Photo The venue for the "Makoto Wada Exhibition" that opened at the Contemporary Art Museum Kumamoto = Chuo-ku, Kumamoto

### Experience overwhelming paintings and designs "Makoto Wada Exhibition" opens Kumamoto City Museum of Contemporary Art

** ***If you write the contents roughly*

You can experience the overwhelming amount of work and high quality.** **

Makoto Wada (1936-2019), an illustrator and graphic designer known for her various creative activities ...** → Continue reading**

**Kumamoto Daily Newspaper**

The Kumamoto Nichinichi Shimbun is a local newspaper in Kumamoto. Full of information about Kumamoto such as news and sports.

### Wikipedia related words

If there is no explanation, there is no corresponding item on Wikipedia.

# Work (physics)

physicsIn**work**(Work,English: work) IsobjectJoinPowerVector and objectDisplacementVectorinner productDefined byPhysical quantity.

Job is,EnergyIt is a physical quantity that defines, and is involved in various principles and laws in physics.

## Overview

When multiple forces are applied to an object, the work for each force can be considered.When object A moves while one object A is exerted by another object B, such as "object A did work from object B" or "object B did work on object A". Express.However, since only the component of the force in the moving direction affects the work, the force is the moving direction of the object.OrthogonalIf so, the work is zero, and it is expressed as "object B does not work on object A".If the force is in the opposite direction of movement, the work will be negative.These thingsDisplacementAnd powervector Ofinner productIt is mathematically expressed by defining the work as.That is, work takes a positive or negative signScalar amount.

When work is done, there is an increase or decrease in energy.Work takes a positive or negative signScalar amountThe positive and negative signs are confusing, but when the object does positive work, the energy of the object decreases, and when the object does negative work, the energy of the object increases.As another form of energy transfer of workheatThere,thermodynamicsIn through workInternal energyThermodynamic functions such as are defined,Conservation of energyHeat is defined so that

Law of action / reactionMore forces are reciprocal, but work is not.When object B exerts a force on object A, object B exerts the same amount of force in the opposite direction from object A.However, when object B does work on object A, object B does not necessarily do the work of inverse sign from object A.For example, when an object moves on a fixed rigid surface such as the floor, between the floor and the objectFriction dragThe floor does work on the object, but the floor does not move, so the object does not work on the floor.

## Mechanics

For example, considering a ball thrown by a baseball pitcher, the pitcher swings his arm while applying force to give speed to the ball.In other words, the ball is from the pitcher**Doing a positive job**, Of the ballPhysical energyWill increase.

Next, an example in which work does not occur is given.

- It is assumed that the carrier is holding a package and is stationary, including the position of the package.In a situation where the carrier is carrying the package, the energy of the stationary package does not change, so it can be seen that the package is not being worked by the carrier.In reality, the carrier's muscles consume energy to generate an upward force that balances the gravity of the load, which ultimately results in Heat energy It changes to.
- electric motorConsider (electric motor) as an example.The electric motor rotates when an electric current is applied, but if the shaft is fixed so that the electric motor does not rotate while the electric current is flowing, the electric motorElectric resistanceFever (Joule heat Occurs).At this time, a rotational force is applied to the electric motor, but this is also not called work because it is fixed and nothing is moving.
- Consider the ball that a baseball catcher receives.At this time, let's assume that the catcher's mitt does not move at all and the ball stands still in an instant.This situation isInelastic collisionIn this case, the work that the ball did in the mitt is zero.That is, the energy of the stationary mitt does not increase, and the kinetic energy of the ball is lost to zero.In reality, the kinetic energy of a ball changes to the energy to distort the ball or mitt in a minute time until the moving ball comes to rest (Imagine an image taken with a high-speed camera).This kind of energy transfer is not called the work that the ball mitts.

### Formulation of work to make an object

Force on the object **F** Acts and its position Δ**x** When only changed, power **F** Worked on this object W The

Defined by.Power **F** And displacement Δ**x** TheVector quantityAnd the job is thatinner productGiven inScalar amountIs.The geometric meaning of the inner product is to extract the contribution of the applied force to the direction of movement of the object.Displacement Δ**x** The component of the force parallel to F_{∥} If you express, this job is

It can be expressed as.here Δx Is displacement Δ**x** Represents the size of.

