Short Answer

The work-energy theorem states that the work done on an object by a net force results in a change in its kinetic energy. In simple words, when work is done on an object, its speed changes because its kinetic energy increases or decreases.

For example, when you push a bicycle, you do work on it, and it speeds up because its kinetic energy increases. Similarly, when brakes are applied, negative work is done, and the bicycle slows down as its kinetic energy decreases. This theorem connects work and motion directly.

Detailed Explanation :

Work-Energy Theorem

The work-energy theorem is an important principle in physics that shows the relationship between the work done on an object and the change in its kinetic energy. It tells us that whenever a force acts on an object and causes motion, the work done by that force directly affects the object’s kinetic energy.

This theorem is useful in understanding how objects speed up, slow down, stop, or change direction. It helps us study motion in a simple way without focusing on every small detail of the force. Engineers, scientists, and students use this theorem to solve problems in mechanics, vehicle motion, machines, and many natural processes.

Meaning of the Work-Energy Theorem

The work-energy theorem states:

“The net work done on an object is equal to the change in its kinetic energy.”

Mathematically,

 

This tells us:

• If the net work is positive → kinetic energy increases → object speeds up
• If the net work is negative → kinetic energy decreases → object slows down
• If no net work is done → kinetic energy remains the same → motion continues at constant speed

This idea comes from Newton’s laws and helps us understand motion more easily.

How the Theorem Works

1. When Work is Positive

If the applied force helps the motion, work done is positive.
Example: Pushing a trolley forward makes it move faster.
So, its kinetic energy increases.

2. When Work is Negative

If the applied force opposes the motion, work done is negative.
Example: Applying brakes on a car reduces its speed.
So, kinetic energy decreases.

3. When Work is Zero

If force is perpendicular to motion, no work is done.
Example: Carrying a bag while walking on a flat road.
Kinetic energy remains unchanged.

Explanation Through kinetic Energy

Kinetic energy is given by:

When work is done, the velocity changes. Because velocity changes, kinetic energy also changes. This is why work directly affects kinetic energy.

For example:

• If velocity increases from 5 m/s to 10 m/s, kinetic energy increases.
• If velocity decreases from 10 m/s to 5 m/s, kinetic energy decreases.

The work-energy theorem helps calculate how much force or work caused these changes.

Examples of Work-Energy Theorem in Daily Life

1. Pushing a Vehicle

When you push a stopped scooter, you do work on it. The work increases its kinetic energy, and it starts moving faster.

2. Applying Brakes

Brakes apply a force opposite to motion. They do negative work, which decreases kinetic energy and stops the vehicle.

3. Falling Objects

Gravity does positive work on a falling stone. As it falls, its potential energy changes into kinetic energy and its speed increases.

4. Throwing a Ball

When you throw a ball, your hand does work on it. The ball gains kinetic energy and moves forward.

5. Lifting Weights in Gym

When lifting weights, you do work against gravity. Although the kinetic energy may not change much, the work changes potential energy, showing how work affects energy.

Derivation (Simple Explanation)

Though the question does not ask for mathematical derivation, understanding the idea helps:

Newton’s Second Law:

Work done:

Using equations of motion, we get:

This shows:

Thus, work equals change in kinetic energy.

Importance of the Work-Energy Theorem

The theorem is important because:

• It explains how forces cause changes in motion.
• It helps calculate speeds, stopping distances, and accelerations.
• It is used in designing vehicles, brakes, machines, and safety systems.
• It simplifies solving physics problems by avoiding detailed force analysis.
• It connects the concept of energy with the concept of motion.

It also helps understand many natural phenomena such as running, jumping, falling, and collisions.

Conclusion

The work-energy theorem states that the net work done on an object results in a change in its kinetic energy. If positive work is done, the object speeds up; if negative work is done, it slows down. This theorem provides a simple and powerful way to understand motion, energy transfer, and the effect of forces. It is widely used in physics, engineering, and daily-life applications.