was rolled down the hill along three different smooth grooves (convex, straight and concave). At the beginning of the path, the speeds of the ball are the same. In which case is the speed of the ball at the end of the path the greatest? Ignore friction.
	1) in the first 2) in the second 3) in the third 4) in all cases the speed is the same

	A stone is thrown vertically upwards. At the time of the throw, it had a kinetic energy of 30 J. What potential energy relative to the earth's surface will the stone have at the top of its flight path? Ignore air resistance.
	1) 0 J 2) 15 J	3) 30 J 4) 60 J
	A stone is thrown vertically upwards. At the time of the throw, it had a kinetic energy of 20 J. What kinetic energy will the stone have at the top of its flight path? Ignore air resistance.
	1) 0 J 2) 10 J	3) 20 J 4) 40 J
	A mass of 100 g falls freely from a height of 10 m with zero initial velocity. Determine the kinetic energy of the load at a height of 6 m.
	A mass of 100 g falls freely from a height of 10 m with zero initial velocity. Determine the potential energy of the load at the moment when its speed is 8 m/s. Assume that the potential energy of the load is zero on the Earth's surface.
	A body of mass 0.1 kg is thrown horizontally at a speed of 4 m/s from a height of 2 m relative to the ground. What is the kinetic energy of the body at the time of its landing? Air resistance is ignored.

A body with a mass of 1 kg, thrown vertically upwards from the surface of the earth, reached a maximum height of 20 m. With what modulo speed did the body move at a height of 10 m? Ignore air resistance.
1) 7 m/s 2) 10 m/s		3) 14.1 m/s 4) 20 m/s
The speed skater, having accelerated, drives onto an icy mountain inclined at an angle of 30 o to the horizon and drives to a complete stop of 10 m. What was the speed of the skater before the start of the ascent? Neglect friction
1) 5 m/s 2) 10 m/s		3) 20 m/s 4) 40 m/s
A projectile with a mass of 3 kg, fired at an angle of 45° to the horizon, flew horizontally for a distance of 10 km. What will be the kinetic energy of the projectile just before it hits the Earth? Ignore air resistance

A projectile with a mass of 200 g, fired at an angle of 30 o to the horizon, rose to a height of 4 m. What will be the kinetic energy of the projectile immediately before it falls to the Earth? Ignore air resistance
	4) it is impossible to answer the question of the problem, because the initial velocity of the projectile is unknown
A body of mass 0.1 kg is thrown upwards at an angle of 30° to the horizontal with a speed of 4 m/s. What is the potential energy of the body at the highest point of the ascent? Assume that the potential energy of the body is zero on the surface of the Earth.
Which of the following formulas can be used to determine kinetic energy? , which the body had at the top point of the trajectory?
1)
3)		4)

	The figure shows the positions of a freely falling ball after a time interval equal to With. The mass of the ball is 100 g. Estimate, using the law of conservation of energy, the height from which the ball fell


	The ball on the thread, which is in the equilibrium position, was told a small horizontal speed (see Fig.). How high will the ball rise?
	1) 2)	3) 4)
	A ball on a thread in the equilibrium position was given a small horizontal velocity of 20 m/s. How high will the ball rise?
	1) 40 m 2) 20 m	3) 10 m 4) 5 m

		The ball is thrown vertically upwards. The figure shows a graph of the change in the kinetic energy of the ball as it rises above the point of throw. What is the kinetic energy of the ball at a height of 2 m?


		The ball is thrown vertically upwards. The figure shows a graph of the change in the kinetic energy of the ball as it rises above the point of throw. What is the potential energy of the ball at a height of 2 m?


		The ball is thrown vertically upwards. The figure shows a graph of the change in the kinetic energy of the ball as it rises above the point of throw. What is the total energy of the ball at a height of 2 m?


