House
A system of interacting bodies has potential energy. But an individual deformed body also possesses this type of energy. In this case, the potential energy depends on the relative position of the parts of the body.
Elastic deformation energy If a load suspended on a wire stretches the suspension and falls, it means that the force of gravity does 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 increase in internal energy of the body consists in increasing potential energy , which is related to the relative arrangement 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. During plastic deformation solids
can significantly increase their temperature. An increase in temperature, and therefore in the kinetic energy of molecules, reflects an increase in the internal energy of a body during plastic deformation. In this case, the increase in internal energy also occurs due to the work of forces causing deformation.
In order to stretch or compress a spring, work () must be performed equal to:
where is the value characterizing the change in the length of the spring (spring elongation); - spring elasticity coefficient. This work is used to change the potential energy of the spring ():
When writing expression (2), we assume that the potential energy of the spring without deformation is 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; - volume of the rod. For a homogeneous rod with uniform deformation, the elastic deformation energy density can be found as:
If the deformation of the rod is uneven, then when using formula (3) to search for energy at a point on the rod, the value for the point in question is substituted into this formula.
where is the shear modulus; - relative shift.
Examples of problem solving
EXAMPLE 1
| Exercise | When fired from a slingshot, a stone with mass begins to fly at a speed of . What is the coefficient of elasticity of the rubber cord of a slingshot if, when fired, the cord receives an elongation? Consider that the change in the cross-section of the cord can be neglected. |
| Solution | At the moment of the shot, the potential energy of the stretched cord () transforms into kinetic energy stone(). According to the law of conservation of energy, we can write: We find the potential energy of elastic deformation of the rubber cord as:
where is the rubber elasticity coefficient, kinetic energy of stone:
hence
Let us express the rubber stiffness coefficient from (1.4): |
| Answer |
EXAMPLE 2
| Exercise | A spring having 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 by another ? |
| Solution | Let's make a drawing. |
A deformed elastic body (for example, a stretched or compressed spring) is capable of doing work on the bodies in contact with it, returning to an undeformed state. Consequently, an elastically deformed body has potential energy. It depends on the relative position of body parts, for example the 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 a stretched spring can do when returning to an unstretched state, i.e., we'll find the potential energy of a stretched spring.
Let a stretched spring be fixed at one end, and let the other end, moving, do work. It must be taken into account that the force with which the spring acts does not remain constant, but changes in proportion to the stretch. If the initial stretch of the spring, counting from the unstretched state, was equal to , then the initial value of the elastic force was , where is the proportionality coefficient, which is called the spring stiffness. As the spring contracts, this force decreases linearly from value to zero. This means that 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), potential energy is expressed in terms of the spring stiffness and its tension. 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) by force. From this formula it is clear that by stretching different springs with the same force, we will give them different reserves 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 greater the energy it stores for a given tensile force. This can be clearly understood if we consider that for the same current forces The stretch of a soft spring is greater than that of a hard spring, and therefore the product of the force and the displacement of the point of application of the force is greater, i.e. work.
This pattern is of great importance, for example, when designing various springs and shock absorbers: when landing an aircraft on the ground, the landing gear shock absorber, compressing, must produce great job, dampening the vertical speed of the aircraft. In a shock absorber with 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, when bicycle tires are inflated tightly, road shocks are felt more sharply than when inflated weakly.
In Laos, where the Mekong, the “father of rivers,” flows smoothly, lies the Mountain of Wonders. 328 steps lead to the top of Mount Phousi. Climbing the Mountain of Miracles under the scorching rays of the sun is a serious test. But at the same time a miracle occurs: the pilgrim gets rid of the burden of worldly worries and gains complete self-confidence. The pagoda standing at the 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 concerns of a layman decrease. What is he increasing?
