# Understanding Work: A High Schooler's Guide

• manujnaik
In summary, Work is a scalar quantity because it depends upon angle between the point of application of force and the object.
manujnaik
Hi, I'm a bit confused on how 'work' can be scalar. I understand that W=FSCosX where X is the angle between the point of application of force and the object. So if the Work depends upon the angle, shouldn't that mean it depends on direction of force applied making it a vector? I'm a high school student so please don't kill me because I'm honestly confused.

In what direction does work point?

W=FSCosX

You are nearly there, but look more closely at your formula.

A vector, multiplied by a number is still a vector.

cosX is a number so any single vector, multiplied by cosX is a vector.

But in your formula both F and S are vectors.

So you have two vectors multiplied together and their product multiplied by cosx.

Whenever you have this situation the result is a scalar.

manujnaik said:
Hi, I'm a bit confused on how 'work' can be scalar.

Force is a vector (3D). The "difference" from point A to B can be called a vector (d=(x1,y1,z1)-(x2,y2,z2)). Between, there is a so called scalar product. Meaning:
Fx * dx + Fy * dy + Fz * dz = W (Work). Do you understand that the scalar product between vectors is a number and in this case: Work is scalar?
If not, try in mind to move a body where you live. Take the body and have a nice trip to Regensburg in Germany. Move the body there (cheaper to do it in your neighboorship but nevertheless a nice journey). The energy you will spend is the same. And the direction is not important, there is no east or west or north or south energy.

Jens

F.Scos x=W
S is displacement i.e. a vector quantity
i.e.
Scosx is also a vector
F is force i.e. a vector
u must remember that the dot product of two vectors is scalar
thus W=F.S cosx is a scalar quantity

/
_

if you look at the two lines above, the dot product is like asking how much the top line lays over the bottom line. As you change the angle between the two lines, you will have different lengths of overlap (the "projection" it's called, since you're essentially measuring the length of the shadow the top line casts on the bottom line). No direction required to answer that question.

yeah absolutrly pythagorean

shubhxxx said:
F.Scos x=W
S is displacement i.e. a vector quantity
i.e.
Scosx is also a vector
F is force i.e. a vector
u must remember that the dot product of two vectors is scalar
thus W=F.S cosx is a scalar quantity

Okay so the product of two vectors is scalar and thus Work is scalar. Am I right?

manujnaik said:
Hi, I'm a bit confused on how 'work' can be scalar. I understand that W=FSCosX where X is the angle between the point of application of force and the object. So if the Work depends upon the angle, shouldn't that mean it depends on direction of force applied making it a vector? I'm a high school student so please don't kill me because I'm honestly confused.

Are you asking why work (i.e. *energy*) is a scalar, or are you asking why 'FSCosX' is a scalar?

Andy Resnick said:

Are you asking why work (i.e. *energy*) is a scalar, or are you asking why 'FSCosX' is a scalar?

I am asking why Work is scalar but I think I understand it now.

## 1. What is the definition of work in physics?

In physics, work is defined as the transfer of energy from one object to another, resulting in a displacement of the object in the direction of the applied force.

## 2. How is work calculated?

Work is calculated by multiplying the force applied to an object by the distance it moves in the direction of the force. This can be represented by the equation W = Fd, where W is work, F is force, and d is distance.

## 3. What is the unit of measurement for work?

The unit of measurement for work is the joule (J). One joule is equal to one newton-meter (N*m).

## 4. How is power related to work?

Power is the rate at which work is done. It is calculated by dividing the amount of work done by the time it takes to do the work. This can be represented by the equation P = W/t, where P is power, W is work, and t is time.

## 5. What are some examples of work in everyday life?

Examples of work in everyday life include pushing a shopping cart, lifting a backpack, and walking up stairs. Work is also done when cooking, cleaning, and exercising. Essentially, any activity that requires the application of force and results in a displacement can be considered work.

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