Generalised Energy Conservation Theorem 😍✨| Work by Non Conservative Force

When a non-conservative force acts on an object and displaces it, work is done on the object, but the work is not path-independent. This means that the amount of work done depends on the specific path taken by the object during its displacement. In contrast, conservative forces, like gravity and spring forces, have path-independent work, and the work done by these forces only depends on the initial and final positions of the object.
The work done by a non-conservative force can be calculated using the work-energy principle. The work-energy principle states that the net work done on an object is equal to the change in its kinetic energy. It is given by the equation:
Net work (W) = Change in Kinetic Energy (ΔKE)
The change in kinetic energy (ΔKE) is the final kinetic energy (KE_f) minus the initial kinetic energy (KE_i):
ΔKE = KE_f - KE_i
So, the work done by non-conservative forces can be written as:
W_non-conservative = KE_f - KE_i
Non-conservative forces may include friction, air resistance, tension in a non-ideal pulley system, or any force that causes energy to be dissipated or transferred to other forms like heat or sound.
For example, if you push a box across a rough surface with friction, the work done by the force you apply will result in an increase in the box's kinetic energy, assuming it accelerates. The frictional force will oppose the motion and do negative work, converting some of the kinetic energy back into other forms (like heat). The total work done on the box will be the net sum of the work done by your applied force and the work done by friction.
It is essential to understand the distinction between conservative and non-conservative forces when analyzing systems in physics, as it impacts how energy is transferred and transformed within the system.
The conservation of mechanical energy is a fundamental principle in physics that states that the total mechanical energy of a system remains constant as long as no external work or non-conservative forces act upon it. Mechanical energy is the sum of an object's potential energy and kinetic energy.
The potential energy of an object is the energy associated with its position or configuration relative to other objects. It depends on factors such as height, elasticity, and the strength of forces acting on the object. The most common forms of potential energy are gravitational potential energy and elastic potential energy.
The kinetic energy of an object is the energy associated with its motion and is determined by its mass and velocity. It is given by the equation:
KE = (1/2) * m * v^2
where KE represents kinetic energy, m is the mass of the object, and v is its velocity.
According to the conservation of mechanical energy, if an object is isolated from external forces or work, the sum of its kinetic and potential energies remains constant over time. This means that as the object moves, potential energy can be converted into kinetic energy and vice versa, but the total mechanical energy remains unchanged.
A common example of the conservation of mechanical energy is a simple pendulum. As the pendulum swings back and forth, its potential energy is highest at the maximum height of its swing, and its kinetic energy is highest at the lowest point of its swing. However, the sum of its potential and kinetic energies remains constant, neglecting any energy losses due to friction or air resistance.
It is important to note that the conservation of mechanical energy is a simplified principle that assumes no energy losses due to factors such as friction, air resistance, or non-conservative forces. In real-world situations, these factors often come into play, causing energy to be dissipated or transferred to other forms (such as heat or sound), resulting in a decrease in the total mechanical energy of the system.
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