Work and energy Mechanical work and powerWhat are work and power from the point of view of physics? How to calculate them? What are the similarities and differences between the concepts of “work” and “power” in life and in physics? Simple mechanisms What is “ golden rule» mechanics? Are there “golden rules” in life? What mechanisms are used to make work easier? How to calculate the efficiency? Energy What are the similarities and differences physical concept“mechanical energy” and the common everyday concept of “energy”? What types of mechanical energy are there? What examples of the transformation of one type of energy into another do you know?
Mechanical work and power1. Mechanical work = force times path.
2. Mechanical work can be performed only when the body moves under the influence of a force, and the force must either promote or hinder the movement.
Work is positive when the force is directed in the direction of body motion. Otherwise, the work is negative.
3. Power is the speed at which work is done.
Power shows how much work is done per unit of time.
Simple mechanisms 4. The “golden rule” of mechanics: if, when performing work, they gain several times in strength, then they lose the same number of times in distance.
Mechanisms (lever, gate, inclined plane) are devices that allow you to convert force.
5. Lever – solid having an axis of rotation.
The rule for equilibrium of a lever is as follows: the lever is in equilibrium when the moment of the force rotating it clockwise is equal to the moment of the force rotating the lever counterclockwise.
Arm of force = the distance from the axis of rotation to the straight line along which the force acts.
Moment of force = force multiplied by its arm.
6. A block is a wheel with a groove into which a cable (chain, belt, rope) is passed.
A stationary block only changes the direction of the force, while a movable block still gives a double gain in force.
7. Coefficient of efficiency (efficiency) = ratio of useful work to total work.
When using a mechanism, the total work done is always greater than the useful work. In other words, efficiency is always less than 100%.
Energy 8. Energy is the ability to do work.
The greater the body's energy, the great job it can do. When work is done, the energy of the body decreases.
9. Kinetic energy is the energy of motion of a body or system of bodies.
The greater the mass and the greater the speed of a given body, the greater its kinetic energy.
10. Potential energy is the energy of interaction of bodies (or parts of one body) depending on their relative position.
The potential energy of a body of mass m raised to a height h is equal to the product mgh.
11. Mechanical energy can change from one type to another.
The golden rule of mechanics
On a gate or on a spire, it means that a significant load can be set in motion with a small force. But the speed of this movement in such cases is small - less than the speed with which the force applied to the gate moves.
Consider the last example with a spire: with one full rotation, the end of the pole where the force is applied describes a path of length
2? 3.14? 350 = 2200 cm.
Meanwhile, the shaft will also make one revolution, winding a piece of rope around itself, length
2? 3.14? 21 = 130 cm.
Consequently, the load will be pulled up only 130 cm. The force traveled 2,200 cm, and the load in the same time only 130 cm, i.e. almost 17 times less. If you compare the size of the load (500 kg) with the amount of force applied to the spire (30 kg), then make sure that the same relationship exists between them:
500: 30 = about 17.
You see that the path of the load is as many times less than the path of the force as this force is less than the load. In other words: the number of times one gains in strength, the same number of times one loses in speed.
Rice. 17. Explanation of the golden rule of mechanics
This rule applies not only to a gate or a spire, but also to a lever, and to any machine in general (it has long been called the “golden rule of mechanics”).
Consider, for example, the lever discussed on p. 51. Here the gain in strength is 3 times, but while the long arm of the lever (see Fig. 17) describes a large arc with its end MN, the end of the short arm describes a three times smaller arc OR. Consequently, in this case, the path traversed by the load is 3 times less than the path traversed at the same time by the force - the same number of times as this force is less than the load.
Now you will understand why in some cases it is advantageous to use levers in reverse: applying a large force to the short arm in order to move a small load at the end of the long arm. What is the benefit of doing this? After all, we are losing power here! Of course, but we gain the same amount of times in speed. And when we need greater speed, we buy it at this price. Such levers represent the bones of our hands (Fig. 18): in them the muscle is attached to the short arm of a lever of the 2nd kind and causes the hand to move quickly.
Rice. 18. Our hand is a lever. What kind?
In this case, the loss of strength is rewarded with a gain in speed. We would be extremely slow creatures if the bones of our skeleton were designed like levers, gaining strength and therefore losing speed.
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When people began to use blocks, levers, and gates, they discovered that the movements made during the operation of simple mechanisms turned out to be associated with the forces developed by these mechanisms.
This rule in ancient times was formulated as follows: what we gain in strength, we lose in the way. This provision is general, but very important, and is called the golden rule of mechanics.
Let's balance the lever using two different magnitude forces. On the shoulder l 1 force acts F 1 , on the shoulder l 2 force acts F 2 , under the influence of these forces the lever is in equilibrium. Then we set the lever in motion. At the same time, the point of application of force F 1 will pass the path S 1, and the point of application of the force F 2 will pass the path S 2 (Fig. 1).
Rice. 1
If we measure the modules of these forces and the paths traversed by the points of application of the forces, we obtain the equality: .
From this equality we see how many times the forces applied to the lever differ, and how many times the paths taken by the points of application of the force will differ in inverse proportion to the same number of times.