10th century Potential energy of an elastically deformed body
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An undeformed spring with a stiffness of 30 N/m is stretched by 4 cm. What is the potential energy of the stretched spring? |
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How does the potential energy of an elastically deformed body change when its deformation increases by 3 times? |
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1) will increase 9 times |
2) will increase 3 times |
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3) will decrease by 3 times |
4) will decrease by 9 times |
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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. |
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1) 25 J 2) 0.16 J |
3) 0.08 J 4) 0.04 J |
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The student investigated the dependence of the modulus of elastic force
Determine the potential energy of the spring when stretched by 0.08 m |
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1) 0.04 J 2) 0.16 J |
3) 25 J 4) 0.08 J |
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A load weighing 0.4 kg was suspended vertically from the dynamometer. The dynamometer spring 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? |
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1) 0.1 J 2) 0.2 J |
3) 4 J 4) 4.2 J |
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springs from its extension 
and got the following results:
11. Kinetic energy theorem
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The work of the resultant of all forces acting on a material point when the module of its velocity changes from |
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The speed of a car weighing 1 ton increased from 10 m/s to 20 m/s. The work done by the resultant force is equal to |
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To communicate a given speed to a stationary body |
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What work must be done to increase the speed of this body from value to value 2? |
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before 
equal to
work required 
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Ball mass
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moves at speed. |
After an elastic collision with the wall, it began to move in the opposite direction, but with the same speed in magnitude. What is the work done by the elastic force that acts on the ball from the wall?
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A load weighing 1 kg, under the influence of a force of 50 N, directed vertically upward, rises to a height of 3 m. The change in the kinetic energy of the load is equal to |
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2)
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A ball weighing 100 g rolled down a hill 2 m long, making an angle of 30 degrees with the horizontal. |
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Determine the work done by gravity. |
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J |
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The student lifted a 0.5 m long ruler lying on the table by one end so that it was in a vertical position. |
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What is the minimum amount of work done by the student if the mass of the ruler is 40 g? |
The student lifted a 1 m long ruler lying on the table by one end so that it was inclined to the table at an angle of 30 degrees. |
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What is the minimum amount of work done by the student if the mass of the ruler is 40 g? |
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The student lifted a ruler 0.5 m long lying on the table by one end so that it was inclined to the table at an angle of 30 degrees. |
What is the minimum amount of work done by the student if the mass of the ruler is 40 g? |
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12. Work of gravity and change in potential energyA man grabbed the end of a homogeneous log with a mass of 80 kg and a length of 2 m lying on the ground and raised this end so that the log was in a vertical position.
What kind of work did the person do?
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1) 160 J 2) 800 J |
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Using a stationary block fixed to the ceiling, a load weighing 20 kg is lifted to a height of 1.5 m. How much work is done if the efficiency of the block is 90%? |
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Using a system of blocks, a load weighing 10 kg is evenly lifted, applying a force of 55 N (Fig.) The efficiency of such a mechanism is equal to |
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1) 5,5 % 2) 45 % |
3) 55 % 4) 91 % |
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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 is raised to a height of 0.4 m. If we consider as useful that part of the work that went to increase the potential energy of the load, then the efficiency of the inclined plane in this process is equal to 40%. What is the mass of the cargo? |
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The angle of inclination of the plane to the horizon is 30 degrees. A box with a mass of 90 kg is dragged up this plane, applying to it a force directed parallel to the plane and equal to 600 N. Coefficient useful action the inclined plane is equal to |
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The efficiency of an inclined plane is 80%. The angle of inclination of the plane to the horizon is 30 degrees. |
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To drag a box weighing 120 kg up along this plane, a force must be applied to it, directed parallel to the plane and equal to  |
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A plane inclined to the horizontal at an angle 
, are used to uniformly pull the load to a certain height. The force is applied along the plane.|
The coefficient of friction of the load on the plane is equal to .
