Studying Work, Power, and Energy is crucial as it helps us understand the fundamental principles governing the conversion and transfer of energy in various systems. This knowledge is essential for designing efficient machines, optimizing industrial processes, and developing sustainable energy solutions.
Brief overview of Work, Power and Energy
Work is defined as the product of the constant force applied on an object and the displacement of the object in the direction of the applied force.
For work to be done, two essential conditions must be met:
(i) the application of a force on the object, and
(ii) the displacement of the object in the direction of the force.
Mathematically, work (W) can be calculated as :
W = F x s,
where F represents the constant force applied and s represents the displacement along the direction of the force.
Work Done
Example: A force of 10 Newtons is applied to an object, causing it to be displaced by 5 meters. What is the work done on the object?
Solution: We can use the equation W = F x s, where:
W represents the work done,
F represents the force applied,
s represents the displacement.
Given:
F = 10 Newtons
s = 5 meters
Plugging these values into the equation, we have:
W = 10 N x 5 m
W = 50 Joules
Therefore, the work done on the object is 50 Joules.
Positive and Negative Work Done
Example: Work done by a man is taken positive when he moves from ground floor to second floor of his house. But work done by the same man is negative when he is descending from second floor of house to ground floor.
What is Zero Work Done?
If displacement of an object is in a direction perpendicular to the application of force, work done is zero inspite of the fact that force is acting and there is some displacement too.
Example: Imagine a person pushing a lawn roller across a lawn. The person applies a force horizontally to push the roller, while the displacement of the roller is also horizontal. Meanwhile, the force of gravity acts vertically downwards on the roller, but this force does not contribute to the work done on the roller, as it is perpendicular to the direction of displacement. Therefore, the work done by gravity in this case is zero, even though there is a force acting and displacement occurring.
In everyday life, we often use the term "work" to describe activities that involve physical or mental effort. However, according to the scientific definition of work, it may not always align with our common understanding.
Example: in the context of pushing a rock, even if we exert a lot of effort and get exhausted, if the rock doesn't move, no work is done according to the scientific definition.
Scientifically, work is defined as the application of force on an object resulting in its displacement. Let's consider a few situations to better understand this concept:
Work done by a constant force can be calculated using the formula:
Work = Force × Distance × cos(θ)
Work Done
where:
Work = Force × Distance
An object having the capability to do work is said to possess energy. Hence, the energy of an object is defined as its capacity of doing work. Energy of an object is measured by the total amount of work done by the object.
Energy Transformation
Unit of energy is same as the unit of work. So, SI unit of energy will be joule (J). Energy too has magnitude only.
Energy has many forms. Some important forms of energy are mechanical energy, heat energy, electrical energy, light energy, chemical energy, nuclear energy etc.
Mechanical energy is of two kinds, namely,
(i) Kinetic energy
(ii) Potential energy
Potential and Kinetic Energy
Kinetic Energy of an object is the energy possessed by it by virtue of its state of motion. A speeding vehicle, a rolling stone, a flying aircraft, flowing water, blowing wind, a running athlete possess kinetic energy.
For an object of mass m and having a speed v, the kinetic energy is given by
Example: An object of mass 15 kg is moving with a uniform velocity of 4 m s^{–1}. What is the kinetic energy possessed by the object?
Solution: The kinetic energy (KE) possessed by an object can be calculated using the formula:
KE = (1/2) mv^{2}
where:
In this case, the mass of the object is given as 15 kg and the velocity is given as 4 m/s. Plugging these values into the formula, we can calculate the kinetic energy:
KE = (1/2) * 15 kg * (4 m/s)^{2}
= 0.5 * 15 kg * 16 m^{2}/s^{2}
= 120 Joules (J)
Therefore, the object possesses a kinetic energy of 120 Joules.
Potential energy possessed by an object is the energy present in it by virtue of its position or configuration (i.e., size and shape) or change thereof.
Water stored in a dam, a stretched or compressed spring, stretched bow and arrow, an object situated at a height possess potential energy.
Example: An object with a mass of 2 kilograms is lifted to a height of 10 meters. What is its gravitational potential energy?
Solution:
We can use the equation Ep = mgh, where:
Given:
m = 2 kilograms
g = 9.8 m/s^2 (approximate value for acceleration due to gravity on Earth)
h = 10 meters
Plugging these values into the equation, we have:
Ep = 2 kg x 9.8 m/s^2 x 10 m
Ep = 196 Joules
Therefore, the gravitational potential energy of the object is 196 Joules.
Conversion of Kinetic energy to Potential energyIn the above diagram, a ball is at the top and bottom of a slope. When the ball is at the top, it has a high potential energy (PE) due to its position and the gravitational force acting on it. As the ball rolls down the slope, it gains speed, and its potential energy is converted into kinetic energy (KE), which is the energy of its motion.
According to the law of conservation (transformation) of energy, we can neither create nor destroy energy. Energy may only be transformed from one form to another such that total energy before and after the transformation remains exactly the same.
Example of Law of conservation of Energy
A Pendulum
The above diagram shows a pendulum, which is consists of a mass (m) connected to a fixed pivot point via a string of length (L).
Here's a description of the pendulum at different positions to explain the law of conservation of energy:
1. At the highest point (A): At this point, the pendulum is momentarily at rest and all its energy is potential energy (PE). The height (h) of the mass above the lowest point determines the amount of potential energy. PE = m * g * h, where g is the acceleration due to gravity.
2. At the lowest point (B): As the pendulum swings down, its potential energy is converted into kinetic energy (KE). At the lowest point, its height (h) is zero, so it has no potential energy. At this point, all its energy is kinetic energy, and the pendulum is moving at its highest velocity. KE = 0.5 * m * v^2, where v is the velocity of the mass.
3. At the highest point on the other side (C): As the pendulum swings upward, its kinetic energy is converted back into potential energy.
The rate of doing work or the rate of transfer of energy is known as the power.
∴ Power = work / time
=> P = W/t
If power of a person/machine varies with time, then his average power may be obtained by dividing the total energy consumed (or total work done) by the total time taken.
Average Power = Total energy consumed(or total work done) / Total time
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