Conservation of mechanical energy — KCSE Physics

The law of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. In mechanical systems, this principle can be expressed as:

Kinetic Energy (KE) + Potential Energy (PE) = Constant

This means that the total mechanical energy of an isolated system remains constant if only conservative forces (like gravity) are acting on it.

Key Forms of Energy:

• Kinetic Energy (KE): Energy of an object due to its motion, given by the formula KE = 1/2 mv², where m is mass and v is velocity.
• Potential Energy (PE): Energy stored in an object due to its position, commonly gravitational potential energy, calculated as PE = mgh, where h is height above a reference point.

When an object falls, its potential energy decreases while its kinetic energy increases, keeping the total mechanical energy constant.

For example, if a ball is dropped from a height of 10 meters, its potential energy at the top converts to kinetic energy as it falls. At the highest point:

• PE = mgh = 10m
• KE = 0

At the lowest point, just before it hits the ground:

• PE = 0
• KE = 10m

Thus, KE + PE = constant.

In physics, the conservation of mechanical energy states that the total mechanical energy (kinetic + potential) in a closed system remains constant if only conservative forces are acting. For free-falling objects, as they descend, potential energy (PE) converts to kinetic energy (KE).

• Potential Energy (PE) is given by the formula:
  ( PE = mgh )
  where m is mass, g is gravitational acceleration (9.8 m/s²), and h is height.
• Kinetic Energy (KE) is calculated as:
  ( KE = \frac{1}{2} mv^2 )
  where v is velocity.

When an object falls freely, its potential energy decreases while its kinetic energy increases. At the highest point, all energy is potential, and just before hitting the ground, all energy is kinetic.

Example Problem:
A 2 kg ball is dropped from a height of 10 m. Calculate the kinetic energy just before it hits the ground.

1. Calculate PE at the top:
   ( PE = mgh = 2 \times 9.8 \times 10 = 196 J )
2. At the bottom, all PE converts to KE:
   ( KE = 196 J )
   Thus, the kinetic energy just before impact is 196 J.

In physics, collisions can be classified into two main types: elastic and inelastic collisions. The key distinction between them lies in the conservation of kinetic energy.

• Elastic Collisions: In these collisions, both momentum and kinetic energy are conserved. This means that the total kinetic energy before the collision equals the total kinetic energy after the collision.
• Inelastic Collisions: In these collisions, momentum is conserved, but kinetic energy is not. Some kinetic energy is transformed into other forms of energy, such as heat or sound, during the collision.

To illustrate:

• In an elastic collision, two identical billiard balls collide and bounce off each other, conserving their total kinetic energy.
• In an inelastic collision, a car crashes into a stationary object, crumpling and losing kinetic energy in the process.

Understanding these differences is crucial for solving problems related to energy conservation in mechanics.