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The cannon, mounted at a height of 5 m, fires projectiles weighing 10 kg in the horizontal direction. Due to recoil, its barrel, which has a mass of 1000 kg, compresses the spring by 1 m, which reloads the gun. Wherein |
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relative share |
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The cannon, mounted at a height of 5 m, fires projectiles weighing 10 kg in the horizontal direction. Due to recoil, its barrel, which has a mass of 1000 kg, compresses a spring with a stiffness of 6000 N/m by 1 m, which reloads the gun. What fraction of the recoil energy is used to compress the spring if the projectile's flight range is 600 m? |
The efficiency of such a mechanism
The recoil energy goes into compressing this spring.15. Law of conservation of mechanical energy
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A car moves uniformly along a bridge spanning a river. The mechanical energy of a car is determined only by its speed and mass only the height of the bridge above the water level in the river only by its speed, mass, height of the bridge above the water level in the river |
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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 during interactions by any forces in inertial reference systems 3) a closed system of bodies interacting only with the forces of elasticity and the forces of universal gravitation, in inertial frames of reference |
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4) a closed system of bodies interacting by any forces in inertial frames of reference |
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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 greatest? Ignore friction. 1) in the first 2) in the second |
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3) in the third |
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4) in all cases the speed is the same |
A stone is thrown vertically upward. At the moment of the throw, it had a kinetic energy of 30 J. What potential energy relative to the surface of the earth will the stone have at the top point of its flight path? Neglect air resistance. |
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1) 0 J 2) 15 J |
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3) 30 J 4) 60 J |
A stone is thrown vertically upward. At the moment of the throw, it had a kinetic energy of 20 J. What kinetic energy will the stone have at the top point of its flight path? Neglect air resistance. |
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1) 0 J 2) 10 J |
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3) 20 J 4) 40 J |
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A body with a mass of 0.1 kg is thrown horizontally at a speed of 4 m/s from a height of 2 m relative to the surface of the earth. What is the kinetic energy of the body at the moment of its landing? |
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Ignore air resistance. |
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A body with a mass of 1 kg, thrown vertically upward from the surface of the earth, reached a maximum height of 20 m. At what absolute speed did the body move at a height of 10 m? Neglect air resistance. |
1) 7 m/s 2) 10 m/s |
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3) 14.1 m/s 4) 20 m/s |
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The skater, having accelerated, enters an ice mountain inclined at an angle of 30 o to the horizon and drives 10 m until it comes to a complete stop. What was the speed of the skater before the start of the ascent? |
Neglect friction |
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1) 5 m/s 2) 10 m/s |
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3) 20 m/s 4) 40 m/s |
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A projectile weighing 3 kg, fired at an angle of 45 o 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? Neglect air resistance |
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A projectile weighing 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 hits the Earth? Neglect air resistance |
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4) it is impossible to answer the question of the problem, because the initial velocity of the projectile is unknown |
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A body with a mass of 0.1 kg is thrown upward 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 its rise? Assume that the potential energy of a body is zero on the surface of the Earth.
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Which formula can be used to determine kinetic energy? |
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The figure shows the positions of a freely falling ball after a time interval equal to |
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With. The mass of the ball is 100 g. Using the law of conservation of energy, estimate the height from which the ball fell |
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The ball on the string, located in the equilibrium position, was given a small horizontal speed (see figure). How high will the ball rise? |
A ball on a string in equilibrium is given a small horizontal speed of 20 m/s. How high will the ball rise? |
, which the body had at the top point of the trajectory?
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1) 40 m 2) 20 m |
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3) 10 m 4) 5 m |
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The ball is thrown vertically upward. The figure shows a graph of the change in kinetic energy of the ball as it rises above the throwing point. What is the total energy of the ball at a height of 2 m? |
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N |
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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. |
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In this case, the buffer spring is compressed. Which of the following energy transformations occurs in this process? 1) the kinetic energy of the car is converted into potential energy of the spring 2) the kinetic energy of the car is converted into its potential energy |
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3) the potential energy of the spring is converted into its kinetic energy |
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, and the deformation before the shot |
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? |
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Neglect friction and mass of the spring, assuming much less. |
When a spring pistol is fired vertically upward, a ball weighing 100 g rises to a height of 2 m. What is the stiffness of the spring if before the shot the spring was compressed by 5 cm? |
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A weight suspended from a spring stretches it by 2 cm. The student raised the weight up so that the tension of the spring is zero, and then released it from his hands. |
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The maximum stretch 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 it has kinetic energy, which it acquired by reducing |
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4) the internal energy of the spring is converted into kinetic energy of the car 
The attached spring gun fires vertically upward. To what height will the bullet rise if its mass 
, spring stiffness
2)
4)
1) internal energy of water
2) potential energy of the ball
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3) potential energy of water 4) kinetic energy of water 16. Elastic central blow 17. Law of conservation of momentum and law of conservation of energy Are the laws of conservation of mechanical energy and momentum of the system of bodies on which don't work external forces? |
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1) both laws are always satisfied |
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2) the law of conservation of mechanical energy is always satisfied, the law of conservation of momentum may not be satisfied |
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It hits a stationary cart of mass 0.1 kg attached to a spring and sticks to the cart (see figure). What is the total mechanical energy of the system during its further oscillations? Ignore friction. |
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. |
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A plasticine ball weighing 0.1 kg has a speed of 1 m/s.
