Work, Energy and Power

Work is simply the energy you transfer when you apply a force to move something. Think of it this way: when you push your school desk across the classroom floor, you're doing work because the force from your muscles moves the desk. The amount of work done equals the force you apply multiplied by the distance the desk travels. Without movement, there's no work—pushing a wall transfers no energy because the wall doesn't move.

Consider a trader pushing heavy bags of rice at Lekki Market. The harder she pushes and the farther she carries each bag, the more work she does and the more energy she uses. Energy transfer happens through this work. Understanding this relationship helps you solve physics problems because work is literally energy changing form or moving from one object to another.

Energy is simply the ability or capacity to do work. Think of it like this: when you have money in your pocket, that money has the capacity to buy things. Similarly, energy has the capacity to cause change or do work on objects around us.

A practical example is a charged mobile phone battery. That battery possesses electrical energy, which is its ability to power your phone and make it work. Without that energy, your phone cannot do anything useful. The same applies to a moving football—it has kinetic energy because it can do work by knocking down objects in its path.

Energy exists in many forms: mechanical, thermal, electrical, chemical, and nuclear. The key point to remember is that whenever work is done, energy is transferred from one object to another or changes form.

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When you lift an object against Earth's gravitational pull, you're doing work in the gravitational field. The work done equals the force you apply multiplied by the vertical distance moved. The formula is W = mgh, where m is mass in kilograms, g is gravitational acceleration (9.8 m/s²), and h is the height in metres.

Think of a water seller in Lagos carrying a 20 kg container of water up three flights of stairs. The work done against gravity depends only on the vertical height gained, not the path taken. Whether the seller climbs straight stairs or a slanted ramp, the work remains the same if the vertical height is identical.

Remember that only vertical displacement matters in gravitational work—horizontal movement does no work against gravity. Energy transferred this way becomes gravitational potential energy stored in the object.

Mechanical energy comes in two main forms: kinetic energy and potential energy. Kinetic energy is the energy something has because it's moving. Think of a moving car on Lagos-Ibadan Expressway—the faster it moves, the more kinetic energy it possesses. Potential energy, on the other hand, is stored energy waiting to be released. When you lift a bucket of water up to a rooftop, you're storing energy in it because of its position. This is gravitational potential energy.

These two types work together beautifully. When you drop that bucket, its potential energy converts into kinetic energy as it falls. The total mechanical energy (potential plus kinetic) remains constant if no friction acts on the object. Understanding how energy transforms between these forms is crucial for solving WAEC problems about motion and heights.

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Potential energy is the energy stored in an object because of its position or condition. When you lift a bucket of water from the ground to the roof of a building, that bucket gains potential energy. The higher you lift it, the more energy it stores. This stored energy can be released—imagine the bucket falling; that potential energy converts to kinetic energy as it drops.

The most common type is gravitational potential energy, calculated using P.E. = mgh, where m is mass, g is gravity (10 m/s²), and h is height. Think of a mango hanging on a tree: the higher the mango sits on the branch, the greater its potential to do damage when it falls.

Another type is elastic potential energy, found in stretched springs or compressed objects. When you wind up a toy car, you're storing elastic potential energy that later propels it forward.

Kinetic energy is the energy an object possesses because it is moving. Any object in motion has kinetic energy. The faster something moves or the heavier it is, the more kinetic energy it has. Think about a moving lorry on the Lagos-Ibadan expressway—it has kinetic energy because of its speed and mass. The formula is K.E = ½mv², where m is mass in kilograms and v is velocity in meters per second. Notice that velocity is squared, meaning doubling your speed quadruples your kinetic energy. This is why speeding vehicles cause terrible accidents. When a moving object stops, its kinetic energy converts to other forms like heat and sound through friction and impact. Understanding kinetic energy helps explain why heavy, fast-moving objects are dangerous and why seatbelts save lives.

Mechanical energy is the sum of potential energy and kinetic energy in a system. The law of conservation of mechanical energy states that when no external forces like friction act on an object, the total mechanical energy remains constant. This means potential energy can transform into kinetic energy and vice versa, but the total stays the same.

Imagine a mango falling from a tree. At the top, it has maximum potential energy and zero kinetic energy. As it falls, potential energy decreases while kinetic energy increases. When it hits the ground, all potential energy converts to kinetic energy. Throughout this motion, the total mechanical energy remains unchanged.

In real situations, friction and air resistance do work, so mechanical energy isn't perfectly conserved. However, in ideal physics problems, you should assume no external forces unless stated otherwise. This makes calculations simpler and helps you solve many WAEC questions.