# Work Done

If you’ve ever visited a railway station, you’ve probably seen the station’s coolies. The coolie places the baggage on the ground and grabs it to protect it from toppling over. The coolie then pulls up and lowers the baggage till it reaches the ground. What exactly is going on here? We can see that some work has been done in this area. So, what exactly is work? Let’s have a look at the information below.

We use terms such as overworked and hard workers to describe the effort put in by a person. But what is the meaning of work, and how do we quantify it? In this article, we will learn the definition of work in terms of physics and the factors on which work depends.

Work, Energy, and Power are fundamental concepts of Physics. Work is said to be done when a force (push or pull) applied to an object causes a displacement of the object. We define the capacity to do the work as energy. Power is the work done per unit of time. This article discusses work, energy, and power in detail.

## Defining Work

Work is the force that causes an item to move or be displaced. In the case of a constant force, it is the scalar product of the force exerted on an object and the displacement generated by that force.

Despite the fact that both force and displacement are vector variables, it has no direction owing to the nature of a scalar product. When we apply a force that produces a movement in an item across a distance, we are said to be doing work. Work occurs only when an item is raised or moved, according to the physics definition. It is not, however, about an item in a fixed location.

Work is expressed in a variety of ways depending on the situation. For example, the work done while compressing gas at a constant temperature is the product of pressure times volume change. It transmits energy to the body, thus the amount of work done on the body is proportional to the increase in the body’s energy. If the applied force is in opposition to the object’s motion, the work done is deemed negative, implying that energy is being removed from the item.

“Despite Working Hard, No Work is Completed”Consider the following scenario,

A waiter is carrying a tray high over his head with one arm while strolling at a steady speed across a room, despite the fact that you might believe he’s working hard.

However, he is not working in the scientific sense. The waiter is pushing the tray over his head with focre, and the tray is going across the room as he goes. However, the waiter’s lifting of the tray has no effect on the tray’s movement. To create a work, there must be a force in the direction of the displacement.

**Work Done by a Constant Force**

When a force acts on an item over a long distance, the thing undergoes work. Physically, the work done on an item is the change in energy that the object possesses.

Thus, we can define the work done as the change in the energy of the object(either kinetic or potential). The total energy of the system is always constant and it can be converted to other forms using the work done.

**Work Done by the System**

When we talk about work, we focus on the impact that the system has on its surroundings. As a result, we consider work to be positive when the system makes an attempt to improve the environment (i.e., energy leaves the system). If work is done on the system, the work is negative (i.e., energy added to the system).

Examples of the work done by the system are,

- The output from the turbine.
- A rocket is being launched.
- A pump used to draw water.
- A vehicle running with an Internal Combustion Engine.

## Formula for Work Done

Consider a block that is resting on a smooth horizontal surface. This block is subjected to a constant force F. The goal of this force is to propel the body a particular distance in a straight line in the force’s direction. The product of the magnitude of applied force and the distance travelled by the body equals the total work done by this force.

The formula for scientifically completed work will be as follows:

**W = F d**

The force acting on the block is constant in this example, but the direction of the force and the direction of displacement impacted by it are not. Force F reacts at an angle θ to the displacement d in this case.

W = (|F| cosθ) |d|where,

Wis the work done by the force.Fis the force,θis the angle between the force vector and the displacement vector,dis the displacement caused by the force.

**Unit of Work**

The** Joule (J)** is the SI unit of work, and it is defined as the work done by a force of **1 Newton** in moving an item a distance of **1 metre** in the force’s direction.

- Work has the same dimension as energy and is represented by
**[ML**. It is defined as the product of the magnitude of displacement d and the component of the force acting in the displacement direction.^{2}T^{–2}]

## Factors Affecting Work

Various factors affect the work done by an object which are,

- Force applied
- Displacement
- Angle Between Force Vector and Displacement Vector

Let’s look at some of the factors that affect the work done by an object.

**Force Applied**

It is described as a push or a pull that may cause any massed object’s velocity and acceleration to alter. The amount and direction of force are both vector quantities. If the force acting on an item is zero, regardless of whether the object is in a dynamic or static state, the force does not work.

**Displacement**

It is a vector quantity that represents the smallest distance between an object’s starting and final positions. The net work done by a force acting on an item is zero if the resultant displacement in the direction of force is zero. For example, if we push a hard wall with all our might but still fail to move it, we might say we have done no work on the wall.

**Angle Between Force Vector and Displacement Vector**

Depending on the direction of displacement of the item with regard to the force, the work done by the force might be positive, negative, or zero. The work done by the force of friction on an item moving in the opposite direction to the direction of force, such as friction acting on an object travelling forward, is negative. When the angle of displacement is perpendicular to the direction of the force, an item experiences zero force.

