# Work Done

## Measuring Work

Work in physics has a very specific meaning, which is very different compared to the use of the word, ‘work’ in everyday language.

*Work is a measure of the amount of energy transferred to a object when it is moved by a force.*

To measure the work done in moving an object, two quantities need to be measured. The force to move the object and the distance over which this force was applied to the object.

Forces can be measured using a Newton (or Force) meter and distance by any suitable device or ruler. For an object being lifted vertically upwards the upwards lifting force is equal to the weight of the object (weight is the pull of gravity on a mass).

Work Done = Force x distance moved. _E = F d _ in Nm or Joules.

Work is a measure of the energy transferred to an object, as such it can be measured in Joules.

Example: A roller coaster is pulled up the first part of a track by the electrical motor acting against gravity. The work done to the cars (and the passengers) by the motor will be equal to the gravitational potential energy at the top of the slope (if we ignore frictional heat loss).

Note: In this exam all forces will act in the same direction as the movement of the object.

## Calculating Work

*_Work Done = Force x distance moved. __ _ E = F d* __in Nm or Joules. __

Example A:

A shopping trolley is pushed with a force of 250 N for a distance of 20m, calculate the work done to the trolley.

*E = Fd 250 N x 20 m = 5000 J*

Example B:

A sports bag has a mass of 8 Kg and is lifted into the boot of a car from the ground, a height of 85cm.

Force required to lift the bag is equal to the weight of the bag (pull of gravity on the mass). Gravity on Earth is 9.8 N/kg. Weight = mass x gravity = 8 x 9.8 = 78.4 N

E = Fd = 78.4 *N* x 0.85 *m* = 66.64 *J*

(recall distances must be in meters when performing calculations).

Example C:

If a force of 300 N is applied to a car,how far will it move if the work done to the car was 50 KJ?

E= Fd ∴ *d = E ÷ F* = 50,000 *J* ÷ 300 *N* = 166.67 *m*

Before performing any calculations in an exam always check the units to be used. All calculations should use SI units such as meters, seconds, etc. Check what units have been given in the question and change them if you need to.

If like many people you find it hard to pick out the numbers from the sentence try this simple trick. (This is very useful if you are dyslexic)

As you read the question, every time you come across a number, stop and write down what the quantity is and the value in the margin of the paper or on a scrap piece of paper so you end up with a list. For the value you have been asked to find put a ‘?’

Example:

If a force of 300 N is applied to a car, how far will it move if the work done to the car was 50 KJ?

F = 300 N

Distance = ?

Work done = 50 KJ ≣ 50,000 J (Joules, not Kilo-Joules, are the SI unit)

- A parachutist is pulled to the Earth with a weight of 833 N and 3332 KJ of work are done in the fall. How far did they fall? (in km)
- Your answer should include: 4 / 4km

Explanation:*E = 3332 KJ = 3,332,000 J d = ? F = 833 N E = Fd So d = E ÷ F = 3,322,000 J ÷ 833 N = 4000 m or 4 Km.*