The efficiency ratio shows the ratio of the useful work that is performed by a mechanism or device to the expended. Often, work expended is taken as the amount of energy that a device consumes in order to perform work.
You will need
- - automobile;
- - thermometer;
- - calculator.
Instruction
- In order to calculate the ratio useful actions(efficiency) divide the useful work Ap by the work expended Az, and multiply the result by 100% (efficiency = Ap/Az∙100%). Get the result as a percentage.
- When calculating the efficiency of a heat engine, consider the mechanical work performed by the mechanism as useful work. For the work expended, take the amount of heat released by the burnt fuel, which is the source of energy for the engine.
- Example. The average traction force of a car engine is 882 N. It consumes 7 kg of gasoline per 100 km. Determine the efficiency of its engine. Find a useful job first. It is equal to the product of the force F by the distance S, overcome by the body under its influence Ап=F∙S. Determine the amount of heat that will be released when burning 7 kg of gasoline, this will be the expended work Аз=Q=q∙m, where q is the specific heat of combustion of the fuel, for gasoline it is 42∙10^6 J/kg, and m is the mass this fuel. Engine efficiency will be equal to efficiency=(F∙S)/(q∙m)∙100%= (882∙100000)/(42∙10^6∙7)∙100%=30%.
- In general, to find the efficiency of any heat engine (internal combustion engine, steam engine, turbine, etc.), where the work is done by gas, has a coefficient useful actions equal to the difference in the heat given off by the heater Q1 and received by the refrigerator Q2, find the difference in the heat of the heater and the refrigerator, and divide by the heat of the heater Efficiency = (Q1-Q2)/Q1. Here, the efficiency is measured in submultiples from 0 to 1, to convert the result into a percentage, multiply it by 100.
- To obtain the efficiency of an ideal heat engine (Carnot engine), find the ratio of the temperature difference between the heater T1 and cooler T2 to the temperature of the heater COP=(T1-T2)/T1. This is the maximum possible efficiency for a specific type of heat engine with given temperatures of the heater and refrigerator.
- For an electric motor, find the work expended as the product of power and the time it is performed. For example, if a crane electric motor with a power of 3.2 kW lifts a load of 800 kg to a height of 3.6 m in 10 s, then its efficiency is equal to the ratio of useful work Ap=m∙g∙h, where m is the mass of the load, g≈10 m / s² free fall acceleration, h - the height to which the load was lifted, and the expended work Az \u003d P∙t, where P is the engine power, t is the time of its operation. Get the formula for determining efficiency = Ap / Az ∙ 100% = (m ∙ g ∙ h) / (Р ∙ t) ∙ 100% =% = (800 ∙ 10 ∙ 3.6) / (3200 ∙ 10) ∙ 100% =90%.
What is the formula for useful work?
Using this or that mechanism, we do work, which always exceeds that which is necessary to achieve the goal. In accordance with this, a distinction is made between the total or expended work Az and the useful work An. If, for example, our goal is to lift a load of mass m to a height H, then useful work is that which is due only to overcoming the force of gravity acting on the load. With a uniform lifting of the load, when the force applied by us is equal to the force of gravity of the load, this work can be found as follows:
An =FH= mgH
Useful work is always only a part of the total work that a person does using a mechanism.
The physical quantity showing what proportion of useful work is from all the work expended is called the efficiency of the mechanism.
What is work in physics definition formula. nn
Help decipher the physics formula
Efficiency of heat engines. physics (formulas, definitions, examples) write! physics (formulas, definitions, examples) write!
The energy characteristics of motion are introduced on the basis of the concept of mechanical work or the work of a force.
Definition 1Work A performed by a constant force F → is a physical quantity equal to the product of the modules of force and displacement, multiplied by the cosine of the angle α located between force vectors F → and displacement s → .
This definition is discussed in Figure 1 . 18 . 1 .
The work formula is written as,
A = F s cos α .
Work is a scalar quantity. This makes it possible to be positive at (0 ° ≤ α< 90 °) , отрицательной при (90 ° < α ≤ 180 °) . Когда задается прямой угол α , тогда совершаемая сила равняется нулю. Единицы измерения работы по системе СИ - джоули (Д ж) .
A joule is equal to the work done by a force of 1 N to move 1 m in the direction of the force.
Picture 1 . 18 . 1 . Work force F → : A = F s cos α = F s s
When projecting F s → force F → onto the direction of movement s → the force does not remain constant, and the calculation of work for small displacements Δ s i summed up and produced according to the formula:
A = ∑ ∆ A i = ∑ F s i ∆ s i .
