Work, Energy and Power

Work Done

• In the field of physics, work occurs when an external force is applied in the direction of an object’s displacement, causing it to move over a distance

• In the given diagram, the man’s exertion of force on the block is causing work to be done as it transfers energy to the block, thereby increasing its kinetic energy

• The act of performing work involves transferring energy from one object to another
• The quantity of energy transferred is what constitutes work done, and it is measured in Joules (J)
• Generally, if a force is applied in the direction of an object’s movement, the object will acquire energy
• Conversely, if the force is exerted in the opposite direction to the object’s movement, the object will lose energy.

The Law of Energy Conservation

• The Law of Energy Conservation specifies that:
  • Energy cannot be created nor destroyed; it can only be transformed from one form to another
• Therefore, the total quantity of energy in a closed system remains constant, while the amount of each form of energy may vary
• Examples of common energy transformations include:
  • A falling object (in a vacuum): conversion of gravitational potential energy into kinetic energy
  • A battery: conversion of chemical energy into electrical energy into light energy (when connected to a bulb)
  • A horizontal mass on a spring: conversion of elastic potential energy into kinetic energy

Varieties of Energy

Energy dissipation

• During the process of energy transfer, it is not guaranteed that the entirety of the energy will be converted to the desired form or location
• The term “dissipation” refers to various methods in which energy is not utilized efficiently, resulting in wastage
• Any energy that is not converted to a productive energy source is considered lost, as it is released into the surroundings
• Typically, this energy is emitted as heat, light, or sound
• The categorization of energy as wasteful or useful is dependent on the specific system in question
• For example, car braking system:

When a driver applies the brakes in a car, the kinetic energy of the vehicle is converted into thermal energy due to friction between the brake pads and the wheels. This thermal energy is then dissipated into the surroundings, resulting in a loss of energy. This loss of energy manifests as heat, which can be felt when touching the wheels after a prolonged period of braking. Although the braking system is designed to transform the car’s kinetic energy into heat, a portion of that energy is dissipated and wasted in the form of heat to the surroundings.

• Another example, turning on an incandescent light bulb:

the electrical energy flowing through the bulb’s filament is converted to both light and heat energy. However, a significant portion of the energy is dissipated as heat and is lost to the surrounding environment, rather than being utilized for the intended purpose of producing light. This is an example of energy dissipation in which the wasted energy is released into the atmosphere, rather than being harnessed for useful work.

System Efficiency

• The efficiency of a system can be defined as the fraction of the total energy input that is converted into useful energy output
  • A system with a high efficiency indicates that a significant portion of the energy being transferred is being utilized for useful work
  • Conversely, a system with a low efficiency indicates that a substantial amount of the energy being transferred is being lost or wasted
• The efficiency can be expressed as a percentage by multiplying the efficiency ratio by 100
• The efficiency of a system is calculated using the following formula:

Efficiency = Useful energy output

                        Total energy input              x 100%

• Alternatively, efficiency can be represented in terms of power, which is the energy per unit time:

Efficiency = Useful power output

Total power input                x 100%

Power Definition

• Power is a measure of how quickly a machine transfers energy
• Alternatively, power can be defined as the rate at which work is done, or the amount of work done per unit of time

The standard unit of power in the International System of Units (SI) is the watt (W), which is equivalent to one joule per second (1 J/s)

• You might have noticed labels on light bulbs that indicate their power consumption, such as 60 W or 100 W. These ratings describe the amount of electrical energy that is being transferred, rather than the force required to perform work.

Work Done

To calculate the work done on an object by an applied force, you multiply the force by the distance traveled in the direction of the force. However, in situations where the force is applied at an angle, it is necessary to take this into account as well.

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion. In this video, I explain the derivation of the equation and address the v-squared term through stop-frame animation.

Potential Energy

Gravitational potential energy refers to the energy an object possesses due to its position in a gravitational field. It is dependent on the object’s mass, height, and the strength of the gravitational field (g).

Conservation of Energy

The law of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another.

Conservation of Mechanical Energy

Energy cannot be created or destroyed; instead, it is converted from one form to another. This principle is particularly useful when considering the conversion of kinetic energy to potential energy or vice versa.

Power

Power is defined as the rate at which energy is transferred, and the formula P = W/t can be used to calculate it.

Mechanical Power

The rate at which energy is transferred is sometimes more significant than the total amount transferred. P = E/t, but it can also be expressed as P = Fv.

Efficiency

It is not always the case that 100% of the energy is transferred from one form to another. When energy is lost from the system (for example, in the form of thermal energy), the efficiency decreases.