		H The figure shows a graph of the change over time in the kinetic energy of a child swinging on a swing. At the moment corresponding to point A on the graph, its kinetic energy is equal to

	A freight car moving along a horizontal track at low speed collides with another car and stops. This compresses the buffer spring. Which of the following energy transformations occurs in this process?
	1) the kinetic energy of the car is converted into the potential energy of the spring 2) the kinetic energy of the car is converted into its potential energy 3) the potential energy of the spring is converted into its kinetic energy 4) the internal energy of the spring is converted into the kinetic energy of the car

	A fixed spring gun fires vertically upwards. How high will the bullet rise if its mass is , spring stiffness , and the deformation before the shot ? Neglect the friction and mass of the spring, assuming much less .
	1) 2)	3) 4)
	When a ball of mass 100 g is fired vertically upwards from a spring pistol, it rises to a height of 2 m. What is the stiffness of the spring if the spring was compressed by 5 cm before the shot?
	A weight suspended from a spring stretches it by 2 cm. The student lifts the weight up so that the tension of the spring is zero, and then releases it from his hands. The maximum extension of the spring is
	1) 3 cm 2) 1 cm	3) 2 cm 4) 4 cm
	A ball floats up from the bottom of the aquarium and jumps out of the water. In the air, he has kinetic energy, which he acquired by reducing
	1) internal energy of water 2) potential energy of the ball 3) potential energy of water 4) kinetic energy of water

16. Springy center kick

17. The law of conservation of momentum and the law of conservation of energy

	Are the laws of conservation of mechanical energy and momentum of the system of bodies always satisfied in inertial frames of reference? do not work outside forces? 1) both laws are always satisfied 2) the law of conservation of mechanical energy is always satisfied, the law of conservation of momentum may not be satisfied 3) the law of conservation of momentum is always satisfied, the law of conservation of mechanical energy may not be satisfied 4) both laws are not fulfilled
	A meteorite fell to Earth from outer space. Did the mechanical energy and momentum of the Earth-meteorite system change as a result of the collision?
	P A plasticine ball with a mass of 0.1 kg has a speed of 1 m/s. It hits a stationary trolley with a mass of 0.1 kg attached to a spring and sticks to the trolley (see figure). What is the total mechanical energy of the system during its further vibrations? Ignore friction.


	Bar mass slides down an inclined surface from a height of 0.8 m and, moving along a horizontal surface, collides with a fixed block of mass . Assuming that the collision is absolutely inelastic, determine the change in the kinetic energy of the first block as a result of the collision. Ignore friction during motion. Assume that the inclined plane smoothly turns into a horizontal one.
	A bullet flying at a horizontal speed of 400 m/s hits a bag stuffed with foam rubber, weighing 4 kg, hanging on a length of thread. The height to which the bag will rise if the bullet gets stuck in it is 5 cm. What is the mass of the bullet? Express your answer in grams.

	A piece of plasticine weighing 200 g is thrown upwards with an initial speed = 9 m/s. After 0.3 seconds of free flight, plasticine encounters a bar weighing 200 g hanging on a thread (Fig.). What is the kinetic energy of the block with plasticine adhering to it? straightaway after the hit? Consider the impact instantaneous, neglect the air resistance.


	A piece of plasticine weighing 200 g is thrown upwards with an initial speed = 8 m/s. After 0.4 seconds of free flight, plasticine encounters a 200 g bowl on its way, mounted on a weightless spring (Fig.). What is the kinetic energy of the bowl together with plasticine adhering to it immediately after their interaction? The impact is assumed to be instantaneous, air resistance is neglected.

	A piece of sticky putty weighing 100 g with zero initial velocity is dropped from a height H= 80 cm (Fig.) for a bowl weighing 100 g, mounted on a spring. What is the kinetic energy of the bowl with putty adhering to it straightaway after their interaction? Consider the impact instantaneous, neglect the air resistance.
	1) 0.4 J 2) 0.8 J	3) 1.6 J 4) 3.2 J

	A piece of plasticine weighing 60 g is thrown upwards with an initial speed = 10m/s. After 0.1 s of free flight, the plasticine encounters a bar weighing 120 g hanging on a thread (Fig.). What is the kinetic energy of the bar together with plasticine adhering to it immediately after their interaction? The impact is assumed to be instantaneous, air resistance is neglected.


