Comprehensive theory, key formulas, diagrams, and memory aids for Work and Energy.
In previous chapters, we learned about motion, the laws of motion, and gravitation. Another crucial concept that helps us understand and interpret many natural phenomena is "work." Closely related to work are energy and power. All living beings need food to perform activities like playing, singing, reading, and writing—these require energy. Similarly, machines need "food" in the form of fuel or electricity to do work.
In this chapter, we will explore the scientific definitions of work, energy, and power.
What is work? There is a difference between the way we use the term 'work' in day-to-day life and the way we use it in science. If you push a huge rock for hours but it doesn't move, you might be completely exhausted. In daily life, you did a lot of "hard work." However, in science, you did zero work on the rock because it did not move.
Two conditions need to be satisfied for work to be done: 1. A force should act on an object. 2. The object must be displaced.
Definition: Work done by a constant force is the product of the magnitude of the force and the distance moved in the direction of the force. $$\text{Work} = \text{Force} \times \text{Displacement}$$ $$W = F \times s$$
Life is impossible without energy. The biggest natural source of energy for us is the Sun. We can also get energy from the nuclei of atoms, the interior of the earth, and the tides. In science, an object having a capability to do work is said to possess energy. The object which does the work loses energy and the object on which the work is done gains energy.
There are various forms of energy: mechanical energy (potential + kinetic), heat energy, chemical energy, electrical energy, and light energy.
A moving object can do work. An object moving faster can do more work than an identical object moving relatively slowly. Kinetic energy is the energy possessed by an object due to its motion. The kinetic energy of an object increases with its speed. * Formula: $E_k = \frac{1}{2} m v^2$ (Where $m$ is mass and $v$ is velocity).
Stretch a rubber band; it acquires energy. Lift an object to a certain height; it acquires energy. The energy possessed by an object is the energy present in it by virtue of its position or configuration. This is known as potential energy. * Gravitational Potential Energy: The energy acquired by an object when it is raised to a height $h$. Work is done against gravity to raise the object. $$\text{Work} = \text{Force} \times \text{Displacement} = (mg) \times h$$ $$E_p = mgh$$ * Note: The potential energy of an object at a height depends only on the initial and final positions, not on the path taken.
Yes. We find many instances in nature where energy changes from one form to another. Green plants convert light energy into chemical energy during photosynthesis. An electric motor converts electrical energy into mechanical energy.
This law states that energy can neither be created nor destroyed; it can only be transformed from one form to another. The total energy before and after the transformation remains exactly the same. $$\text{Potential Energy} + \text{Kinetic Energy} = \text{Constant}$$
Do all of us work at the same rate? Do machines consume or transfer energy at the same rate? A strong person may do certain work in less time than a weak person. A more powerful car will reach a destination faster.
Power measures the speed of work done, that is, how fast or slow work is done. Power is defined as the rate of doing work or the rate of transfer of energy. $$\text{Power} = \frac{\text{Work}}{\text{Time}}$$ $$P = \frac{W}{t}$$
The Joule is a very small unit of energy and is inconvenient for expressing large quantities of energy used in households or industries. We use a bigger unit called the kilowatt-hour (kWh). * What is $1 \text{ kWh}$? If a machine that uses $1000 \text{ J}$ of energy every second ($1 \text{ kW}$) is run continuously for one hour, it will consume $1 \text{ kWh}$ of energy. * $1 \text{ kWh} = 1 \text{ kW} \times 1 \text{ h} = 1000 \text{ W} \times 3600 \text{ s} = 3,600,000 \text{ J} = 3.6 \times 10^6 \text{ J}$. * The electrical energy used in households is measured in kWh, often simply called "units" on electricity bills (e.g., consuming 100 units means consuming 100 kWh).
In physics, work is only done when a force causes a displacement. This work transfers energy to the object. Energy comes in many forms, particularly mechanical kinetic and potential energy, and strictly follows the Law of Conservation of Energy, transforming but never vanishing. Power measures how rapidly this energy is transferred or work is done. Grasping these interrelated concepts helps us calculate the efficiency of machines, understand the forces of nature, and even read our home electricity bills!