A block of mass 
slides down an inclined surface from a height of 0.8 m and, moving along a horizontal surface, collides with a stationary block of mass|
Assuming the collision to be completely inelastic, determine the change in kinetic energy of the first block as a result of the collision. Neglect friction during movement. Assume that the inclined plane smoothly turns into a horizontal one. |
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straightaway after the impact? |
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A bullet flying at a horizontal speed of 400 m/s hits a bag filled with foam rubber, weighing 4 kg, hanging on a length of thread. The height to which the bag will rise if a bullet gets stuck in it is 5 cm. What is the mass of the bullet? Express the answer in grams. A piece of plasticine weighing 200 g is thrown upward with an initial speed = 9 m/s. After 0.3 s of free flight, the plasticine meets on its way a block weighing 200 g hanging on a thread (Fig.). What is the kinetic energy of a block with plasticine stuck to it?
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Consider the impact instantaneous, neglect air resistance. A piece of plasticine weighing 200 g is thrown upward with an initial speed = 8 m/s. After 0.4 s of free flight, the plasticine meets on its way a bowl weighing 200 g, mounted on a weightless spring (Fig.). What is the kinetic energy of the bowl along with the plasticine stuck to it immediately after their interaction? Consider the impact instantaneous, neglect air resistance. Express the answer in grams. A piece of sticky putty weighing 100 g is dropped from a height with zero initial velocity N. |
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= 80 cm (Fig.) per bowl weighing 100 g, mounted on a spring. What is the kinetic energy of the bowl along with the putty stuck to it? |
after their interaction? |
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Consider the impact instantaneous, neglect air resistance 1) 0.4 J 2) 0.8 J |
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A piece of plasticine weighing 200 g is thrown upward with an initial speed = 10 m/s. After 0.4 s of free flight, the plasticine meets on its way a block weighing 200 g hanging on a thread. What is the potential energy of the block with the plasticine stuck to it relative to the initial position of the block at the moment of its complete stop? Consider the impact instantaneous, neglect air resistance. |
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The initial speed of a projectile fired vertically upward from a cannon is 10 m/s. At the point of maximum ascent, the projectile exploded into two fragments, the masses of which are in the ratio 1:2. A smaller fragment fell to Earth at a speed of 20 m/s. What is the speed of the larger fragment as it falls to Earth? |
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Assume the Earth's surface is flat and horizontal. |
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The initial speed of a projectile fired vertically upward from a cannon is 10 m/s. At the point of maximum ascent, the projectile exploded into two fragments, the masses of which are in the ratio 2:1. The larger fragment fell to Earth first at a speed of 20 m/s. To what maximum height can a fragment of smaller mass rise? |
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Assume the Earth's surface is flat and horizontal. The initial speed of a projectile fired vertically upward is 160 m/s. At the point of maximum ascent, the projectile exploded into two fragments, the masses of which are in the ratio 1:4. The fragments scattered in vertical directions, with the smaller fragment flying down and falling to the ground at a speed of 200 m/s. Determine the speed that the larger fragment had at the moment it hit the ground. Neglect air resistance. 1
The initial speed of a projectile fired vertically upward is 300 m/s. At the point of maximum ascent, the shell exploded into two fragments. The first fragment weighs The initial speed of a projectile fired vertically upward is 160 m/s. At the point of maximum ascent, the projectile exploded into two fragments, the masses of which are in the ratio 1:4. The fragments scattered in vertical directions, with the smaller fragment flying down and falling to the ground at a speed of 200 m/s. Determine the speed that the larger fragment had at the moment it hit the ground. Neglect air resistance. 2
m |