## Types of Work Done

On the basis of the angle between the force and the displacement work done can be categorized into three types,

- Positive Work
- Negative Work
- Zero Work

**Positive Work**

When a force moves an item in a positive direction, the work done is considered positive. The motion of a ball falling towards the earth, with the displacement of the ball in the direction of gravity, is an example of this sort of labour.

When force is applied to an item at an angle **0 ≤ θ < 90°**, it is said to be positive work.

**Negative Work**

When force and displacement are in opposite directions, it is considered that the work is negative. For example, if a ball is thrown upwards, the displacement will be upwards; nevertheless, the force due to gravity will be downwards.

When force is applied to an item at an angle of **90° ≤ θ < 180°**, it is said to be positive work.

**Zero Work**

The total work done by the force on the item is 0 if the direction of the force and the displacement are perpendicular to each other. When we push forcefully against a wall, for example, the force we are exerting on the wall is ineffective since the wall’s displacement equals d = 0.

**Related Resources**

## Solved Examples on Work

**Example 1: The rope pulls the box along the floor, creating a 30° angle with the horizontal surface. The box is dragged for 20 metres, with a force of 90 N applied by the rope. Where can I find the force’s final work?**

**Answer:**

Here,

The angle between force and displacement, θ = 30°

The displacement of the box, d = 20 m

The force applied on the box, F = 90 N

So, total work done by the force is,

W = F d cosθ = 90 × 20 × 0.866 J

= 1558.8 J ≈ 1560 J

Hence, the work done by the force is

1560 J.

**Example 2**:** With Force 10 N engaged at an angle of** **60**°** from the horizontal, a girl thrusts a toy car from the stationary state on the horizontal floor. The toy car weighs 4 kg. In 10 seconds, can you find the girl’s work?**

**Answer:**

Initially, we can resolve the force into two components such as horizontal and vertical component;

Horizontal component = 10 cos60° = 5 N

Vertical component = 10 sin60° = 8.66 N

Now we need to figure out how much work we’ve done and how far we’ve travelled.

Horizontal force will now be the sole source of acceleration for that toy cart.

Acceleration, a = F⁄m = 5 N ⁄ 4 kg = 1.25 m ⁄ s²

We can obtain displacement from the formula:

s = u t + 1⁄2 a t² = 0 + 0.5 × 1.25 × 10² m = 62.5 m

So, the work done will be:

W = F × s

= 5 × 62.5 J

= 312.5 JHence, the work done by the car is

312.5 J

**Example 3: Calculate the Work Done on the Body when a force pg 50 N displaces it by 5m**

**Solution: **

Formula for the work done is,

W = F × d

Given,

F = 50 N

d = 5mSubstituting these values in the above formula we get

W = 50 × 5

= 250 Joule

Thus, the work done on the body is 250 J.

**Example 4: A Box is pulled over an inclined plane with a force of 5 KN. If the displacement of the box is 5 m and the inclination of the plane is 30°. Find the work done (neglecting the weight of the box and friction between the plane and the box)**

**Solution:**

Force applied on the box is 5 KN = 5000 N.

As the box is placed on an inclined plane with an angle of 30

°the two components of the forces are, F cos 30° and F sin 30°.The force which displace the body is F cos 30°= 5000 × (√3 / 2)

= 2500√3

Displacement of the box is 5 m.

Work done is given by the formula,

W = F × d

= 2500√3 × 5

= 12500√3 Joule

Thus, the work done is 12500√3 J

## FAQs on Work

### Question 1: What is Work?

**Answer:**

The transfer of energy in displacing an object against the force F is defined as the work done and it is calculated using the formula,

W = Fd cos θ

### Question 2: What is the SI unit of work?

**Answer:**

The SI unit for measuring the work done is Joule. One Joule is equal to 1N-m and its dimensional formula is [ML

^{2}T^{-2}]

### Question 3: When is work done negative?

**Answer:**

If the displacement is against the force applied i.e the angle between displacement vector and the force vector is 180° then the work done is negative. Example work done by friction in case of stopping a moving vehicle.

### Question 4: When is work done zero?

**Answer:**

If there is no displacement when the force is applied or the angle between displacement vector and the force vector is 90° then the work done is zero. Example work done by potter when he put your luggage on his add and moved is zero.

### Question 5: Why is work done a scalar quantity?

**Answer:**

Work done only has magnitude and no direction hence it is a scalar quantity.

### Question 6: Why work done by the centripetal force is zero?

**Answer:**

The work done by the centripetal force is always zero because the centripetal force is always toward the centre and the displacement of the object at any point is along the tangent at that point and the angle between the force vector and the displacement vector is 90° and thus the work done by the centripetal force is zero.

**Question 7: What is the work done when a body falls freely under gravity?**

**Answer:**

The work done by a force acting on a body is positive if the force has a component in the direction of displacement. As a result, when a body falls freely under gravity’s influence, the work done by gravity is positive.

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