What is the Relation Between Work and Energy?
Energy must be transferred to an object to help it move, and the energy can be transferred in the form of force. The energy transferred by force to move any object is known as work or work done. Therefore, work and energy have a direct relationship. The difference in the kinetic energy of an object is called work done by the object. Work and energy are common terms in Physics and can be considered two sides of a coin. This article is necessary to state the relationship between work and energy.
What is Work and Energy ?
Work
When a force causes motion, work is said to done. A person climbing a flight of stairs is an illustration of this. Because he is moving against the force of gravity, the person has done work in this case. Any force's work is influenced by a number of factors. The distance the body moves in the direction of the force is one of the elements. The force is the second factor. Work is defined as the product of a body's displacement and force in the direction of the force. Work equals F*S, where F stands for force and S stands for distance. Work is equal to FS Cosθ when a body is displaced by a distance with a force operating on it.
Work = force × displacement towards the force
Energy
When you play for a long term or do quite a little physical work at your own home or out of doors you get tired, i.e., your body indicates unwillingness or reluctance towards similar play or work. at the moment you could also experience hunger. After taking a rest for some time or/ and eating something you may once more be ready for work. How does one provide an explanation for those experiences? In reality, when you do work, you expend strength and extra energy is needed to do extra work. The capability of a body to do work is decided by the energy possessed with the aid of it. i.e.,
The energy possessed with the aid of a body = overall work that the body can do. Energy has the same unit as work, i.e., joule denoted by means of J. however, conversion of 100% of energy might not usually be doable, because, within the process of conversion of energy into work a few energy may additionally remain unused or can be wasted.
Relation between Work and Energy
The capacity to do work is referred as energy. This refers to the force that one thing will put on another object in order to displace it and cause a change in its location. Work is defined as the action of displacing an object by exerting a particular amount of force on it. One would expect a shift in position as a result of doing so. The rate at which work is completed or the amount of work completed per unit of time is referred to as power.
Based on these criteria, it is safe to conclude that energy is a fundamental requirement for completing work. The amount of work completed in a given time period is referred to as power. Work, on the other hand, is the action required to change the object's location. To do work, you require energy, and power is the rate at which you can do work, whereas energy is the capacity to accomplish work.
Work and energy are related to each other i.e, with an increase in work results increase in energy, or vice versa. Work done can be explained mathematically by:
\[W = \frac{1}{2}mv^{2}_{f} - \frac{1}{2}mv^{2}_{i}\]
in which,
W is the work achieved through an object in terms of Joules.
m is the mass of the object measured in terms of kilograms.
vi is the initial velocity in m/s.
Vf is the final velocity of an object measured by the usage of m/s.
Hence, the work-energy theorem states that total work done by the net force on an object is equal to change in its kinetic strength.
FAQs on Relation Between Work and Energy
1. What is the fundamental relationship between work and energy as per the CBSE syllabus?
The fundamental relationship is that work is the transfer of energy. When work is done on an object, energy is transferred to it, and when an object does work, it transfers energy away from itself. Energy is defined as the capacity to do work. This core concept is mathematically described by the Work-Energy Theorem.
2. What is the Work-Energy Theorem and what is its formula?
The Work-Energy Theorem states that the net work done by all the forces acting on an object is equal to the change in its kinetic energy. It provides a direct link between the work done (W) and the change in motion (energy).
The formula is: W_net = ΔKE = K_f - K_i
Where:
- W_net is the net work done on the object.
- ΔKE is the change in kinetic energy.
- K_f is the final kinetic energy (½mv_f²).
- K_i is the initial kinetic energy (½mv_i²).
3. How are the SI units of work and energy related?
The SI units of work and energy are directly related because they measure the same physical quantity. Both work and energy are measured in Joules (J). This shared unit reinforces the concept that work is simply a measure of energy being transferred. One Joule is defined as the work done when a force of one Newton displaces an object by one meter (1 J = 1 N·m).
4. Can you provide a real-world example explaining the relation between work and energy?
A simple real-world example is a person pushing a shopping cart.
- The person applies a force to the cart, pushing it over a certain distance. This action is the work done by the person.
- As a result of this work, the cart, which was initially at rest, starts moving and gains speed. This motion represents its kinetic energy.
5. Does doing work on an object always increase its kinetic energy?
No, not always. The Work-Energy Theorem states that net work equals the change in kinetic energy. This change can be positive, negative, or zero.
- Positive Work: If the net force is in the direction of motion, work is positive, and kinetic energy increases (e.g., pushing a car to speed it up).
- Negative Work: If the net force opposes the direction of motion, work is negative, and kinetic energy decreases. For example, the force of friction does negative work on a sliding block, converting its kinetic energy into heat.
- Zero Work: If the force is perpendicular to the motion (like in uniform circular motion), no work is done, and the kinetic energy remains constant.
6. What is the key difference between the concepts of work, energy, and power?
While related, these three concepts are distinct:
- Energy is the capacity or ability to do work. It's a stored quantity. Its unit is the Joule (J).
- Work is the process of transferring energy by applying a force over a distance. It's energy in transit. Its unit is also the Joule (J).
- Power is the rate at which work is done or energy is transferred. It tells you how fast the energy is being used. Its unit is the Watt (W), which is Joules per second (J/s).
7. How does the Work-Energy Theorem account for potential energy from conservative forces?
The general Work-Energy Theorem (W_net = ΔKE) can be expanded to show the role of potential energy. The net work is the sum of work done by conservative forces (W_c) and non-conservative forces (W_nc). The work done by a conservative force, like gravity, is equal to the negative change in potential energy (W_c = -ΔPE). By substituting this, the theorem becomes:
W_nc = ΔKE + ΔPE = ΔE_mechanical
This shows that the work done by non-conservative forces (like friction or an external push) equals the change in the total mechanical energy (kinetic + potential) of the system.
8. If the net work done on an object is zero, does it mean that no forces are acting on it?
No, it does not. Zero net work means the object's kinetic energy does not change. This can happen in several scenarios where forces are still acting:
- An object moving at a constant velocity on a frictionless surface has zero net force and thus zero net work.
- An object being pushed at a constant velocity against friction has a net force of zero (pushing force equals friction force), so the net work is zero.
- An object in uniform circular motion has a constant centripetal force acting on it, but since this force is always perpendicular to the direction of displacement, the work done by it is zero.