	A piece of plasticine weighing 200 g is thrown upwards with an initial speed = 10 m/s. After 0.4 seconds of free flight, plasticine meets a bar of mass 200 g hanging on a thread. What is the potential energy of the bar with plasticine adhering to it relative to the initial position of the bar at the moment of its complete stop? The impact is assumed to be instantaneous, air resistance is neglected.

The initial velocity of a projectile fired vertically upwards from a cannon is 10 m/s. At the point of maximum rise, the projectile exploded into two fragments, the mass ratio of which is 1:2. A fragment of a smaller mass fell to the Earth with a speed of 20 m/s. What is the speed of the larger fragment as it falls to Earth? Consider the surface of the earth to be flat and horizontal.

The initial velocity of a projectile fired vertically upwards from a cannon is 10 m/s. At the point of maximum rise, the projectile exploded into two fragments, the masses of which are related as 2:1. A fragment of a larger mass fell to Earth first at a speed of 20 m/s. What is the maximum height that a fragment of smaller mass can reach? Consider the surface of the earth to be flat and horizontal.

		The initial velocity of a projectile fired vertically upwards is 160 m/s. At the point of maximum rise, the projectile exploded into two fragments, the mass ratio of which is 1:4. The fragments scattered in vertical directions, and the smaller fragment flew down and fell to the ground at a speed of 200 m/s. Determine the speed that the larger fragment had at the moment of impact on the ground. Ignore air resistance.
		The initial velocity of a projectile fired vertically upwards is 300 m/s. At the point of maximum rise, the projectile exploded into two fragments. The first piece of mass m 1 fell to the ground near the point of the shot, having a speed of 2 times the initial speed of the projectile. The second piece of mass m 2 has a speed of 600 m/s near the surface of the earth. What is the mass ratio
		The initial velocity of a projectile fired vertically upwards is 100 m/s. At the point of maximum rise, the projectile exploded into two fragments. The first piece of mass m 1 fell to the ground near the point of the shot, having a speed of 3 times the initial speed of the projectile. The second piece of mass m 2 rose to a height of 1.5 km. What is the mass ratio these fragments? Ignore air resistance.
		At the point of maximum lift, a projectile fired from a gun vertically upwards exploded into two fragments. The first piece of mass m 1 moving vertically down fell to the ground, having a speed of 1.25 times the initial velocity of the projectile, and the second fragment with a mass m 2 when touching the surface of the earth had a speed of 1.8 times greater. What is the ratio of the masses of these fragments? Ignore air resistance.
		The initial velocity of a projectile fired vertically upwards is 120 m/s. At the point of maximum rise, the projectile exploded into two identical fragments. The first fell to the ground near the point of the shot, having a speed of 1.5 times the initial speed of the projectile. To what maximum height above the explosion site did the second fragment rise? Ignore air resistance.
		The initial velocity of a projectile fired vertically upwards is 200 m/s. At the point of maximum rise, the projectile exploded into two identical fragments. The first fell to the ground near the point of the shot, having a speed of 2 times the initial velocity of the projectile. What is the maximum height reached by the second fragment? Ignore air resistance.
		The initial velocity of a projectile fired vertically upwards from a cannon is 10 m/s. At the point of maximum rise, the projectile exploded into two fragments, the mass ratio of which is 1:2. A fragment of a smaller mass flew horizontally at a speed of 20 m/s. At what distance from the point of the shot will the second fragment fall? Consider the surface of the earth to be flat and horizontal.
		The initial velocity of a projectile fired vertically upwards from a cannon is 20 m/s. At the point of maximum rise, the projectile exploded into two fragments, the mass ratio of which is 1:4. A fragment of a smaller mass flew horizontally at a speed of 10 m/s. At what distance from the point of the shot will the second fragment fall? Consider the surface of the earth to be flat and horizontal.
		Bar mass \u003d 500 g slides down an inclined plane from a height \u003d 0.8 m and, moving along a horizontal surface, collides with a stationary block of mass \u003d 300 g. Assuming the collision is absolutely inelastic, determine the total kinetic energy of the bars after the collision. Ignore friction during motion. Assume that the inclined plane smoothly turns into a horizontal one.
		A bar of mass = 500 g slides down an inclined plane from a height of = 0.8 m and, moving along a horizontal surface, collides with a fixed bar of mass = 300 g. Considering the collision to be absolutely inelastic, determine the change in the kinetic energy of the first bar as a result of the collision. Ignore friction during motion. Assume that the inclined plane smoothly turns into a horizontal one.
	Two balls, the masses of which are 200 g and 600 g, hang, touching, on identical threads 80 cm long. The first ball was deflected at an angle of 90 o and released. To what height will the balls rise after the impact if this impact is absolutely inelastic?

