Work, power and efficiency

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Work and energy

Middle School Physics

Work, Power, and Efficiency

Let's start with the basic definition of work from a scientific perspective.

To determine scientific work, a force must cause a displacement in the same direction as the force.

Three conditions must be met in order for scientific work to happen:

  1. A force must be applied.
  2. The object must move.
  3. The movement must be in the same direction as the force.

If any of these three conditions are not met, then the scientific work is not done.

Now, let's consider what we do in our daily activities.

When you walk upstairs, carry your school bag, or push a grocery cart, you feel the work you have done.

But do you think physics would agree with you?

Doing work in physics is very specific and different from just feeling tired.

For example, you could push a wall and feel very tired, but in physics, you have done no work at all.

What Is Work?

We can say that work in our daily activities doesn't sit right with the definition of work in physics.

But let's not forget that in our daily activities, we're not pushing a wall.

In our daily activities, we're not defining work as the push of a wall.

In our daily activities, we're not limiting ourselves to just activities that involve pushing a wall.

Work Formula

To calculate work, we can use the following formula:

W = F × d

Where:

  • W = work done (in joules, J)
  • F = force applied (in newtons, N)
  • d = distance moved in the direction of the force (in meters, m)

Work done is a scalar quantity, meaning it does not have a direction, it is just a number. The SI Unit of work is joules (J). 1J equals the work done when a force of 1 Newton acts on a body and displaces it by 1 meter in the direction of the force.

When is work done and when is it not?

Let's look at a few scenarios and see how work is done.

Work done:

  • You lift a book from the floor to a table. You exert an upward force, and the book moves up. Work is done.
  • A horse is pulling a cart on the road. The pulling force moves the cart in the direction of the force. Work is done.
  • You push a box on the floor. The pushing force moves the box; Work is done, in this case, it is done against friction.

Work is NOT done when:

  • A person pushes a wall, but the wall does not move. The wall is not displaced, so no work is done.
  • Carrying a bag is the same as pushing it. The force that is being applied upwards is not working because the motion is horizontal. If a person is going on the bus and is holding a bag. The force being applied by the person going on the bus to the bag is not doing work.
  • A satellite is permanently in motion, so as it is orbiting the Earth at a constant speed, the force that is exerted by gravity on the satellite is not working.
  • The moon is in orbit around the Earth. It is moving, but because of the massive gravitational force that is exerted on the moon.

Energy in relation to work

Energy is the ability to do work. Work done on an object results in the transfer of energy to that object. When an object does work, it transfers energy to something else.

Let us think of energy as a currency. When work occurs, energy is transferred from one object to another, just like a transaction using currency.

Kinetic Energy (KE)

One of these is Kinetic Energy (KE), the energy of an object due to its motion. Kinetic energy can be found using the following formula:

KE = ½mv²

Where:

  • KE = kinetic energy (in joules, J)
  • m = mass (in kilograms, kg)
  • v = velocity (in meters per second, m/s)

Kinetic energy is directly proportional to the answer and is dependent on Mass (m) and Velocity (v), which is different from mass. When velocity is squared, this means that it is doubled from the original mass, and the kinetic energy will increase by four times. That is a lot of energy.

Examples of kinetic energy: Moving cars, birds that are flying, balls being rolled, and water flowing.

Gravitational Potential Energy (GPE)

The other one is Gravitational Potential Energy (GPE), the energy stored in an object due to its position in a gravitational field. An object that is positioned higher will have more gravitational potential energy.

The equation to find the gravitational potential energy is as follows:

GPE = mgh

Where:

  • GPE = gravitational potential energy (joules, J)
  • m = mass (kilograms, kg)
  • g = strength of the gravitational field (9.8 N/kg on Earth)
  • h = reference height (in meters, m)

A book on a shelf, water in a dam, and a rock on a cliff all have gravitational potential energy.

Principle of Conservation of Energy

One of the most important and basic principles in physics is the law of conservation of energy.

The energy in the universe is constant; it can't be created nor destroyed. Energy can transform into different forms, and the total amount of energy in a closed system will always be the same.

