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What is Work? Definition, Formula, Types, Problems

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  • Last Updated : 21 Sep, 2021
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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.

What is 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 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 vigour, 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 displacement, 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 kinetic energy that the object goes through.

  • 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 good 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).

Scientifically, the places where scientific activity is done is as follows:

  1. The output from the turbine.
  2. A rocket is being launched.
  3. A pump is used to draw water.
  4. A vehicle 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|


  • F is the force,
  • θ is the angle between the force vector and the displacement vector,
  • d is the displacement caused by the force, &
  • W is the work done by the force.

Dimension formula and Units of Work:

  • Work has the same dimension as energy and is represented by [ML2T–2]. It is defined as the product of the magnitude of displacement d and the component of the force acting in the displacement direction.
  • 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.

Factors Affecting Work

Let’s look at the elements that influence how much work a force can accomplish on an object.

  1. Force: 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 no work.
  2. 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.
  3. The Angle between the Force Vector and the 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 

  • 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 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.

Sample Questions

Question 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?



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.

Question 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?


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.

The 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 J

Hence, the work done by the car is 312.5 J.

Question 3: Is the effort done by gravity when a body falls freely under gravity positive or negative?


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.

Question 4: Is the work done by friction when a body slides against a rough surface positive or negative?


When a force acting on a body has a component in the opposite direction of displacement, the force’s work is negative. As a result, the frictional force on the body does negative work.

Question 5: Superman uses force to stop a vehicle from rolling downhill. Is this an example of work that has been completed?


No. There is no work done since there is no displacement. He’s only holding the automobile up to keep it from tumbling down the slope.

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