To be able to characterize energy characteristics movement, the concept was introduced mechanical work. And it is to her in her different manifestations the article is devoted to. The topic is both easy and quite difficult to understand. The author sincerely tried to make it more understandable and accessible to understanding, and one can only hope that the goal has been achieved.
What is mechanical work called?
What is it called? If some force works on a body, and as a result of its action the body moves, then this is called mechanical work. When approached from the point of view scientific philosophy here several additional aspects can be highlighted, but the article will cover the topic from the point of view of physics. Mechanical work is not difficult if you think carefully about the words written here. But the word “mechanical” is usually not written, and everything is shortened to the word “work.” But not every job is mechanical. Here is a man sitting and thinking. Does it work? Mentally yes! But is this mechanical work? No. What if a person walks? If a body moves under the influence of force, then this is mechanical work. It's simple. In other words, a force acting on a body does (mechanical) work. And one more thing: it is work that can characterize the result of the action of a certain force. So if a person walks, then certain forces (friction, gravity, etc.) perform mechanical work on a person, and as a result of their action, the person changes his point of location, in other words, moves.
Work how physical quantity equals the force that acts on the body, multiplied by the path that the body has made under the influence of this force and in the direction indicated by it. We can say that mechanical work was done if 2 conditions were simultaneously met: a force acted on the body, and it moved in the direction of its action. But it did not occur or does not occur if the force acted and the body did not change its location in the coordinate system. Here are small examples when mechanical work is not performed:
- So a person can lean on a huge boulder in order to move it, but there is not enough strength. The force acts on the stone, but it does not move, and no work occurs.
- The body moves in the coordinate system, and the force is equal to zero or they have all been compensated. This can be observed while moving by inertia.
- When the direction in which a body moves is perpendicular to the action of the force. When the train moves along horizontal line, then gravity does not do its work.
Depending on certain conditions, mechanical work can be negative and positive. So, if the directions of both the forces and the movements of the body are the same, then positive work occurs. An example of positive work is the effect of gravity on a falling drop of water. But if the force and direction of movement are opposite, then negative mechanical work occurs. An example of such an option is a balloon rising upward and the force of gravity, which makes negative work. When a body is subject to the influence of several forces, such work is called “resultant force work.”
Features of practical application (kinetic energy)
Let's move from theory to practical part. We should talk separately about mechanical work and its use in physics. As many probably remember, all the energy of the body is divided into kinetic and potential. When an object is in equilibrium and not moving anywhere, its potential energy is equal to total energy, and the kinetic one is equal to zero. When the movement starts potential energy begins to decrease, the kinetic one begins to increase, but in total they are equal to the total energy of the object. For material point kinetic energy is defined as the work of a force that accelerates a point from zero to the value H, and in formula form the kinetics of a body is equal to ½*M*N, where M is mass. To find out the kinetic energy of an object that consists of many particles, you need to find the sum of all kinetic energy particles and it will be kinetic energy bodies.
Features of practical application (potential energy)
In the case when all the forces acting on the body are conservative, and the potential energy is equal to the total, then no work is done. This postulate is known as the law of conservation of mechanical energy. Mechanical energy V closed system is constant in the time interval. The conservation law is widely used to solve problems from classical mechanics.
Features of practical application (thermodynamics)
In thermodynamics, the work done by a gas during expansion is calculated by the integral of pressure times volume. This approach is applicable not only in cases where there is an exact volume function, but also to all processes that can be displayed in the pressure/volume plane. It also applies knowledge of mechanical work not only to gases, but to anything that can exert pressure.
Features of practical application in practice (theoretical mechanics)
In theoretical mechanics, all the properties and formulas described above are considered in more detail, in particular projections. She also gives her own definition for various formulas mechanical work (an example of a definition for the Rimmer integral): the limit to which the sum of all forces tends basic work, when the fineness of the partition tends to zero, is called the work of force along the curve. Probably difficult? But nothing, s theoretical mechanics All. Yes, all the mechanical work, physics and other difficulties are over. Further there will be only examples and a conclusion.
Units of measurement of mechanical work
The SI uses joules to measure work, while the GHS uses erg:
- 1 J = 1 kg m²/s² = 1 N m
- 1 erg = 1 g cm²/s² = 1 dyne cm
- 1 erg = 10 −7 J
Examples of mechanical work
In order to finally understand such a concept as mechanical work, you should study several individual examples that will allow you to consider it from many, but not all, sides:
- When a person lifts a stone with his hands, mechanical work occurs with the help of the muscular strength of his hands;
- When a train travels along the rails, it is pulled by the traction force of the tractor (electric locomotive, diesel locomotive, etc.);
- If you take a gun and fire from it, then thanks to the pressure force created by the powder gases, work will be done: the bullet is moved along the barrel of the gun at the same time as the speed of the bullet itself increases;
- Mechanical work also exists when the friction force acts on a body, forcing it to reduce the speed of its movement;
- The above example with balls, when they rise into the opposite side relative to the direction of gravity, is also an example of mechanical work, but in addition to gravity, the Archimedes force also acts when everything that is lighter than air rises upward.
What is power?