18. The law of conservation of energy and Newton's second law

	A load weighing 100 g is tied to a thread 1 m long. The thread with the load is taken away from the vertical at an angle of 90 o. What is the centripetal acceleration of the load when the string makes an angle of 60° with the vertical?
	pendulum thread length \u003d 1 m, to which the weight of the mass is suspended m = 0.1 kg, deflected by an angle from the vertical position and released. The tension force of the thread T at the moment the pendulum passes the equilibrium position is 2 N. What is the angle ?

19. Change of mechanical energy and work of external forces

A car with a mass of 1000 kg is approaching at a speed of 20 m/s to a rise of 5 m. At the end of the rise, its speed decreases to 6 m/s. What is the change in the mechanical energy of the car?

The speed of the thrown ball just before hitting the wall was twice its speed just after hitting it. How much heat was released during the impact if the kinetic energy of the ball before the impact was 20 J?

The speed of the thrown ball just before hitting the wall was twice its speed just after hitting it. Upon impact, an amount of heat equal to 15 J was released. Find the kinetic energy of the ball before impact.

the potential energy of the skydiver is completely converted into its kinetic energy

the kinetic energy of the skydiver is completely converted into its potential energy

the kinetic energy of the skydiver is completely converted into the internal energy of the skydiver and air

the energy of the interaction of the skydiver with the Earth is converted into the internal energy of the interacting bodies due to the forces of air resistance

In the wood of the African baobab, a tree with a height of about 20 m and a trunk reaching a girth of 20 m, up to 120 thousand liters of water can accumulate. Baobab wood is very soft and porous, easily rots, forming hollows. (So, in Australia, a hollow of one baobab with an area of 36 m 2 was used as a prison.) The softness of the tree is evidenced by the fact that a bullet fired from a rifle easily pierces through the trunk of a baobab with a diameter of 10 m. Determine the drag force of the baobab wood if the bullet had a speed of 800 m / s at the moment of impact and completely lost speed before leaving the tree. Bullet weight 10 g.

	A skier weighing 60 kg descended from a mountain 20 m high. What was the resistance force to his movement along a horizontal ski track after the descent if he stopped after driving 200 m? Assume that he glided along the slope of the mountain without friction.
	A boy on a sled with a total mass of 60 kg descends from an icy mountain and stops after driving 40 m on a horizontal surface after the descent. What is the height of the mountain if the force of resistance to movement on a horizontal section is 60 N. Consider that the sledge glided along the slope of the mountain without friction.
	A boy on a sled descended from an ice mountain 10 m high and drove horizontally to a stop of 50 m. The friction force during his movement on a horizontal surface is 80 N. What is the total mass of the boy with the sled? Assume that the sledge glided along the slope of the mountain without friction.
	What is the stopping distance of a 1000 kg car moving at a speed of 30 m/s on a horizontal road? The coefficient of sliding friction between the road and the car tires is 0.3?
	A board is fixed on the table . On the board at its left end lies a small bar. Coefficient of sliding friction of a bar on a board . What minimum speed must be imparted to the block in order for it to slide off the right end of the board?

