重力によって行われる仕事

When an object moves upward, gravity acts downward—opposite to the displacement direction. Work is the dot product of force and displacement vectors. Since these vectors point in opposite directions, their dot product is negative. Gravity does negative work by converting the object's kinetic energy into potential energy during the upward motion.

During descent, gravity acts downward and the object's displacement is also downward. Since the gravitational force and displacement vectors point in the same direction, their dot product is positive. Gravity does positive work by converting potential energy back into kinetic energy as the object falls toward Earth's center.

The work-energy theorem states that net work equals the change in kinetic energy. When lifting a stationary object that remains stationary afterward, the kinetic energy change is zero. Therefore, the net work is zero, meaning the work done by the applied force exactly equals the negative of the work done by gravity.

Gravity does no work when an object moves parallel to Earth's surface with no displacement toward or away from Earth's center. Work requires a component of force in the direction of displacement. Horizontal motion perpendicular to gravity's downward pull results in zero work, since the force and displacement are perpendicular.

For composite objects, the center of mass framework simplifies gravitational analysis. A single particle with mass equal to the object's total mass is considered at the center of mass. This approach bypasses the complexity of treating every point in the object separately, allowing gravity's work to be calculated using the center of mass displacement.

Gravity transforms an object's mechanical energy between kinetic and potential forms. Negative work by gravity during upward motion converts kinetic energy to potential energy. Positive work during downward motion converts potential energy back to kinetic energy. This energy transformation is fundamental to understanding how gravity influences motion.

When both applied force and gravity act on an object, each force contributes to the total work. The net work is the sum of work done by all forces. Using the work-energy theorem, this net work equals the change in kinetic energy. Understanding work done by many forces helps predict how objects accelerate under combined gravitational and applied forces.