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fell to the ground near the point of the shot, having a speed 2 times greater than the initial speed of the projectile. The second fragment weighs The initial speed of a projectile fired vertically upward is 160 m/s. At the point of maximum ascent, the projectile exploded into two fragments, the masses of which are in the ratio 1:4. The fragments scattered in vertical directions, with the smaller fragment flying down and falling to the ground at a speed of 200 m/s. Determine the speed that the larger fragment had at the moment it hit the ground. Neglect air resistance. 1
has a speed of 600 m/s at the surface of the earth. What is the mass ratio The initial speed of a projectile fired vertically upward is 160 m/s. At the point of maximum ascent, the projectile exploded into two fragments, the masses of which are in the ratio 1:4. The fragments scattered in vertical directions, with the smaller fragment flying down and falling to the ground at a speed of 200 m/s. Determine the speed that the larger fragment had at the moment it hit the ground. Neglect air resistance. 2
The initial speed of a projectile fired vertically upward is 100 m/s. At the point of maximum ascent, the shell exploded into two fragments. The first fragment weighs |
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rose to a height of 1.5 km. What is the mass ratio The initial speed of a projectile fired vertically upward is 160 m/s. At the point of maximum ascent, the projectile exploded into two fragments, the masses of which are in the ratio 1:4. The fragments scattered in vertical directions, with the smaller fragment flying down and falling to the ground at a speed of 200 m/s. Determine the speed that the larger fragment had at the moment it hit the ground. Neglect air resistance. 1 moving vertically down fell to the ground, having a speed 1.25 times greater than the initial speed of the projectile, and the second fragment weighed The initial speed of a projectile fired vertically upward is 160 m/s. At the point of maximum ascent, the projectile exploded into two fragments, the masses of which are in the ratio 1:4. The fragments scattered in vertical directions, with the smaller fragment flying down and falling to the ground at a speed of 200 m/s. Determine the speed that the larger fragment had at the moment it hit the ground. Neglect air resistance. 2 when touching the surface of the earth, the speed was 1.8 times greater. |
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What is the ratio of the masses of these fragments? Neglect air resistance. |
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The initial speed of a projectile fired vertically upward is 120 m/s. At the point of maximum lift, 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? Neglect air resistance. |
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The initial speed of a projectile fired vertically upward is 200 m/s. At the point of maximum lift, 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 speed of the projectile. To what maximum height did the second fragment rise? |
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Neglect air resistance. |
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The initial speed of a projectile fired vertically upward from a cannon is 10 m/s. At the point of maximum ascent, the projectile exploded into two fragments, the masses of which are in the ratio 1:2. A fragment of smaller mass flew horizontally at a speed of 20 m/s. |
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A block 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 stationary block of mass = 300 g. Assuming the collision to be absolutely inelastic, determine the change in the kinetic energy of the first block as a result of the collision. Neglect friction during movement. Assume that the inclined plane smoothly turns into a horizontal one. |
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Two balls, the masses of which are 200 g and 600 g, hang in contact on identical threads 80 cm long. The first ball is deflected at an angle of 90° and released. To what height will the balls rise after the impact if the impact is absolutely inelastic? |
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fell to the ground near the point of the shot, having a speed 3 times greater than the initial speed of the projectile. The second fragment weighs
At what distance from the point of the shot will the second fragment fall? Assume the Earth's surface is flat and horizontal. 
The initial speed of a projectile fired vertically upward from a cannon is 20 m/s. At the point of maximum ascent, the projectile exploded into two fragments, the masses of which are in the ratio 1:4. A fragment of 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? Assume the Earth's surface is flat and horizontal.18. The law of conservation of energy and Newton’s second law
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A load weighing 100 g is tied to a thread 1 m long. The thread with the load is moved from the vertical to an angle of 90 o. |
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What is the centripetal acceleration of the load at the moment when the thread forms an angle of 60° with the vertical? |
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Pendulum thread length The initial speed of a projectile fired vertically upward is 160 m/s. At the point of maximum ascent, the projectile exploded into two fragments, the masses of which are in the ratio 1:4. The fragments scattered in vertical directions, with the smaller fragment flying down and falling to the ground at a speed of 200 m/s. Determine the speed that the larger fragment had at the moment it hit the ground. Neglect air resistance.
= 1 m from which the mass is suspended= 0.1 kg, deflected at an angle from the vertical position and released.
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The tension force of the thread T at the moment the pendulum passes the equilibrium position is 2 N. What is the angle ? |
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19. Change in mechanical energy and work of external forces |
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A car weighing 1000 kg approaches a rise of 5 m at a speed of 20 m/s. At the end of the rise its speed decreases to 6 m/s. What is the change in mechanical energy of the car?
In the wood of the African baobab, a tree with a height of about 20 m and a trunk reaching 20 m in girth, up to 120 thousand liters of water can accumulate. Baobab wood is very soft and porous; it rots easily, forming hollows. (For example, in Australia, the hollow of one baobab tree with an area of 36 m2 was used as a prison.) The softness of the tree is indicated by the fact that a bullet fired from a rifle easily pierces through the trunk of a baobab tree with a diameter of 10 m. Determine the resistance force of baobab wood if the bullet at the moment of impact it had a speed of 800 m/s and completely lost speed before flying out of the tree. Bullet weight 10 g.
After how many complete oscillations does the ball on the string deflect by 60°? 20. Law of conservation of momentum, change in mechanical energy and work of external forces |
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4) this condition does not allow us to determine the initial speed of the bullet, since the law of conservation of mechanical energy during the interaction of a bullet and a block is not satisfied Small cube of mass 2 kg |
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There is a small block on the board at its left end. Coefficient of sliding friction between a block and a board|
can slide without friction along a cylindrical recess with a radius of 0.5 m. Having started moving from above, it collides with another similar cube resting below. What is the amount of heat released as a result of a completely inelastic collision? |
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2 = 2kg, slide on a smooth horizontal table (see picture). The speed of the first body is v 1 = 3 m/s, the speed of the second body is 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. Neglect 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. |
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D The initial speed of a projectile fired vertically upward is 160 m/s. At the point of maximum ascent, the projectile exploded into two fragments, the masses of which are in the ratio 1:4. The fragments scattered in vertical directions, with the smaller fragment flying down and falling to the ground at a speed of 200 m/s. Determine the speed that the larger fragment had at the moment it hit the ground. Neglect air resistance. wa bodies whose masses are respectively The initial speed of a projectile fired vertically upward is 160 m/s. At the point of maximum ascent, the projectile exploded into two fragments, the masses of which are in the ratio 1:4. The fragments scattered in vertical directions, with the smaller fragment flying down and falling to the ground at a speed of 200 m/s. Determine the speed that the larger fragment had at the moment it hit the ground. Neglect air resistance. 1 = 1 kg and
An ap weighing 1 kg, suspended on a thread 90 cm long, is moved from the equilibrium position to an angle of 60° and released. At the moment the ball passes the equilibrium position, it is hit by a bullet weighing 10 g, 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 deflect after a bullet hits it? (The mass of the ball is assumed to be constant, the diameter of the ball is negligible compared to the length of the thread).|
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. |
An ap weighing 1 kg, suspended on a thread 90 cm long, is removed from its equilibrium position and released. At the moment the ball passes the equilibrium position, it is hit by a bullet weighing 10 g, 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 and deflects at an angle of 39 degrees. Determine the initial deflection angle of the ball.(The mass of the ball is considered unchanged, the diameter of the ball is negligible compared to the length of the thread, cos 39 = equal to the distance traveled body... impact force, if his duration 1 s. b) For how long 100
body mass G will change my