Finally, I would like to touch on the topic of power. The work done by a force in one unit of time is called power. In fact, power is a physical quantity that is a reflection of the ratio of work to a certain period of time during which this work was done: M=P/B, where M is power, P is work, B is time. The SI unit of power is 1 W. A watt is equal to the power that does one joule of work in one second: 1 W=1J\1s.
You are already familiar with mechanical work (work of force) from the basic school physics course. Let us recall the definition of mechanical work given there for the following cases.
If the force is directed in the same direction as the movement of the body, then the work done by the force
In this case, the work done by the force is positive.
If the force is directed opposite to the movement of the body, then the work done by the force
In this case, the work done by the force is negative.
If the force f_vec is directed perpendicular to the displacement s_vec of the body, then the work done by the force is zero:
Job - scalar quantity. The unit of work is called the joule (symbol: J) in honor of the English scientist James Joule, who played important role in the discovery of the law of conservation of energy. From formula (1) it follows:
1 J = 1 N * m.
1. A block weighing 0.5 kg was moved along the table 2 m, applying an elastic force of 4 N to it (Fig. 28.1). The coefficient of friction between the block and the table is 0.2. What is the work acting on the block?
a) gravity m?
b) normal reaction forces?
c) elastic forces?
d) sliding friction forces tr?
The total work done by several forces acting on a body can be found in two ways:
1. Find the work of each force and add up these works, taking into account the signs.
2. Find the resultant of all forces applied to the body and calculate the work of the resultant.
Both methods lead to the same result. To make sure of this, go back to the previous task and answer the questions in task 2.
2. What is it equal to:
a) the sum of the work done by all forces acting on the block?
b) the resultant of all forces acting on the block?
c) work resultant? IN general case(when the force f_vec is directed under arbitrary angle to the displacement s_vec) the definition of the work of force is as follows.
Job A constant force is equal to the product of the force modulus F by the displacement modulus s and the cosine of the angle α between the direction of force and the direction of displacement:
A = Fs cos α (4)
3. Show what general definition The work follows to the conclusions shown in the following diagram. Formulate them verbally and write them down in your notebook.
4. A force is applied to a block located on the table, the modulus of which is 10 N. Why angle is equal between this force and the movement of the block, if when moving the block along the table by 60 cm, this force did the work: a) 3 J; b) –3 J; c) –3 J; d) –6 J? Make explanatory drawings.
2. Work of gravity
Let a body of mass m move vertically from the initial height h n to the final height h k.
If the body moves downwards (h n > h k, Fig. 28.2, a), the direction of movement coincides with the direction of gravity, therefore the work of gravity is positive. If the body moves upward (h n< h к, рис. 28.2, б), то работа силы тяжести отрицательна.
In both cases, the work done by gravity
A = mg(h n – h k). (5)
Let us now find the work done by gravity when moving at an angle to the vertical.
5. A small block of mass m slid along an inclined plane of length s and height h (Fig. 28.3). The inclined plane makes an angle α with the vertical.
a) What is the angle between the direction of gravity and the direction of movement of the block? Make an explanatory drawing.
b) Express the work of gravity in terms of m, g, s, α.
c) Express s in terms of h and α.
d) Express the work of gravity in terms of m, g, h.
e) What is the work done by gravity when the block moves upward along the entire same plane?
Having completed this task, you are convinced that the work of gravity is expressed by formula (5) even when the body moves at an angle to the vertical - both down and up.
But then formula (5) for the work of gravity is valid when a body moves along any trajectory, because any trajectory (Fig. 28.4, a) can be represented as a set of small “ inclined planes"(Fig. 28.4, b). 
Thus,
the work done by gravity when moving along any trajectory is expressed by the formula
A t = mg(h n – h k),
where h n is the initial height of the body, h k is its final height.
The work done by gravity does not depend on the shape of the trajectory.
For example, the work of gravity when moving a body from point A to point B (Fig. 28.5) along trajectory 1, 2 or 3 is the same. From here, in particular, it follows that the force of gravity when moving along a closed trajectory (when the body returns to the starting point) is equal to zero. 
6. A ball of mass m hanging on a thread of length l was deflected 90º, keeping the thread taut, and released without a push.
a) What is the work done by gravity during the time during which the ball moves to the equilibrium position (Fig. 28.6)?
b) What is the work done by the elastic force of the thread during the same time?
c) What is the work done by the resultant forces applied to the ball during the same time?
3. Work of elastic force
When the spring returns to an undeformed state, the elastic force always does positive work: its direction coincides with the direction of movement (Fig. 28.7). 
Let's find the work done by the elastic force.
The modulus of this force is related to the modulus of deformation x by the relation (see § 15)
The work done by such a force can be found graphically.
Let us first note that the work done by a constant force is numerically equal to the area of the rectangle under the graph of force versus displacement (Fig. 28.8). 
Figure 28.9 shows a graph of F(x) for the elastic force. Let us mentally divide the entire movement of the body into such small intervals that the force at each of them can be considered constant. 
Then the work on each of these intervals is numerically equal to the area of the figure under the corresponding section of the graph. All work is equal to the sum of work in these areas.
Consequently, in this case, the work is numerically equal to the area of the figure under the graph of the dependence F(x). 
7. Using Figure 28.10, prove that
the work done by the elastic force when the spring returns to its undeformed state is expressed by the formula
A = (kx 2)/2. (7)
8. Using the graph in Figure 28.11, prove that when the spring deformation changes from x n to x k, the work of the elastic force is expressed by the formula
From formula (8) we see that the work of the elastic force depends only on the initial and final deformation of the spring. Therefore, if the body is first deformed and then returns to its initial state, then the work of the elastic force is zero. Let us recall that the work of gravity has the same property.
9. B starting moment the stretch of a spring with a stiffness of 400 N/m is 3 cm. The spring is stretched by another 2 cm.
a) What is the final deformation of the spring?
b) What is the work done by the elastic force of the spring?
10. At the initial moment, a spring with a stiffness of 200 N/m is stretched by 2 cm, and at the final moment it is compressed by 1 cm. What is the work done by the elastic force of the spring?
4. Work of friction force
Let the body slide along a fixed support. The sliding friction force acting on the body is always directed opposite to the movement and, therefore, the work of the sliding friction force is negative in any direction of movement (Fig. 28.12). 
Therefore, if you move the block to the right, and the peg the same distance to the left, then, although it will return to starting position, the total work done by the sliding friction force will not be equal to zero. This is the most important difference the work of the sliding friction force from the work of gravity and elasticity. Let us recall that the work done by these forces when moving a body along a closed trajectory is zero.
11. A block with a mass of 1 kg was moved along the table so that its trajectory turned out to be a square with a side of 50 cm.
a) Has the block returned to its starting point?
b) What is the total work done by the frictional force acting on the block? The coefficient of friction between the block and the table is 0.3.
5.Power
Often it is not only the work being done that is important, but also the speed at which the work is being done. It is characterized by power.
The power P is the ratio perfect work A to the time period t during which this work was completed:
(Sometimes power in mechanics is denoted by the letter N, and in electrodynamics by the letter P. We find it more convenient to use the same designation for power.)
The unit of power is the watt (symbol: W), named after the English inventor James Watt. From formula (9) it follows that
1 W = 1 J/s.
12. What power does a person develop by uniformly lifting a bucket of water weighing 10 kg to a height of 1 m for 2 s?
It is often convenient to express power not through work and time, but through force and speed.
Let's consider the case when the force is directed along the displacement. Then the work done by the force A = Fs. Substituting this expression into formula (9) for power, we obtain:
P = (Fs)/t = F(s/t) = Fv. (10)
13. A car is traveling on a horizontal road at a speed of 72 km/h. At the same time, its engine develops a power of 20 kW. What is the force of resistance to the movement of the car?
Clue. When a car is moving on a horizontal road with constant speed, the traction force is equal in magnitude to the resistance force to the movement of the car.
14. How long will it take to uniformly lift a concrete block weighing 4 tons to a height of 30 m if the power of the crane motor is 20 kW and the efficiency of the electric motor of the crane is 75%?
Clue. Electric motor efficiency equal to the ratio work on lifting loads for engine operation. 
Additional questions and tasks
15. A ball with a mass of 200 g was thrown from a balcony with a height of 10 and an angle of 45º to the horizontal. Reaching in flight maximum height 15 m, the ball fell to the ground.
a) What is the work done by gravity when lifting the ball?
b) What is the work done by gravity when the ball is lowered?
c) What is the work done by gravity during the entire flight of the ball?
d) Is there any extra data in the condition?
16. A ball with a mass of 0.5 kg is suspended from a spring with a stiffness of 250 N/m and is in equilibrium. The ball is raised so that the spring becomes undeformed and released without a push.
a) To what height was the ball raised?
b) What is the work done by gravity during the time during which the ball moves to the equilibrium position?
c) What is the work done by the elastic force during the time during which the ball moves to the equilibrium position?
d) What is the work done by the resultant of all forces applied to the ball during the time during which the ball moves to the equilibrium position?
17. A sled weighing 10 kg slides down without initial speed with snowy mountain with an inclination angle α = 30º and travel a certain distance along horizontal surface(Fig. 28.13). The coefficient of friction between the sled and snow is 0.1. The length of the base of the mountain is l = 15 m. 
a) What modulus is equal frictional forces when the sled moves on a horizontal surface?
b) What is the work done by the friction force when the sled moves along a horizontal surface over a distance of 20 m?
c) What is the magnitude of the friction force when the sled moves along the mountain?
d) What is the work done by the friction force when lowering the sled?
e) What is the work done by gravity when lowering the sled?
f) What is the work done by the resultant forces acting on the sled as it descends from the mountain?
18. A car weighing 1 ton moves at a speed of 50 km/h. The engine develops a power of 10 kW. Gasoline consumption is 8 liters per 100 km. The density of gasoline is 750 kg/m 3, and its specific heat combustion 45 MJ/kg. What is the efficiency of the engine? Is there any extra data in the condition?
Clue. The efficiency of a heat engine is equal to the ratio of the work performed by the engine to the amount of heat released during fuel combustion.