Using the properties of proportion, we transform this expression into another form: 
- the product of force F 1 by path S 1 is equal to the product of force F 2 by path S 2. The product of force by path is called work, in this case the work is equal to A 1 = A 2. The lever does not provide any benefit in work; the same conclusion can be drawn about any other simple mechanism.
The golden rule of mechanics: no mechanism gives a gain in operation. While we gain in strength, we lose in transit and vice versa.
Let's consider a stationary block. Let's fix the block in the axis and attach two weights to the ropes of the block, then move one weight down, the weight moved downwards has traveled a distance S, and the load that has moved upwards has traveled the same distance S.
The forces are equal, the paths traveled by the bodies are also equal, this means that the work is also equal, and a stationary block does not provide a gain in work.
Let's consider a moving block. Let's fasten one end of the rope, pass it through a moving block and attach the second end to the dynamometer, and hang weights from the block. Let's mark the position of the weights on the tripod, raise the weights to a distance S 1, also mark and return them to their original position, now mark the position of the dynamometer hook on the tripod. Again we lift the loads to a distance S 1 and mark the position of the dynamometer hook in this case (Fig. 2).
Rice. 2
To lift the load to a height S 1, it was necessary to extend the rope almost twice as far as the distance traveled by the load. The movable block gives a gain in strength, but does not give in work, the number of times we gain in strength, the number of times we lose along the way.
Condition. Using a movable block, the loader raised the toolbox to a height of S 1 = 7 m, applying a force F 2 = 160 N. What work did the loader A 2 do?
In order to find a job, you need the following: .
S 2 - the amount of movement of the rope.
The number of times we win in strength, the number of times we lose along the way, therefore, then.
Answer: the work done by the loader is 2.24 kJ.
Centuries-old practice proves that not a single simple mechanism gives a gain in work; it is possible, while winning in strength, to lose along the way and vice versa - depending on the conditions of the problem that needs to be solved.
- Lukashik V.I., Ivanova E.V. Collection of problems in physics for grades 7-9 of general education institutions. - 17th ed. - M.: Education, 2004.
- Peryshkin A.V. Physics. 7th grade - 14th ed., stereotype. - M.: Bustard, 2010.
- Peryshkin A.V. Collection of problems in physics, grades 7-9: 5th ed., stereotype. - M: Publishing House “Exam”, 2010.
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Homework
- Why are simple mechanisms used if they do not provide benefits in work?
- Using a lever, a load weighing 200 kg was lifted. To what height was the load raised if the force acting on the long arm of the lever did 400 J of work?
- Using a moving block, the load was raised 3 m. How far did you have to stretch the free end of the rope?
Do you know what a block is? This is a round thing with a hook that is used to lift loads to heights on construction sites.
Does it look like a lever? Hardly. However, the block is also a simple mechanism. Moreover, we can talk about the applicability of the law of equilibrium of the lever to the block. How is this possible? Let's figure it out.
Application of the law of equilibrium
The block is a device that consists of a wheel with a groove through which a cable, rope or chain is passed, as well as a clip with a hook attached to the wheel axle. The block can be fixed or movable. A fixed block has a fixed axis and does not move when lifting or lowering a load. The stationary block helps change the direction of the force. By throwing a rope over such a block, suspended at the top, we can lift the load upward, while ourselves being below. However, using a fixed block does not give us any gain in strength. We can imagine a block in the form of a lever rotating around a fixed support - the axis of the block. Then the radius of the block will be equal to the arms applied on both sides of the forces - the traction force of our rope with a load on one side and the gravitational force of the load on the other. The shoulders will be equal, so there is no gain in strength.
The situation is different with a moving block. The moving block moves along with the load, as if it were lying on a rope. In this case, the fulcrum at each moment of time will be at the point of contact of the block with the rope on one side, the impact of the load will be applied to the center of the block, where it is attached to the axis, and the traction force will be applied at the point of contact with the rope on the other side of the block . That is, the shoulder of the body weight will be the radius of the block, and the shoulder of the force of our thrust will be the diameter. The diameter, as is known, is twice the radius; accordingly, the arms differ in length by two times, and the gain in strength obtained with the help of a movable block is equal to two. In practice, a combination of a fixed block and a movable one is used. A fixed block attached at the top does not provide any gain in strength, but it does help lift the load while standing at the bottom. And the moving block, moving along with the load, doubles the applied force, helping to lift large loads to a height.
The golden rule of mechanics
The question arises: do the devices used provide benefits in operation? Work is the product of the distance traveled and the force applied. Consider a lever with arms that differ by a factor of two in arm length. This lever will give us a gain in strength of two times, however, twice as much leverage will travel twice as far. That is, despite the gain in strength, the work done will be the same. This is the equality of work when using simple mechanisms: the number of times we gain in strength, the number of times we lose in distance. This rule is called the golden rule of mechanics, and it applies to absolutely all simple mechanisms. Therefore, simple mechanisms make a person’s work easier, but do not reduce the work he does. They simply help translate one type of effort into another, more convenient in a particular situation.
