The relationship between the work done by a force and the change in kinetic energy of an object is governed by the work-energy theorem. According to the work-energy theorem, the net work done on an object is equal to the change in its kinetic energy. Mathematically, it can be expressed as:
Work = Change in Kinetic Energy
This means that when a force acts on an object and does work, it transfers energy to the object, resulting in a change in its kinetic energy. If the net work done on the object is positive, it increases the kinetic energy, while negative work decreases the kinetic energy.
Now, let's consider the potential energy changes due to gravity when lifting an object vertically above the Earth's surface. When an object is lifted vertically against gravity, work is done against the gravitational force.
The work done against gravity is equal to the change in potential energy of the object. This change in potential energy is due to the object's change in height above the reference level (usually the Earth's surface). Mathematically, it can be expressed as:
Work = Change in Potential Energy
When lifting an object vertically, the work done is positive, as energy is transferred to the object, increasing its potential energy. The potential energy of an object in a gravitational field is given by the equation:
Potential Energy = mgh
Where "m" is the mass of the object, "g" is the acceleration due to gravity, and "h" is the height above the reference level.
In summary, when a force does work on an object, it changes the object's kinetic energy according to the work-energy theorem. When lifting an object vertically against gravity, the work done is equal to the change in potential energy, resulting in an increase in the object's potential energy.