	A boy on a sled with a total mass of 50 kg descended from an icy mountain. The coefficient of friction when it moves along a horizontal surface is 0.2. The distance that the boy traveled horizontally to the stop is 30 m. What is the height of the mountain? Assume that the sledge glided along the slope of the mountain without friction.
	Sledges with riders with a total mass of 100 kg start to move down a mountain 8 m high and 100 m long. What is the average resistance force to the movement of the sled if at the end of the mountain they reached a speed of 10 m/s?
	A body of mass 200 g is thrown vertically upwards from a height of 5 m with an initial velocity of 2 m/s. When falling to the Earth, the body deepens into the ground to a depth of 5 cm. Find the average resistance force of the soil to the movement of the body. (Ignore air resistance).
		From the impact of a copra with a mass of 450 kg, falling freely from a height of 5 m, a pile with a mass of 150 kg is immersed in the ground by 10 cm. Determine the resistance force of the soil, considering it constant, and the impact is absolutely inelastic. Ignore the change in the potential energy of the pile. .
	Ball mass m \u003d 0.1 kg on a thread of length L \u003d 0.4 m is swinged so that each time the ball passes the equilibrium position, it is on it for a short period of time equal to t= 0.01 s the force acts F = 0.1 N, directional parallel
	Ball mass m \u003d 0.2 kg on a thread of length L \u003d 0.9 m is swinged so that each time the ball passes the equilibrium position, it is on it for a short period of time equal to t= 0.01 s the force acts F = 0.1 N, directional parallel speed. After how many complete oscillations will the ball on the thread deviate by 60 o?

20. The law of conservation of momentum, the change in mechanical energy and the work of external forces

4) this condition does not allow to determine the initial velocity of the bullet, because the law of conservation of mechanical energy is not fulfilled during the interaction of the bullet and the bar

Small mass cube 2 kg can slide without friction along a cylindrical recess with a radius of 0.5 m. Starting from above, it collides with another similar cube resting below. What is the amount of heat released as a result of a perfectly inelastic collision?

	D va bodies, the masses of which, respectively m 1 = 1 kg and m 2 = 2kg, slide on a smooth horizontal table (see picture). The speed of the first body v 1 = 3 m/s, the speed of the second body v 2 = 6 m/s. How much heat will be released when they collide and move on, clinging together? There is no rotation in the system. Ignore the action of external forces.
		The bullet flies horizontally at a speed of 400 m/s, pierces a box standing on a horizontal rough surface and continues to move in the same direction at a speed of ¾. The mass of the box is 40 times the mass of the bullet. Coefficient of sliding friction between box and surface		W an arm weighing 1 kg, suspended on a thread 90 cm long, is taken away from the equilibrium position at an angle of 60 ° and released. At the moment the ball passes the equilibrium position, a bullet of mass 10 g hits it, flying towards the ball at a speed of 300 m/s. It breaks through it and continues to move horizontally at a speed of 200 m/s, after which the ball continues to move in the same direction. What is the maximum angle will the ball deviate after being hit by a bullet? (The mass of the ball is considered unchanged, the diameter of the ball is negligible compared to the length of the thread).

W
an arm weighing 1 kg, suspended on a thread 90 cm long, is removed from the equilibrium position and released. At the moment the ball passes the equilibrium position, a bullet of mass 10 g hits it, flying towards the ball at a speed of 300 m/s. It breaks through it and continues to move horizontally at a speed of 200 m / s, after which the ball continues to move in the same direction, deviates at an angle of 39 o. Determine the initial deflection angle of the ball. (The mass of the ball is assumed to be unchanged, the diameter of the ball is negligible compared to the length of the thread, cos 39 = equal to the path traveled body... impact force if his duration 1 s. b) How long body weight 100 G will change my speed from 5 m/s to...