Mechanical energy is the sum of the potential energy and kinetic energy possessed by an object due to its position and motion. It represents the total energy available to do work or cause change in a mechanical system.
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Mechanical energy is conserved in a closed, isolated system, meaning it can be transformed between potential and kinetic energy but not created or destroyed.
The work-energy theorem establishes a direct relationship between the net work done on an object and the change in its mechanical energy.
Power is the rate at which mechanical energy is transferred, and it is calculated as the product of force and velocity.
Mechanical energy can be increased or decreased by the application of external work, which can be positive or negative.
The principle of conservation of mechanical energy states that in the absence of non-conservative forces, the total mechanical energy of a system remains constant.
Review Questions
Explain how the work-energy theorem relates the net work done on an object to the change in its mechanical energy.
The work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy. This means that the application of a net force that does work on an object will cause a corresponding change in the object's kinetic energy, and hence its mechanical energy. Conversely, the change in an object's mechanical energy can be determined by calculating the net work done on it.
Describe the role of conservative and non-conservative forces in the conservation of mechanical energy.
In a closed, isolated system, mechanical energy is conserved if only conservative forces, such as gravity and spring forces, are acting on the object. Conservative forces do not dissipate energy, and the total mechanical energy (potential plus kinetic) remains constant. However, the presence of non-conservative forces, such as friction or air resistance, can cause a change in the mechanical energy of the system. These non-conservative forces can either increase or decrease the total mechanical energy, depending on the direction of the work they do.
Analyze how the concept of mechanical energy can be used to understand the relationship between work, power, and energy transfers in a mechanical system.
Mechanical energy is the sum of an object's potential and kinetic energy, and the work-energy theorem establishes a direct link between the net work done on an object and the change in its mechanical energy. Power, which is the rate of energy transfer, can be calculated as the product of force and velocity. By understanding the principles of mechanical energy and its conservation, one can analyze how work is done to change the energy state of a system, and how power is involved in the transfer of energy. This knowledge is crucial for understanding the efficiency and performance of mechanical systems, as well as for solving problems related to energy transformations.
The stored energy an object possesses due to its position or configuration, such as the energy of a stretched spring or an object raised above the ground.