This amount of work is calculated from the limit (Δ s i → 0), after which it goes into the integral.
The graphic image of the work is determined from the area of the curvilinear figure located under the graph F s (x) of Figure 1. 18 . 2.
Picture 1 . 18 . 2. Graphic definition of work Δ A i = F s i Δ s i .
An example of a coordinate-dependent force is the elastic force of a spring, which obeys Hooke's law. To stretch the spring, it is necessary to apply a force F → , the modulus of which is proportional to the elongation of the spring. This can be seen in Figure 1. 18 . 3 .
Picture 1 . 18 . 3 . Stretched spring. The direction of the external force F → coincides with the direction of displacement s → . F s = k x , where k is the stiffness of the spring.
F → y p p = - F →
The dependence of the module of the external force on the coordinates x can be shown on the graph using a straight line.
Picture 1 . 18 . 4 . Dependence of the external force module on the coordinate when the spring is stretched.
From the above figure, it is possible to find work on the external force of the right free end of the spring, using the area of the triangle. The formula will take the form
This formula is applicable to express the work done by an external force when a spring is compressed. Both cases show that the elastic force F → y p p is equal to the work of the external force F → , but with the opposite sign.
Definition 2
If several forces act on the body, then the formula for the total work will look like the sum of all the work done on it. When the body moves forward, the points of application of forces move in the same way, that is, the total work of all forces will be equal to the work of the resultant of the applied forces.
Picture 1 . 18 . 5 . model of mechanical work.
Determination of power
Definition 3Power is the work done by a force per unit of time.
The record of the physical quantity of power, denoted by N, takes the form of the ratio of work A to the time interval t of the work performed, that is:
Definition 4
The SI system uses the watt (Wt) as the unit of power, which is equal to the power of a force that does work of 1 J in 1 s.
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Almost everyone, without hesitation, will answer: in the second. And they will be wrong. The case is just the opposite. In physics, mechanical work is described the following definitions: mechanical work is done when a force acts on a body and it moves. Mechanical work is directly proportional to the applied force and the distance traveled.
Mechanical work formula
The mechanical work is determined by the formula:
where A is work, F is force, s is the distance traveled.
POTENTIAL(potential function), a concept that characterizes a wide class of physical force fields (electric, gravitational, etc.) and, in general, fields of physical quantities represented by vectors (fluid velocity field, etc.). In the general case, the potential of the vector field a( x,y,z) is such a scalar function u(x,y,z) that a=grad
35. Conductors in an electric field. Electrical capacity.conductors in an electric field. Conductors are substances characterized by the presence in them of a large number of free charge carriers that can move under the influence of an electric field. Conductors include metals, electrolytes, coal. In metals, the carriers of free charges are the electrons of the outer shells of atoms, which, when atoms interact, completely lose their bonds with “their” atoms and become the property of the entire conductor as a whole. Free electrons participate in thermal motion like gas molecules and can move through the metal in any direction. Electric capacity- a characteristic of a conductor, a measure of its ability to accumulate an electric charge. In the theory of electrical circuits, capacitance is the mutual capacitance between two conductors; parameter of the capacitive element of the electrical circuit, presented in the form of a two-terminal network. Such capacitance is defined as the ratio of the magnitude of the electric charge to the potential difference between these conductors
36. Capacitance of a flat capacitor.
Capacitance of a flat capacitor.
That. the capacitance of a flat capacitor depends only on its size, shape and dielectric constant. To create a high-capacity capacitor, it is necessary to increase the area of the plates and reduce the thickness of the dielectric layer.
37. Magnetic interaction of currents in vacuum. Ampere's law.Ampere's law. In 1820, Ampère (a French scientist (1775-1836)) established experimentally a law by which one can calculate force acting on a conductor element of length with current.
where is the vector of magnetic induction, is the vector of the length element of the conductor drawn in the direction of the current.
Force modulus , where is the angle between the direction of the current in the conductor and the direction of the magnetic field. For a straight conductor with current in a uniform field
The direction of the acting force can be determined using left hand rules:
If the palm of the left hand is positioned so that the normal (to the current) component of the magnetic field enters the palm, and four outstretched fingers are directed along the current, then the thumb will indicate the direction in which the Ampère force acts.
38. Magnetic field strength. Biot-Savart-Laplace lawMagnetic field strength(standard designation H ) - vector physical quantity, equal to the difference of the vector magnetic induction B And magnetization vector J .
IN International System of Units (SI): 
Where- magnetic constant.
BSL law. The law that determines the magnetic field of an individual current element 
39. Applications of the Biot-Savart-Laplace law. For direct current field
For a circular loop.
And for the solenoid
40. Magnetic field induction The magnetic field is characterized by a vector quantity, which is called the magnetic field induction (a vector quantity, which is the force characteristic of the magnetic field at a given point in space). MI. (B) this is not a force acting on conductors, it is a quantity that is found through a given force according to the following formula: B \u003d F / (I * l) (Verbally: MI vector modulus. (B) is equal to the ratio of the modulus of force F, with which the magnetic field acts on a current-carrying conductor located perpendicular to the magnetic lines, to the current strength in the conductor I and the length of the conductor l. Magnetic induction depends only on the magnetic field. In this regard, induction can be considered a quantitative characteristic of the magnetic field. It determines with what force (Lorentz Force) the magnetic field acts on a charge moving with speed. 
MI is measured in Tesla (1 T). In this case, 1 Tl \u003d 1 N / (A * m). MI has direction. Graphically, it can be drawn as lines. In a uniform magnetic field, the MIs are parallel, and the MI vector will be directed in the same way at all points. In the case of a non-uniform magnetic field, for example, a field around a conductor with current, the magnetic induction vector will change at each point in space around the conductor, and tangents to this vector will create concentric circles around the conductor.
41. Motion of a particle in a magnetic field. Lorentz force. a) - If a particle flies into a region of a uniform magnetic field, and the vector V is perpendicular to the vector B, then it moves along a circle of radius R=mV/qB, since the Lorentz force Fl=mV^2/R plays the role of a centripetal force. The period of revolution is T=2piR/V=2pim/qB and it does not depend on the speed of the particle (This is true only for V<<скорости света) - Если угол между векторами V и B не равен 0 и 90 градусов, то частица в однородном магнитном поле движется по винтовой линии. - Если вектор V параллелен B, то частица движется по прямой линии (Fл=0). б) Силу, действующую со стороны магнитного поля на движущиеся в нем заряды, называют силой Лоренца.
The L. force is determined by the relation: Fl = q V B sina (q is the magnitude of the moving charge; V is the modulus of its velocity; B is the modulus of the magnetic field induction vector; alpha is the angle between the vector V and the vector B) The Lorentz force is perpendicular to the velocity and therefore it does not do work, does not change the modulus of the speed of the charge and its kinetic energy. But the direction of the speed changes continuously. The Lorentz force is perpendicular to the vectors B and v, and its direction is determined using the same rule of the left hand as the direction of the Ampère force: if the left hand is positioned so that the magnetic induction component B, perpendicular to the charge velocity, enters the palm, and four fingers are are directed along the movement of a positive charge (against the movement of a negative one), then the thumb bent 90 degrees will show the direction of the Lorentz force acting on the charge F l. 
Every body that moves can be described as work. In other words, it characterizes the action of forces.
Work is defined as:
The product of the modulus of force and the path traveled by the body, multiplied by the cosine of the angle between the direction of force and motion.
Work is measured in Joules:
1 [J] = = [kg* m2/s2]
For example, body A, under the influence of a force of 5 N, has passed 10 m. Determine the work done by the body.
Since the direction of movement and the action of the force are the same, the angle between the force vector and the displacement vector will be 0°. The formula is simplified because the cosine of an angle at 0° is 1.
Substituting the initial parameters into the formula, we find:
A= 15 J.
Consider another example, a body with a mass of 2 kg, moving with an acceleration of 6 m / s2, passed 10 m. Determine the work done by the body if it moved upward along an inclined plane at an angle of 60 °.
To begin with, we calculate what force must be applied to inform the body of an acceleration of 6 m / s2.
F = 2 kg * 6 m/s2 = 12 H.
Under the action of a force of 12H, the body traveled 10 m. The work can be calculated using the already known formula:
Where, a is equal to 30 °. Substituting the initial data into the formula, we get:
A= 103.2 J.
Power
Many machines of mechanisms perform the same work for a different period of time. To compare them, the concept of power is introduced.
Power is a value that shows the amount of work done per unit of time.
Power is measured in watts, after the Scottish engineer James Watt.
1 [Watt] = 1 [J/s].
For example, a large crane lifted a load weighing 10 tons to a height of 30 m in 1 minute. A small crane lifted 2 tons of bricks to the same height in 1 minute. Compare crane capacities.
Define the work performed by cranes. The load rises by 30m, while overcoming the force of gravity, so the force expended on lifting the load will be equal to the force of interaction between the Earth and the load (F = m * g). And work is the product of forces and the distance traveled by the goods, that is, the height.
