Conservation of Mechanical Energy: A Ball Dropping From a Height

In physics, the concept of energy conservation is fundamental to understanding the behavior of moving objects. This article will explore the mechanical energy of a 10 kg ball as it falls from a height of 100 meters, focusing on the conservation of energy and the conversion between potential and kinetic energy.

Introduction to Energy Conservation

According to the law of conservation of energy, the total amount of energy in an isolated system remains constant over time. In this case, a 10 kg ball is dropped from a height of 100 meters, and we will use the principle of conservation of energy to determine its total energy after it has fallen a distance of 40 meters. Neglecting air resistance, the total mechanical energy (potential energy plus kinetic energy) of the ball remains constant throughout its motion.

Step-by-step Analysis

Step 1: Calculate Initial Potential Energy

At the initial point, when the ball is at a height of 100 meters, its potential energy (PEinitial) can be calculated using the formula:

PE mgh

where:

m mass of the ball (10 kg) g acceleration due to gravity (9.81 m/s2) h initial height (100 m)

Substituting the values:

PEinitial 10 kg × 9.81 m/s2 × 100 m 9810 Joules (J)

Step 2: Calculate Final Height

After the ball has fallen 40 meters, the final height (hfinal) is given by:

hfinal hinitial - 40 m 100 m - 40 m 60 m

Step 3: Calculate Final Potential Energy

The final potential energy (PEfinal) can be calculated using the same formula:

PEfinal mghfinal

Substituting the values:

PEfinal 10 kg × 9.81 m/s2 × 60 m 5886 J

Step 4: Calculate Final Kinetic Energy

Since the total energy is conserved, the kinetic energy (KEfinal) can be found by subtracting the final potential energy from the initial potential energy:

KEfinal PEinitial - PEfinal

Substituting the values:

KEfinal 9810 J - 5886 J 3924 J

Step 5: Calculate Total Energy

The total energy at the point where the ball has fallen 40 meters is the sum of the final potential and kinetic energy:

Total Energy PEfinal KEfinal

Total Energy 5886 J 3924 J 9810 J

Conclusion

The total energy of the 10 kg ball after it has fallen a distance of 40 meters remains constant at 9810 Joules. This is a clear demonstration of the law of conservation of energy, where the decreased potential energy is converted into kinetic energy, but the total energy of the system remains unchanged.

Further Exploration

Understanding the conversion of potential energy to kinetic energy is crucial for applications in various fields, including mechanical engineering, physics, and sports science. By dissecting the components of mechanical energy, we can gain a deeper insight into the dynamics of falling objects and the principles governing energy transformations.