More generally, when the force changes, the time t Power in **F**(t) And the time is so short that the force can be regarded as constant Δt think of.The change in the position of the object during this time is due to differentiation. Δ**x**= (d**x**/dt) Δt So the work that this force does on the object in this short time is

Will be.Times of Day t_{0} から t_{1} The work that this force does on an object during is defined by the sum of the work done in a short period of time.Δt In the limit of infinitesimalintegralReplaced by

Will be.As is clear from this definition, work is a time like force t It is not a fixed amount at the moment of, but a fixed amount during a certain period of time.

The integrator does not have to be time, without explicit

May be written.This is along the path of motion of the objectLine integralIt has become.

### An example

#### Simple machine

weight w In order to support the object, a vertically upward force is required against the vertically downward gravity.Vertical height of this object h Until, the work done when lifting slowly (so that the effects of acceleration are negligible) wh It is expressed as.The work required to lift to the same heightpulley,LeverSuch asSimple machineDoes not change even if is used.This is called the principle of work.

When a fixed pulley is used, the magnitude of the force that pulls the rope does not change, but the direction changes.At the same time, the direction of pulling the end of the rope changes, but the distance of pulling the end of the rope to lift is equal to the height of lifting.The force and the direction of movement change, but the magnitude of the force and the distance traveled do not change as they were when lifted, and the work does not change.

When the rope is stretched vertically using a moving pulley, it can be lifted with half the weight of the object.However, in order to lift to the same height, the rope end must be pulled at twice the height at which it is lifted.The power is halved, but the distance traveled is doubled, so the work does not change.

When using a lever, the force applied to the point of action is the length of the arm from the fulcrum.Inverse proportionalIt changes with.On the other hand, the distance traveled isSimilar relationshipBy the length of the armDirect proportionIt changes with.Therefore, the work does not change.

#### 流体

Hydraulic systemlike流体Consider the work transmission mechanism by.twopiston-CylinderIn a system in which a fluid is sealed inside, when the piston moves and the fluid moves from one cylinder to the other, the work is an invariant that does not change under appropriate conditions.First, if the fluid compression is negligible, the distance traveled by the piston is inversely proportional to the cross-sectional area of the cylinder.

If the fluid flow is negligible and can be regarded as a stationary fluid,Pascal's principleBy in every respectpressure(Static pressure) Is constant.Therefore, the force applied to the piston is proportional to the cross-sectional area of the cylinder.

Therefore, the work does not depend on the cross-sectional area of the cylinder.

#### Deformation of spring

SpringThink about the work that occurs when you expand and contract^{[Note 1]}..The expansion and contraction of the spring s AndHooke's lawTherefore, the restoring force of the spring is the expansion and contraction of the spring. s ToProportionalSo to deform the spring**Required power** *F*→ Is also proportional to the expansion and contraction of the spring.Appears at this timeProportional constant k TheSpring constantCalled.

This spring *s* = 0 から *s* = *x* When transforming to (x If is positive, the spring is stretched,x If is negative, the spring is shrunk), the work required to deform the spring W It is,

Will be.That is, the work done to deform the spring W Is springElastic energy 1/2*kx*^{2} It is stored as.

#### When the applied force is constant and the direction of the force coincides with the direction of motion of the object

As a special case, when an object moves in the same direction as the applied force**work** W Is power F And the moving distance of the object s Is equal to the product of.

As an example you mass m Object on top h When lifting*W* = *mgh* Only**Worked**It will be.On the contrary, the object is mgh Only**Being a job**,Potential energyTo increase.

#### When the applied force is constant but different from the direction of movement

As shown in the above figure, the applied force is constant, but the direction of motion is an angle with respect to the direction of the force. α Work when only leaning W Is expressed as follows.

Especially in this formula *α* = 0(Ie cos *α* = 1)When the applied force is constant and the direction of the force coincides with the direction of motionIt comes down to the example of.

In addition, *α* = π / 2 (cos *α* = 0) When *W* = 0 Will be.That is, if the force acts perpendicular to the direction of motion, the force does not work.