This is what every other law of physics is based on.

The moment you throw a ball away, the gravitational potential energy will be transformed into an equal amount of kinetic energy as the ball goes down. If you refer to the ground as a point of reference, the ball will have the greatest amount of GPE and zero KE at the highest point. The moment it touches the ground, the ball will have the greatest amount of KE, and the GPE will be zero. This is assuming the energy in the ball is not being considered. The energy in the system remains constant.

When you go upstairs, the chemical energy you have in your body is converted into gravitational potential energy.

What happens when you rub your hands together? You transform kinetic energy in your hands into thermal energy, which warms your hands.

This phenomenon of energy transformation occurs all the time in the world, and it is key to understanding how to analyze systems in the world and predict how they may behave.

What Is Power?

Now consider the following: Two students go up the same staircase to the same height. They each do the same amount of work against gravity. However, one student runs up the staircase, and the other one walks up the staircase.

They have each done the same amount of work, but it still feels different to the students. The difference is power.

Power is the amount of work done in a specific amount of time and is also the amount of energy transferred in a specific amount of time.

Power Formula

P = W/t

Where:

  • P = power in watts
  • W = work done in joules
  • t = time taken in seconds

Power can also be written as:

P = E/t

Where E represents the energy transferred.

The standard scientific unit of power is a watt (W), which is named in honor of the Scottish engineer James Watt. One watt is defined as the transfer of one joule of energy in one second.

Types of larger power measurements include:

  • Kilowatt (kW) = 1000 watts (W)
  • Megawatt (MW) = 1,000,000 watts (W)

A 60 W light bulb emits 60 joules of electrical energy every second. While a 100 kW car engine can do 100,000 joules of work in one second.

The power output of the student running upstairs is greater than that of the one walking, even though they are doing the same work.

Power is a measure of how fast work is done.

What Is Efficiency?

No machine or device is perfect. When a machine or device is used, some energy is always lost, often wasted in the form of heat or sound.

When you ride a bicycle, not all your effort goes into moving it forward. Some energy is lost in the friction in the chain, air resistance, and heat in the tires.

When a light bulb is on, it does not convert all the electrical energy into light. A lot of it gets wasted as heat, which is the reason why light bulbs get hot.

The word efficiency is used to refer to how useful the energy output is in comparison to the energy input, and is often expressed as a percentage.

Efficiency Formula

Efficiency = (Useful energy output / Total energy input) × 100%

Efficiency can also be calculated using power:

Efficiency = (Useful power output / Total power input) × 100%

Efficiency is always less than 100% because some energy is always wasted in real systems. The closer efficiency is to 100%, the better the device is.

Examples of Efficiency

  • An electric motor has 80% efficiency. 80% of the electrical energy converted to kinetic energy is useful movement. The other 20% is wasted and converted to heat and sound.
  • An incandescent light bulb has 5% efficiency. 95% of the electrical energy is wasted as heat instead of light. LED bulbs are better because they are more efficient, with 80-90% efficiency.
  • A Petrol car engine typically has 25-30% efficiency. This is because most of the fuel energy is converted to heat, which escapes through the exhaust and radiator.

Why Efficiency Matters

Efficiency is important for The Sustainable Development Goals and for the conservation of energy.

Engineers aim to find more efficient ways to design vehicles, appliances, and power plants. The more efficient a power plant is, the less fuel it consumes, the less it costs, and the less there is a negative effect on the environment.

Choosing an energy-efficient appliance is using your knowledge of physics to make a responsible choice for the environment.

In relation to energy systems, the concepts of work, power, and efficiency are interconnected.

The amount of energy transferred is described by work, while the rate of the transfer is described by power. The efficiency of a system describes how effectively it accomplishes a transfer.

An engine in a car is able to do a lot of work very quickly; however, if it is inefficient, it will simply burn fuel. An engine that is less powerful overall, but is highly efficient, will be a more practical and economical option.

The efficiencies when analyzing simple machines versus complex industrial systems are what make physics so critical to the fields of engineering, technology, and environmental science.