# Work

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## Introduction

Imagine a vendor carrying a basket of vegetables on her head. Is she doing any work? One would definitely say yes! However, in Physics she is not doing any work! Again, imagine a boy pushing against a wall? Is he doing any work? We can see that his muscles are contracting and expanding. He may even be sweating. But in Physics, he is not doing any work!

If the vendor is carrying a very heavy load for a long distance, we would say she has lot of energy. By this, we mean that she has a lot of stamina. If a car can travel very fast, we describe the car as powerful. So, there is a link between power and speed. However, power means something different in Physics. This chapter describes the links between work, energy and power and what these mean in Physics.

You will learn that work and energy are closely related. You shall see that the energy of an object is its capacity to do work and doing work is the process of transferring energy from one object or form to another. In other words,

• an object with lots of energy can do lots of work.
• when work is done, energy is lost by the object doing work and gained by the object on which the work is done.

Lifting objects or throwing them requires that you do work on them. Even making electricity flow requires that something do work. Something must have energy and transfer it through doing work to make things happen.

## Work

Work

When a force exerted on an object causes it to move, work is done on the object (except if the force and displacement are at right angles to each other).

This means that in order for work to be done, an object must be moved a distance $d$ by a force $F$ , such that there is some non-zero component of the force in the direction of the displacement. Work is calculated as:

$W=F·\Delta xcos\theta .$

where $F$ is the applied force, $\Delta x$ is the displacement of the object and $\theta$ is the angle between the applied force and the direction of motion. The force F causes the object to be displaced by Δ x at angle θ .

It is very important to note that for work to be done there must be a component of the applied force in the direction of motion. Forces perpendicular to the direction of motion do no work.

For example work is done on the object in [link] , (a) The force F causes the object to be displaced by Δ x in the same direction as the force. θ = 0 ∘ and cos θ = 1 . Work is done in this situation. (b) A force F is applied to the object. The object is displaced by Δ y at right angles to the force. θ = 90 ∘ and cos θ = 0 . Work is not done in this situation.

## Investigation : is work done?

Decide whether on not work is done in the following situations. Remember that for work to be done a force must be applied in the direction of motion and there must be a displacement. Give reasons for your answer.

1. Max pushes against a wall and becomes tired.
2. A book falls off a table and free falls to the ground.
3. A rocket accelerates through space.
4. A waiter holds a tray full of meals above his head with one arm and carries it straight across the room at constant speed. (Careful! This is a tricky question.)

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