Understanding the Kinetic Energy of a Moving Jeepney and Its Conversion to Heat

Imagine a jeepney of 1,500 kg traveling at a speed of 30 meters per second (m/s). Suddenly, the driver steps on the brake, and the vehicle glides to a stop due to the force of friction acting against its motion. A fundamental question arises: what was the kinetic energy of the jeepney at the moment the driver applied the brake?

Concept of Kinetic Energy and Conversion to Heat

Kinetic energy is the energy an object possesses due to its motion. The formula to calculate this is:

KE 0.5 * m * v^2,

where 'm' is the mass of the object (in this case, 1,500 kg) and 'v' is the velocity (in this case, 30 m/s).

Substituting the given values into the formula, we get:

KE 0.5 * 1,500 kg * (30 m/s)^2

KE 0.5 * 1,500 * 900

KE 675,000 joules (J)

Alternatively, this can be written as 675 kilojoules (kJ).

Force Required to Stop the Jeepney and Braking Distance

Stopping a vehicle requires a force that is proportional to the mass of the vehicle and the square of its velocity. This can be represented by the formula:

F m * v^2

Substituting the given values:

F 1,500 kg * (30 m/s)^2

F 1,500 * 900

F 1,350,000 newtons (N)

This force is the braking force needed to bring the vehicle to a stop.

The time it takes to stop the jeepney depends on the braking force and the frictional force acting against the motion. Assuming a constant braking force, the stopping distance (s) can be calculated by using the work-energy principle:

Work done by friction (W) Change in kinetic energy (ΔKE)

F * s 0.5 * m * v^2

s (0.5 * m * v^2) / F

s (0.5 * 1,500 kg * 30^2 m/s^2) / 1,350,000 N

s (0.5 * 1,500 * 900) / 1,350,000

s 675,000 / 1,350,000 0.50 meters

Thus, the jeepney will come to a stop in approximately 0.50 meters, given the conditions mentioned.

Conservation of Energy and the Role of Friction

The principle of conservation of energy states that in an isolated system, energy cannot be created or destroyed; it can only be transformed from one form to another. In the context of the jeepney, the kinetic energy of the vehicle is transformed into frictional heat as the vehicle slows down and comes to a stop.

During the braking process, the kinetic energy of the jeepney is converted entirely into work done against friction. The work done (W) can be calculated as:

W -0.5 * m * v^2

W -0.5 * 1,500 kg * (30 m/s)^2

W -675,000 joules

The negative sign indicates the energy is being dissipated as heat due to friction.

Thus, all of the initial kinetic energy (675,000 joules) is converted into the work done by friction, which dissipates as heat energy.

Conclusion

In summary, the kinetic energy of the 1,500 kg jeepney traveling at 30 m/s is 675,000 joules (or 675 kJ) at the moment the brake is applied. This energy is entirely absorbed by friction, transforming into heat energy and bringing the jeepney to a complete stop.