Question

What is energy? Prove that work done by an object is equal to the difference between kinetic energy in its two states.

Answer 1

Hint:The potential energy stored by an object's position in a force field (gravitational, electric, or magnetic), the elastic energy stored by stretching solid objects, the chemical energy released when a fuel burns, the radiant energy carried by light, and the thermal energy due to an object's temperature are all examples of common forms of energy.

Complete step by step answer:
Energy is the quantitative quality that must be supplied to a body or physical system in order to perform work on it or to heat it, according to physics. Energy is a conserved quantity, meaning it may be transformed in form but not generated or destroyed, according to the rule of conservation of energy. The joule is the energy supplied to an item by the effort of moving it a distance of one metre against a force of one newton, as defined by the International System of Units (SI).

Newton's second law may be used to develop the work-energy theorem.Work is the process of transferring energy from one location to another or from one form to another. Work can affect the potential energy of a mechanical device, the heat energy in a thermal system, or the electrical energy in an electrical device in more generic systems than the particle system described here.

The work and kinetic energy principle (also known as the work-energy theorem) says that the work done by all forces acting on a particle equals the change in the particle's kinetic energy. By defining the work of the torque and rotational kinetic energy, this concept may be extended to rigid bodies. The change in kinetic energy KE is equal to the work W done by the net force on a particle:
\[W = \Delta KE = \dfrac{1}{2}m{v_f}^2 - \dfrac{1}{2}m{v_i}^2\]
where${v_i}$ and ${v_f}$ are the particle's initial and final speeds, respectively, and m is the particle's mass.

For the purpose of simplicity, we'll assume that the resulting force F is constant in size and direction, and that it's parallel to the particle's motion. The particle is travelling in a straight path with constant acceleration. The equation F = ma (Newton's second law) describes the link between net force and acceleration, and the particle's displacement d may be calculated using the equation:
\[{\text{v}}_{\text{f}}^2 = {\text{v}}_{\text{i}}^2 + 2{\text{ad}}\]
We obtaining
\[\dfrac{{{\text{v}}_{\text{f}}^2{\text{ - v}}_{\text{i}}^2}}{{2a}}{\text{ = d}}\]

The product of the net force's magnitude (F=ma) and the particle's displacement is used to compute the net force's work. When the aforementioned equations are substituted, we get:
\[W = Fd \\
\Rightarrow W= ma\dfrac{{{v_f}^2 - {v_i}^2}}{{2a}} \\
\Rightarrow W= \dfrac{1}{2}m{v_f}^2 - \dfrac{1}{2}m{v_i}^2 \\
\Rightarrow W= K{E_f} - K{E_i} \\
\therefore W= \Delta KE\]

Note:When energy is trapped in a system with zero velocity and can be weighed, it becomes weight. It's also the same as mass, and it's always connected with mass. As explained in mass-energy equivalence, mass is also comparable to a specific quantity of energy and is always connected with it.