The conservation of energy is a fundamental law in physics that states that energy cannot be created or destroyed, it can only be transformed from one form to another. This means that the total amount of energy in a closed system remains constant.
In order to find the horizontal displacement of an object, we need to know the initial and final energy of the object. By applying the conservation of energy, we can equate the initial and final energies and solve for the horizontal displacement.
The different forms of energy that need to be considered for conservation of energy include kinetic energy (energy of motion), potential energy (energy due to position), thermal energy (energy due to temperature), and other forms such as electrical, chemical, and nuclear energy.
The equation for conservation of energy is: Initial energy = Final energy. This equation can be applied to various situations and can be rearranged to solve for different variables, such as horizontal displacement.
One example is a projectile motion problem, where the initial and final energies of the object are equated to find the horizontal displacement. Another example is a roller coaster, where the initial potential energy at the top of the hill is converted into kinetic energy at the bottom of the hill, and the conservation of energy can be used to find the horizontal distance traveled by the roller coaster.