91Ó°ÊÓ

Before understanding the collision, it's crucial to know what kinetic energy is. Kinetic energy is the energy an object has due to its motion. The formula to calculate kinetic energy is \( E_k = \frac{1}{2} m v^2 \). This means the kinetic energy depends on both the mass (m) and the velocity (v) of the object.
When calculating kinetic energy:

• Double the velocity, and the kinetic energy increases four times.
• Double the mass, and the kinetic energy doubles too.

It’s essential to convert all units into standard units – typically kilograms for mass and meters per second for velocity. In our exercise, we converted the speeds from kilometers per hour (kph) to meters per second (m/s). By correctly converting and applying the formula, we derived the initial kinetic energies of both the vehicles before the collision.

A collision results in various transformations of energy. During a head-on collision, the kinetic energies of the colliding vehicles interact. When two cars collide and come to rest immediately after impact, their kinetic energy gets converted into other forms of energy.

• Heat due to the friction between the car parts.
• Sound waves produced during the impact.
• Deformation energy – that is, the energy used to deform the vehicles.

In our exercise, both cars come to rest upon collision. This means their final kinetic energy is zero \( E_{k_{final}} = 0 \). Thus, the kinetic energies calculated initially become internal energy upon impact. This sort of energy transformation is common in perfectly inelastic collisions where colliding objects stick together or come to rest immediately.

The principle of conservation of energy states that energy cannot be created or destroyed; it can only change forms.
During the collision of the two vehicles, the total initial kinetic energy was transformed into internal energy, showcasing the conservation of energy.
To find the increase in internal energy, we simply calculated the total initial kinetic energy and subtracted the final kinetic energy, which was zero. This transformed energy accounted for all the factors after the collision like heat, sound, and deformation.
Here’s a step by step summary:

• Calculate the initial kinetic energy of both vehicles.
• Note that the final kinetic energy is zero since the cars come to a stop.
• The increase in internal energy equals the initial total kinetic energy.

The conservation of energy helps us understand how energy changes from one form to another, ensuring that the total energy remains constant within a system.