## thermodynamics

Steam engineConsidering that, the piston that heats water and is pushed out by steam pressure produces power by rotating the flywheel.That is, the flywheel is doing a positive job from water vapor,FlywheelRotational energy (and the energy of the entire engine connected to it) increases.In another expression,Heat energyIt is also called taking out work from.

Here is an example where work does not occur.

- Heat conduction is also not included in the definition of work because the kinetic energy of atoms moves between objects due to microscopic atomic collisions, but it is not a force that can be observed macroscopically (what is mechanical work in thermodynamics?) , Limited to macroscopic ones).

### Work done by the system

thermodynamicsでpressure P Ofgas(Generally an object)volume *V*_{i} から *V*_{f} The work that gas does when it changes to**Absolute work**）W Is expressed as the following equation.

Absolute work can be regarded as work that the gas does to the outside by changing the volume of the gas.In a system that traps a certain amount of matter and treats it as an object (closed system), the work that the system does to the outside is an absolute work.

On the other hand, in many actual devices, gas or liquid enters from one side and exits from the other side.In a system that involves the entry and exit of substances (open system), the work of moving substances in and out of the system -d (PV) Is added, and the work done by the system to the outside is as follows.

In other words, in an open system, work can be obtained by reducing the pressure of gas, etc., and the work in this case W^{∗} Distinguish from absolute work
**Industrial work**To say^{[1]}.

## footnote

### 注 釈

**^**here,Hooke's lawAn ideal spring that holdsHarmonic oscillatorTo handle.**現 実 的 な**Even with a spring, Hooke's law holds true depending on the applied force and the magnitude of displacement.

### 引用

**^**Sato & Kunitomo 1984, pp. 11–14.

## References

- Sato, Shun, Kunitomo, Meng "Thermodynamics" Maruzen, 1984.ISBN 4-621-02917-7.

## Related item

# 高 さ

**高 さ**(Takasa) is垂直DirectionalLengthThat is.重力In the working environment, it refers to the length in the direction of gravity.Also, spatialPhysical quantityBesides the height astemperature-ratio·frequency·PriceIt is common to express such things as "height".

That the height is large**high**, The height is small**Low**Say.

## Physical height

### unit

For height weighing, usually the same as lengthunitIs used.International unit system In (SI)Mm,Centimeter,Meters,KilometersEtc.

Geographical height is expressed in meters.There is no clear distinction, but heights above about 10 kilometers are expressed in kilometers.As with distance, do not use units larger than megameter.Shakunuki methodThen, in the unit of height, no matter how large the value isShakuThe following units are used.for exampleJapan AlpsThe height of is said to be "XNUMX shaku".Imperial systemThen the height is exclusivelyフ ィ ー トIs used,YardIs rarely used.

### elevation

The height in geographyAverage sea levelIs the height from**elevation**(Hyokou) is often used.If you take any two points, the difference in elevation between the two points**Ratio**It's called (flying).Regional geographyThen.^{[Question - Note]}For the summit of a mountain or hill, the relative height from the lowest contour line that does not include points higher than the summit among the contour lines surrounding the summit.prominenceThat.

In Japan, except for elevations on remote islands far from the mainlandTokyo BayThe average sea level of "Tokyo Bay average sea level (TP) ”is the standard for altitude.ActualSurveyingAs a reference point forChief of Staff OfLand Survey DepartmentIs on the site whereDiet Front ParkWas installed inJapan's Geodetic OriginIs used.

Incidentally,**Above sea level**(Kaibatsu) is also an expression that expresses height, and is generally used in the same way as "elevation", but it is not near Tokyo Bay but near.PortBased on the average sea level such as^{[1]}^{[2]}.(I.e.MeasuresLowlandMeasures,climaxSince it is more important to compare with the neighboring sea level than Tokyo Bay for countermeasures, the signboards above sea level and ""Zero meters above sea levelIt is common to use "above sea level" in words such as "."

地球Since there is no sea level in other celestial bodies, an appropriate reference plane to be used instead of the sea level is defined for each celestial body.

