In which one of the following circumstances does the principle of conservation of mechanical energy apply, even though a nonconservative force acts on the moving object?
The nonconservative force has a component that points opposite to the displacement of the object.
The nonconservative force points in the same direction as the displacement of the object.
The nonconservative force has a component that points in the same direction as the displacement of the object.
The nonconservative force is perpendicular to the displacement of the object.
The nonconservative force has a direction that is opposite to the displacement of the object.
The nonconservative force is perpendicular the the displacement of the object.
The principle of conservation of mechanical energy applies in the circumstance where the nonconservative force has a component that points perpendicular to the displacement of the object.
To determine in which of the given circumstances the principle of conservation of mechanical energy applies, we need to understand the concept of conservative and nonconservative forces.
Conservative forces are those that do not depend on the path taken by the object and only depend on the initial and final positions. Examples of conservative forces include gravitational force, elastic force, and certain electric forces.
Nonconservative forces, on the other hand, are those that depend on the path taken by the object. Examples of nonconservative forces include friction, air resistance, and any force that involves energy dissipation or transfer.
According to the principle of conservation of mechanical energy, the total mechanical energy of a system is conserved when only conservative forces are present, meaning that the sum of kinetic energy and potential energy remains constant.
However, in some cases, the principle of conservation of mechanical energy can still be applied even when a nonconservative force acts on the moving object. This is possible when the work done by the nonconservative force is completely offset by an equal and opposite work done by another force, such as when an external applied force is balanced by an internal conservative force.
Based on the given circumstances, the only situation where the conservation of mechanical energy can still apply is when the nonconservative force has a component that points in the same direction as the displacement of the object. In this scenario, the work done by the nonconservative force is positive, but there is an equal and opposite work done by another force, resulting in a net work of zero. As a result, the total mechanical energy of the system remains conserved.
Therefore, the correct choice from the given options is:
The nonconservative force has a component that points in the same direction as the displacement of the object.