For a large crane A1 = 10,000 kg * 30 m * 10 m / s2 = 3,000,000 J, and for a small crane A2 = 2,000 kg * 30 m * 10 m / s2 = 600,000 J.
Power can be calculated by dividing work by time. Both cranes lifted the load in 1 min (60 sec).
From here:
N1 = 3,000,000 J/60 s = 50,000 W = 50 kW.
N2 = 600,000 J / 60 s = 10,000 W = 10 kW.
From the above data, it is clearly seen that the first crane is 5 times more powerful than the second.
1. Mechanical work \ (A \) - a physical quantity equal to the product of the force vector acting on the body and its displacement vector:\(A=\vec(F)\vec(S) \) . Work is a scalar quantity, characterized by a numerical value and a unit.
The unit of work is 1 joule (1 J). This is the work done by a force of 1 N on a path of 1 m.
\[ [\,A\,]=[\,F\,][\,S\,]; [\,A\,]=1N\cdot1m=1J \]
2. If the force acting on the body makes a certain angle \(\alpha \) with the displacement, then the projection of the force \(F \) onto the X axis is \(F_x \) (Fig. 42).
Since \(F_x=F\cdot\cos\alpha \) , then \(A=FS\cos\alpha \) .
Thus, the work of a constant force is equal to the product of the modules of the force and displacement vectors and the cosine of the angle between these vectors.
3. If the force \(F \) = 0 or the displacement \(S \) = 0, then the mechanical work is zero \(A \) = 0. The work is zero if the force vector is perpendicular to the displacement vector, t .e. \(\cos90^\circ \) \u003d 0. So, the work of the force that imparts centripetal acceleration to the body during its uniform motion along a circle is equal to zero, since this force is perpendicular to the direction of motion of the body at any point of the trajectory.
4. The work done by a force can be either positive or negative. The work is positive \(A \) > 0 if the angle is 90° > \(\alpha \) ≥ 0°; if the angle is 180° > \(\alpha \) ≥ 90°, then the work is negative \(A \) < 0.
If the angle \(\alpha \) = 0°, then \(\cos\alpha \) = 1, \(A=FS \) . If the angle \(\alpha \) = 180°, then \(\cos\alpha \) = -1, \(A=-FS \) .
5. In free fall from a height \\ (h \) a body of mass \\ (m \) moves from position 1 to position 2 (Fig. 43). In this case, the force of gravity does work equal to:
\[ A=F_th=mg(h_1-h_2)=mgh \]
When a body moves vertically downwards, the force and displacement are directed in the same direction, and gravity does positive work.
If the body rises, then the force of gravity is directed downwards, and moving upwards, then the force of gravity does negative work, i.e.
\[ A=-F_th=-mg(h_1-h_2)=-mgh \]
6.
Work can be represented graphically. The figure shows a graph of the dependence of gravity on the height of the body relative to the surface of the Earth (Fig. 44). Graphically, the work of gravity is equal to the area of \u200b\u200bthe figure (rectangle) bounded by the graph, the coordinate axes and the perpendicular raised to the abscissa axis
at the point \(h \) .
The graph of the dependence of the elastic force on the elongation of the spring is a straight line passing through the origin (Fig. 45). By analogy with the work of gravity, the work of the elastic force is equal to the area of \u200b\u200bthe triangle bounded by the graph, the coordinate axes and the perpendicular raised to the abscissa at the point \ (x \) .
\(A=Fx/2=kx\cdot x/2 \) .
7. The work of gravity does not depend on the shape of the trajectory along which the body moves; it depends on the initial and final positions of the body. Let the body first move from point A to point B along the path AB (Fig. 46). The work done by gravity in this case
\[ A_(AB)=mgh \]
Now let the body move from point A to point B, first along the inclined plane AC, then along the base of the inclined plane BC. The work of gravity when moving along the aircraft is zero. The work of gravity when moving along the AC is equal to the product of the projection of gravity on the inclined plane \(mg\sin\alpha \) and the length of the inclined plane, i.e. \(A_(AC)=mg\sin\alpha\cdot l\). The product \(l\cdot\sin\alpha=h \) . Then \(A_(AC)=mgh \) . The work of gravity when moving a body along two different trajectories does not depend on the shape of the trajectory, but depends on the initial and final positions of the body.
The work of the elastic force also does not depend on the shape of the trajectory.
Let us assume that the body moves from point A to point B along the trajectory ACB, and then from point B to point A along the trajectory BA. When moving along the trajectory ASW, the force of gravity does positive work, while moving along the trajectory B A, the work of gravity is negative, equal in absolute value to the work when moving along the trajectory ASW. Therefore, the work of gravity along a closed trajectory is zero. The same applies to the work of the elastic force.
