Conservation of Energy

The conservation of energy is a fundamental principle in physics that states:

 The total energy of an isolated system remains constant over time. In simpler terms, energy cannot be created or destroyed; it can only change forms or be transferred from one part of the system to another. 

Example:

In a pendulum’s swing, potential energy at the highest point is converted into kinetic energy at the lowest point and vice versa, with the total energy remaining constant. 

As a pendulum swings:

• At the highest point (maximum height), it has maximum potential energy (stored energy).

• At the lowest point (maximum swing), it has maximum kinetic energy (motion energy).

We can also imagine a car or roller coaster along its path. 

• When it’s at the highest point, the height from the earth is maximum and it gives maximum potential energy.

•  When the roller coaster reaches the bottom, it is at the highest velocity due to inertia, so at this point, kinetic energy is the highest

 So, we can conclude that all the potential energy changed into kinetic energy.

Stating, potential energy = kinetic energy    in a closed system

        Mgh = ½ mv2

Analogy:

• Imagine energy as a set number of candies. You can’t create or destroy candies, only move them between jars labeled with different forms of energy.

• – Moving candies from “running fast” (kinetic energy) to “high up” (potential energy) keeps the total number of candies the same.

• – Turning off a light (electrical energy) and using it to heat water (thermal energy) also keeps the total number of candies constant.

• This analogy shows that energy can change forms but the total amount always stays constant, just like your fixed number of candies.

Problem 1: Roller Coaster

Question: A roller coaster car of mass 500 kg is at the top of a hill 50 metres high. Assuming no friction, calculate the speed of the car at the bottom of the hill.

Solution:

Problem 2: Pendulum

Question: A 2 kg pendulum bob is lifted to a height of 0.5 metres above its lowest point and then released. Calculate the speed of the bob at its lowest point.

Solution:

Problem 3: Spring Compression

Question: A spring with a spring constant kkk of 400 N/m is compressed by 0.2 meters. Calculate the potential energy stored in the spring and the speed of a 2 kg mass released from the spring.

Solution: