8.8
Conservation of Energy: Application
When solving problems using the energy conservation law, the object (system) to be studied should first be identified. Often, in applications of energ…
Recall the energy conservation law for solving a numerical problem.
A rock of mass 20 kilograms is situated at the edge of a cliff at a height of 5 meters. After sliding down the cliff, its velocity is 9 meters per second. What will be the change in the internal energy of the rock?
Here, the mass of the rock, the height of the rock from the ground, and the velocity of the rock after sliding down are known quantities, and the change in internal energy is an unknown quantity.
Initially, the kinetic energy of the rock is zero, while the potential energy calculated from the weight and height of the rock is 980 joules.
After sliding, the rock has zero potential energy and the kinetic energy calculated from the mass and velocity is 810 joules.
Lastly, substituting the values of change in kinetic and potential energy in the law of conservation of energy equation gives the change in internal energy of the rock as 170 joules.
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Q1: How do you apply the conservation of energy law to solve physics problems?
First, identify the object or system being studied. Second, identify all forces acting on it and determine whether each is conservative or non-conservative. Third, choose reference points and determine potential energy functions for each force. Finally, apply mechanical energy conservation by setting the sum of kinetic and potential energies equal at every point of interest.
Q2: What happens to mechanical energy when non-conservative forces act on a system?
When non-conservative forces like friction do work on a system, mechanical energy is not conserved. Instead, the system must be analyzed using the work-energy relationship that accounts for non-conservative work. This work converts mechanical energy into other forms, such as internal energy or heat.
Q3: Why is choosing a reference point important when calculating potential energy?
A reference point establishes the zero level for potential energy calculations. Different forces can have reference points at different locations. This flexibility allows you to choose convenient reference points that simplify calculations while maintaining consistency within the energy conservation equation.
Q4: How do you calculate internal energy change in a sliding object?
Use the energy conservation equation by calculating initial and final kinetic and potential energies. The change in internal energy equals the difference between total initial energy and total final mechanical energy. In the cliff example, initial potential energy was 980 joules, final kinetic energy was 810 joules, resulting in 170 joules of internal energy change.
Q5: Can you apply energy conservation to systems with multiple objects?
Yes, conservation of mechanical energy applies to any system, including those with multiple particles or objects. Include the kinetic and potential energies of all particles and account for work done by all non-conservative forces acting on them. This principle remains fundamental regardless of system complexity.
Q6: What is the relationship between gravitational potential energy and height in energy problems?
Gravitational potential energy depends on an object's mass, height above a reference point, and gravitational acceleration. As an object falls, its gravitational potential energy decreases while kinetic energy increases. The total mechanical energy remains constant if only conservative forces act on the system.
Q7: How does work done by external forces affect energy conservation analysis?
Work done by external forces changes the total mechanical energy of a system. When analyzing energy conservation, you must account for work done on the system by external forces alongside conservative and non-conservative internal forces to accurately determine energy transformations.