On a planeMapThen.contourOften represents altitude.Geographic information systemThen,Digital elevation modelDiscrete elevation values by (DEM) are often used.

In 2018, the government decided to change from the manual leveling survey that had been continued for 135 years to the satellite survey that can obtain data faster by using artificial satellites etc. Announced that data is expected to be generally available in 6 years^{[3]}.

### Water depth

The length from the average water surface to a certain position in the water,**depth**(Depth)·**depth**(Shindo) ・**Water depth**It's called (Suishin).In the case of the sea, it is a value obtained by taking a minus from the altitude of the seabed.(I.e.,riverIn the case of, the water depth is calculated from the altitude of the average lake surface.If you pullIt becomes the altitude of the bottom of the water.Alternatively, subtract the bottom elevation from the average lake elevation to get the water depth.

The depth of the coast and lakesIsolinesIt is represented by.

### Water level

Tide ebb and flow-climax-(I.e.-洪水-DroughtWhen paying attention to the height of the water surface (or sea level), such as, the height of the water surface**Water level**It's called (Sui).When expressing the water levelelevationIt may be expressed by the height measured from an arbitrary reference height peculiar to the area without using.The water level at which the river is in danger of overflowing the embankmentDangerous water levelThat.

Not just the surface of the water (or the surface of the sea)ポ ッ ト,boilerIt may also be used for the water surface in a container such as.

### Ground height

The vertical distance from the ground surface to the measurement point of an object existing on the ground**Ground height**It's called (Chijokou).OutdoorSignboardAnd wirelessantennaOften used for heights such as, this is**Installation ground clearance**Also known as (Sekchijokou).For an antenna, it is the vertical distance from the ground to the feeding point.

In general, the term ground clearance is often used for the maximum height above the ground.The ground clearance in a building is the vertical distance from the lowest ground level that the building touches to the highest point of the building.The same applies to the ground clearance of standing trees.

#### Minimum ground clearance

**Minimum ground clearance**What is (Saiichijokou)?AutomobileIn term, it refers to the vertical distance from the horizontal ground surface to the lowest point of the car body.

#### Standard ground clearance

With ladderFire truck Of**Standard ground clearance**In summary, (Kikuchijokou) is in a no-load state.LadderThe vertical distance from the ground surface to the center of the cross rail at the top of the ladder or the support pin of the basket when the ladder is upright and extended to the maximum.Ladder vehicles are classified according to this standard ground clearance, and when a fire engine procures a fire engine.Ministry of Internal Affairs and Communications Fire AgencyThe standard amount of national subsidy will be decided.

### height

When referring to the height of a measurement point in the air, "height"(Altitude) is often used.For this reasonaircraft"Altitude" is also used for the height at which the aircraft flies.Usually, the height from the sea level at that point, that is, "Above sea levelIs displayed.The altitude measured from the ground surface, not from the sea surface, is called "ground altitude".

## Math

The height of a two-dimensional figure is one side底 辺Including the bottomStraight lineTo the point on the farthest figure距離.

For example,triangleIn the case of, for the base of any one selected, the third that does not belong to itvertexDropped from to the bottomPerpendicular lineThe length of is the height.Trapezoid(parallelogramIn the case of), one of the set of parallel sides is the base, and the distance between the two parallel sides is the height.

Similarly, in the case of a three-dimensional figure, when one side is the bottom surface, the bottom surface is included.flatThe distance from the farthest point on the figure is the height.cone-pyramidThen, it is the length of the perpendicular line drawn from the apex to the bottom.Frustum / Pyramid FrustumThen, it is the distance between two parallel planes.

## footnote

**^**Ministry of Land, Infrastructure, Transport and Tourism e-mail magazine dated August 25, 8 "Do you know the origin of Japanese standards?"**^**Geospatial Information Authority of Japan Q & A "What is the difference between altitude and sea level?"**^**How to determine the altitude will changeNHK, September 2018, 3

## Related item

## 外部 リンク

- Geospatial Information Authority of Japan --- Standards and tides
- Trial release of a web map that shows the altitude(Geographical Survey Institute）
- Fire and Disaster Management Agency, Ministry of Internal Affairs and Communications-Standard amount of firefighting facilities covered by government subsidies