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Often you hear the word “work” used in science. But what is “work done” in physics and what does it mean? We are here to help!

What is the Equation for Work Done?

The equation for work done is:

Work (J) = Force (N) x Distance (m)

A useful definition of work is the action of an object moving as a result of a force acting upon the object. The joule is the SI unit of work and a 1 joule is equal to the force of 1 newton on an object moving 1 metre. 

Another way of understanding the concept of work is to think that work done equals displacement whilst a force is being applied. As we know from GCSE Physics, displacement is the movement of an object in a straight line. As we know from our everyday experience, stationary objects don’t move without influence. In fact, this is well explained by Newton’s 1st Law of Motion which is often stated as “Objects in motion, stay in motion and objects at rest stay at rest, unless acted upon by a net external force”. Remember, this is the norm in the universe and objects only slow down on Earth due to friction. 

Work and energy have a close relationship because energy is required to do work, which is why the SI units of energy and work are joules. In fact, energy is the ability to do work!

Use the tool below to calculate work done.

At this point, it is important to take a step back and ask ourselves what is a force in this equation? Forces are the factors that cause objects to change their motion or shape. This is where Newton’s 2nd Law of Motion comes into the picture, it is understood by the following equation:

Force (N) = Mass x Acceleration

This means that a force causes an object to gain kinetic energy and the amount of force is proportional to the mass of an object and the amount of acceleration. Since physicists like to keep things simple, the force defined by 1 newton is equal to the force required to accelerate 1kg of mass by 1m/s². If you are interested in more background around forces then take a look at this article from BBC Bitesize.

The Acceleration Formula and Work Done

Before we look at an example of work done, there is one more concept to understand and this is acceleration. Actually, there are two, including mass, but that can be explained in one line – mass is simply the amount of matter in a given space. 

Acceleration is understood by the following equation:

Acceleration (m/s²) = Change in velocity (m/s) / Time taken (s)

So, acceleration is the rate of change of velocity and velocity is simply speed in a given direction where:

Speed (m/s) = Distance (m) / Time (s) 

Now that we understand all of the working parts and equations that comprise work in physics, let’s work through an example. 

What is an Example of Work Done?

We will move a stationary 10-pin bowling ball 0.5 metres in a straight line in space. To simplify the scenario, let’s pretend that there is no gravity, there is no air and so no other forces are acting upon the ball. Also, let’s assume that the ball weighs 1kg to keep the calculations simple.

The ball begins in a stationary position and accelerates at 1m/s² for 1 second. This requires 1 newton of force and over a period of a second, the ball travels 0.5m. So, we know the force in newtons and the distance the ball has travelled.

Now using the equation: Work (J) = Force (N) x Distance (m) we can calculate the work done. 

1N x 0.5m = 0.5J 

0.5 joules of work has been done on the ball. 

If you’re still struggling to understand the concept of work in physics, why not book a session with a GCSE physics and maths tutor

But hang on a minute, how did we figure out how far the ball travelled in 1 second? Well, we know the rate of acceleration, we know the initial velocity and we know how much time has elapsed. We can use the following equation to calculate the distance travelled:

Displacement = Initial velocity x time + 0.5 x acceleration x time²

In case you can’t be bothered to do this calculation on your own, you can visit Calculator Soup and use their calculator to check our work.

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