Physics | Work and power

Welcome to Work and Power!

Hello future Physicists! This chapter is all about understanding how we measure effort and speed in the world of energy transfers. In everyday life, we use terms like "work" and "power" loosely, but in Physics, they have very precise definitions—and they are key components of the "Energy resources and energy transfers" section of your curriculum.

Don't worry if this seems tricky at first; we will break down the calculations step-by-step. By the end of these notes, you’ll be able to calculate exactly how much work a machine does and how quickly it does it!

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1. Work Done: The Physics Definition of Effort

In Physics, "work" isn't just about feeling tired after studying! Work Done (symbol: \(W\)) is a measure of the energy transferred when a force causes an object to move over a distance.

1.1 Two Essential Conditions for Work

For work to be done in the scientific sense, two conditions MUST be met:

• 1. A Force Must Be Applied: You need a push or a pull.
• 2. Movement Must Occur: The object must move.

Analogy: The Stuck Car

Imagine you spend an hour pushing a huge, heavy car that is stuck in mud. You push with all your might (a huge force!), but the car doesn't move.

In everyday life, you did a lot of work. But in Physics? Zero Work Done! This is because there was no movement (\(d = 0\)). Work is only done when movement occurs in the direction of the applied force.

1.2 The Work Done Formula

We calculate work done using the following simple equation:

$$W = F \times d$$

Where:

• \(W\) is the Work Done (or Energy Transferred).
• \(F\) is the Force applied (in Newtons, N).
• \(d\) is the Distance moved in the direction of the force (in metres, m).

1.3 Units of Work Done

Since Work Done is a measure of energy transferred, its unit is the same as the unit for energy:

• The standard unit for Work Done is the Joule (J).
• Looking at the formula \(W = F \times d\), we can see that 1 Joule is equal to 1 Newton-metre (1 J = 1 N m).

The Crucial Link: Work Done and Energy Transfer

This is the most important takeaway for your section on energy transfers:

Work Done is equivalent to the Energy Transferred.

Example: If you do 500 J of work lifting a heavy box, you have transferred 500 J of chemical energy (from your body) into gravitational potential energy (stored in the box).

1.4 Step-by-Step Calculation Example

A student pushes a trolley with a force of 40 N across a classroom floor for a distance of 5.0 metres. Calculate the work done by the student.

1. Write down the known variables:
   \(F = 40\, \text{N}\)
   \(d = 5.0\, \text{m}\)
2. Write down the formula:
   $$W = F \times d$$
3. Substitute the values and calculate:
   $$W = 40\, \text{N} \times 5.0\, \text{m}$$ $$W = 200\, \text{J}$$
4. State the final answer with units:
   The work done is 200 Joules.

Common Mistake Alert!

Mistake: Mixing up distance and time. Work done only depends on Force and Distance. The time taken doesn't matter for the calculation of work done.

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2. Power: The Rate of Doing Work

You now know that both a slow crane and a fast crane can do the exact same amount of work (transfer the same amount of energy) lifting a beam to the top of a building. What makes the fast crane better? It’s its Power!

2.1 Defining Power

Power (symbol: \(P\)) is defined as the rate at which work is done or, alternatively, the rate at which energy is transferred.

The word "rate" in Physics always means "divided by time."

Analogy: Racing up the Stairs

Two friends, Alex and Ben, weigh the same. They race up the same flight of stairs.

• Since they moved the same weight (force) the same distance, they both did the same amount of Work Done.
• Alex won the race (took less time). Therefore, Alex had more Power because he did the work faster.

2.2 The Power Formulas

Power links work (or energy) to the time taken.

$$P = \frac{W}{t}$$

Since Work Done (\(W\)) equals Energy Transferred (\(E\)), you can also write:

$$P = \frac{E}{t}$$

Where:

• \(P\) is Power.
• \(W\) is Work Done (in Joules, J).
• \(E\) is Energy Transferred (in Joules, J).
• \(t\) is the Time taken (in seconds, s).

2.3 Units of Power

The standard unit for power is named after the Scottish inventor James Watt:

• The standard unit for Power is the Watt (W).
• Looking at the formula \(P = \frac{W}{t}\), we can see that 1 Watt is equal to 1 Joule per second (1 W = 1 J/s).

Did You Know?

A 100 W light bulb transfers 100 Joules of electrical energy into light and heat energy every single second. That's why high power ratings often mean high energy use!

2.4 Step-by-Step Calculation Example

A motor is used to lift a weight. The motor does 1500 J of work in 5.0 seconds. Calculate the power of the motor.

1. Write down the known variables:
   \(W = 1500\, \text{J}\)
   \(t = 5.0\, \text{s}\)
2. Write down the formula:
   $$P = \frac{W}{t}$$
3. Substitute the values and calculate:
   $$P = \frac{1500\, \text{J}}{5.0\, \text{s}}$$ $$P = 300\, \text{W}$$
4. State the final answer with units:
   The power of the motor is 300 Watts.

2.5 Combining Formulas

Sometimes you might have to combine the two formulas, especially if you are only given the force, distance, and time.

Since \(W = F \times d\), we can substitute this into the power formula:

$$P = \frac{F \times d}{t}$$

This combined formula is often useful for questions involving vehicles or constant forces.

Tip for Struggling Students: The Triangle Trick

To rearrange \(P = \frac{W}{t}\) for exams, imagine a triangle with W at the top, and P and t at the bottom.

• Want W? Cover W. You get \(P \times t\).
• Want t? Cover t. You get \(\frac{W}{P}\).
• Want P? Cover P. You get \(\frac{W}{t}\).

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3. Summary and Final Review

Congratulations! You have mastered the fundamental calculations relating to effort and speed in energy transfers. Always remember the fundamental relationship:

Force causes Work, and Work is the transfer of Energy. Power tells us how quickly that transfer happens.

Quick Check List: Must-Know Concepts

• Work Done (\(W\)) requires a force and movement in the direction of the force.
• The unit of work and energy is the Joule (J).
• Power (\(P\)) is calculated by dividing work or energy by the time taken (t).
• The unit of power is the Watt (W), which is Joules per second.

Keep practising those numerical questions. You’ve got this!