Forces whose work does not depend on the shape of the trajectory and is equal to zero along a closed trajectory are called conservative. Conservative forces include the force of gravity and the force of elasticity.
8. Forces whose work depends on the shape of the path are called non-conservative. Friction force is non-conservative. If the body moves from point A to point B (Fig. 47), first along a straight line, and then along a broken line ASV, then in the first case, the work of the friction force in the second \(A_(ABC)=A_(AC)+A_(CB) \) , \(A_(ABC)=-Fl_(AC)-Fl_(CB) \) .
Therefore, the work \(A_(AB) \) is not the same as the work \(A_(ABC) \) .
9. Power is a physical quantity equal to the ratio of work to the time interval for which it is completed. Power refers to the rate at which work is done.
Power is denoted by the letter \(N\).
Power unit: \([N]=[A]/[t] \) . \\([N] \) \u003d 1 J / 1 s \u003d 1 J / s. This unit is called the watt (W). One watt is the power at which 1 J of work is done in 1 second.
10. The power developed by the engine is equal to: The ratio of movement to time is the speed of movement: \(S/t = v \) . Where \(N = Fv \) .
From the obtained formula it can be seen that with a constant resistance force, the speed of movement is directly proportional to the engine power.
In various machines and mechanisms, mechanical energy is converted. When energy is converted, work is done. At the same time, only part of the energy is spent on useful work. Some of the energy is spent on doing work against the forces of friction. Thus, any machine is characterized by a value that shows what part of the energy transmitted to it is used usefully. This value is called efficiency factor (COP).
The efficiency coefficient is called the value equal to the ratio of useful work \((A_p) \) to all the work done \((A_c) \): \(\eta=A_p/A_c \) . Express efficiency as a percentage.
Part 1
1. Work is determined by the formula
1) \(A=Fv \)
2) \(A=N/t\)
3) \(A=mv \)
4) \(A=FS \)
2. The load is evenly lifted vertically upwards by a rope tied to it. The work done by gravity in this case
1) equal to zero
2) positive
3) negative
4) More work force elasticity
3. The box is pulled by a rope tied to it, making an angle of 60 ° with the horizon, applying a force of 30 N. What is the work of this force if the displacement modulus is 10 m?
1) 300 J
2) 150 J
3) 3 J
4) 1.5 J
4. An artificial satellite of the Earth, whose mass is \(m \) , moves uniformly in a circular orbit with a radius \(R \) . The work done by gravity in a time equal to the period of revolution is equal to
1) \(mgR \)
2) \(\pi mgR \)
3) \(2\pi mgR \)
4) \(0 \)
5. A car of mass 1.2 tons travels 800 m on a horizontal road. What work was done in this case by the friction force, if the coefficient of friction is 0.1?
1) -960 kJ
2) -96 kJ
3) 960 kJ
4) 96 kJ
6. A spring with a stiffness of 200 N / m is stretched by 5 cm. What work will be done by the elastic force when the spring returns to equilibrium?
1) 0.25 J
2) 5 J
3) 250 J
4) 500 J
7. Balls of the same mass roll down a hill along three different chutes, as shown in the figure. In which case will the work of gravity be greatest?
1) 1
2) 2
3) 3
4) work in all cases is the same
8. Work on a closed path is zero
A. Forces of friction
B. Forces of elasticity
The correct answer is
1) both A and B
2) only A
3) only B
4) neither A nor B
9. The SI unit of power is
1) J
2) W
3) J s
4) Nm
10. What is the useful work if the work done is 1000 J and the efficiency of the engine is 40%?
1) 40000 J
2) 1000 J
3) 400 J
4) 25 J
11. Establish a correspondence between the work of the force (in the left column of the table) and the sign of the work (in the right column of the table). In your answer, write the chosen numbers under the corresponding letters.
FORCE WORK
A. The work of the elastic force when the spring is stretched
B. Friction force work
B. Work done by gravity when a body falls
SIGN OF WORK
1) positive
2) negative
3) equal to zero
12. From the statements below, choose two correct ones and write down their numbers in the table.
1) The work of gravity does not depend on the shape of the trajectory.
2) Work is done with any movement of the body.
3) The work of the sliding friction force is always negative.
4) The work of the elastic force in a closed loop is not equal to zero.
5) The work of the friction force does not depend on the shape of the trajectory.
Part 2
13. The winch uniformly lifts a load of 300 kg to a height of 3 m in 10 s. What is the power of the winch?
Answers
