Work Energy Theorem and Power

Work Energy Theorem and Power

Introduction

We all are familiar with the term work, but it means something different in physics. In physics, work is the application of force required to move an object. The work-energy principle is among the basic principles of physics. Work energy theorem is also an integral part of physics. Let’s understand it in detail.

The Work-Energy Theorem

Work refers to the application of force, denoted by ‘F.’ This force is used to move an object over a distance, referred to as ‘d’. The force is applied in the direction of the thing. The work done in this process is referred to as ‘W.’

The equation that describes work is:

W=F.d

Here, W refers to work, F refers to force and d is distance.

Let’s take an example:

Activities like reading and writing are not considered work, but lifting a bucket full of water is considered work in science.

The criteria for considering something as work is straightforward; if an object moves in the direction the force is applied, it is called work.

But if an object is moved at a constant velocity without regular movement, it cannot be considered work.

Regular movement is required along with constant velocity for it to be considered work in Physics.

To state the work-energy theorem, we also need to understand the concept of energy. Both work and energy are closely associated with each other. When we try to move an object, we also change the object’s energy. Energy is spent in doing work. We can describe energy as the ability to do any work.

Energy is not limited to one form; it can take many forms. We will learn about mechanical energy now, which has two forms: kinetic energy and potential energy.

Kinetic energy is also known as the energy of motion. Any moving object has kinetic energy in it.

Potential energy is also called stored energy, and it has several forms. For example, gravitational potential energy is stored in the object, and it is due to the object’s position on the earth’s surface. You must be familiar with roller coaster rides. When a roller coaster is on the top, it has the potential gravitational energy to go down.

Now let’s learn how an object’s energy changes. When we try to lift any object like rock from the ground, it increases the object’s potential energy, which is referred to as PE. Likewise, when we put the rock down, gravitational pull increases the kinetic energy of the stone during this process until the rock is back on the ground.

Here, force=m*g= weight

The force needed to lift the object is equal to the weight of the object, w, which is similar to its mass(m), and it is multiplied by the acceleration by gravity (g).

The work done on the object is equal to the exertion multiplied by the distance (d) required to lift the object.

W=PE_e=mgd

PE_e denotes the work done on the object is also equal to the gain in potential energy by gravity.

The kinetic energy of an object depends on its mass and velocity (v). The formula for kinetic energy is:

KE=(1/2)mv²

When we drop the object, the force of gravity starts its work and it provides kinetic energy to the object. As only the kinetic energy is increasing, there is a change in the value of quantity ½mv².

This can be represented mathematically by the work-energy theorem.

W=ΔKE=(1/2)mv₂²  -(1/2) mv₁²

Subscript two and one in this theorem refer to the final and initial velocity of the object.

The work-energy theorem is derived from Newton’s second law of motion and the force applied on a particle. The immediate power added to the system is determined by computing the scalar product of the forces with the particle’s velocity.

Constraints ensure that there is no component of velocity in the direction of the constraint force, thus defining the particle’s movement direction. The constraint forces do not add to the instantaneous power. Hence, this is also true. The instantaneous power produces work, and the scalar product of velocity and acceleration produces kinetic energy.

The work-energy theorem was discovered by James Joule.

The joule (J) is the metric unit to measure work and energy. The same metric unit for work and energy supports the concept that work and energy are connected and can be transformed into one another. 1.0 J = 1.0 N∙m, the units of force multiplied by distance. 1.0 N = 1.0 kg∙m/s² Analysing the units of the term ½mv² will produce the same units for joules.

Work-Energy Theorem Derivation

When the resulting force F is constant in size and direction and parallel to the particle’s movement, we can obtain the equation of the work-energy theorem. The particle follows a straight route and accelerates at a constant rate.
The relationship between net force and acceleration is expressed by the equation F = ma, and the particle’s displacement d may be determined using Newton’s 2nd rule of movement:

v_f² = v_i² + 2ad

Where,

v_f = final velocity,

v_i = initial velocity,

a = constant rate of acceleration

d = the object’s displacement.

Obtaining,

d = (v_f² – v_i²) / 2a

The work of the net force is determined as the product of its magnitude (F=ma) and the displacement of the particle. When the preceding equations are substituted, the following results are obtained:

W= F.d

W= ma . (v_f² – v_i²) / 2a

= (1/2)mv_f²  – (1/2)mv_i²

= KE_f – KE_i

= ΔK

The Work-Energy Theorem is derived in this way. As a result, we can conclude that the work done on an object equals the change in the object’s kinetic energy.

Power

The word “power” is used quite often in our day-to-day life. When we play cricket, people say that he hit a powerful shot. In football, we hear potent kicks by the footballer. But in physics, power has a specific meaning.

In simple words, power signifies the rate at which any work is done. Power is a scalar quantity. Power is denoted by P. the SI unit of power is the Watt, W named by acclaimed Scottish scientist James Watt. James Watt was the person who also invented the steam engine. The SI unit is named after his contribution to the field of physics. The formula for power for a specific period is:

P = Work/ Time

Important Things about Power

(a) It is the speed at which energy has been used

(b) It determines how fast work could be accomplished

(c) It could also change, so two methods can calculate power

• Instant power: The power at any given moment
• Average: The total energy used divided by whole time is the average of all the instant powers

Conclusion

So in this article, we have stated the work-energy theorem, work-energy equation, and the concept of power. These will help you understand the basics of these concepts and score better in your exams.