Mechanical Energy
In the science of physical streams, mechanical energy is the sum of potential energy and kinetic energy. It is the macroscopic energy associated with a system. The conservation principle of mechanical energy states that if an isolated subject of a system is only to conservative forces then the mechanical energy is constant.
If an object really moves in the direction which is opposite of a conservative net force, the energy which is potential will increase and if the speed of the object changes. The kinetic energy of the object also changes.
Conservation of Mechanical Energy
In all systems which are real, the force which is nonconservative. For example, frictional forces will be present but if they are of negligible magnitude the mechanical energy changes a little and its conservation is a useful approximation.
In the elastic collisions, the kinetic energy is conserved. but in the inelastic collisions, some mechanical energy may be converted into thermal energy.
Many devices are used to convert mechanical energy to or from other forms of energy. An electric motor converts electrical energy to mechanical energy while an electric generator converts mechanical energy into electrical energy and a heat engine converts heat energy to mechanical energy.
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Law of Conservation of Mechanical Energy
If we see that according to the principle of conservation of mechanical energy, in an isolated system the mechanical energy remains constant in time, provided the system is free of friction and other forces which are non-conservative. In any situation which is real and frictional forces and other non-conservative forces are present, the energy though cannot be destroyed or created in an isolated system, it can be converted to another energy form.
In a swinging pendulum which is subjected to the conservative gravitational force and frictional forces like air drag and friction, at the pivot are energies which are negligible. The passed energy is back and forth between kinetic and potential energy but never leaves the system. The pendulum reaches the greatest kinetic energy and least potential energy when in a vertical position. This is owing to the greatest speed and be the direction which is nearest to the Earth at this point.
On the other hand, we can see that it will have its least kinetic and greatest potential energy at the extreme positions of its swing because it has zero speed and is at the farthest from the earth at these points. However, taking the frictional force into account, there is a loss of mechanical energy with each swing because of the work which is negatively done on the pendulum by these forces which are non-conservative.
Principle
Mechanical energy is the sum of the kinetic and potential energies in a system. The principle of the conservation of energy states that the total mechanical energy in a system is the sum of the potential and the kinetic energies which remain constant as long as the forces which are acting are conservative forces.
We could easily use a circular definition and that says that a conservative force doesn't change the total energy. Fiction, on the other hand, a force which is non-conservative because it acts to reduce the mechanical energy in a system. Note here that forces which are non-conservative do not always reduce the mechanical energy.
FAQs on Conservation of Mechanical Energy
1. What is the principle of conservation of mechanical energy and its formula?
The principle of conservation of mechanical energy states that for an isolated system where work is done only by conservative forces, the total mechanical energy of the system remains constant. Mechanical energy is the sum of kinetic energy (KE) and potential energy (PE). The formula is expressed as:
ME = KE + PE = Constant
This can also be written as Kᵢ + Uᵢ = Kₒ + Uₒ, where 'i' denotes the initial state and 'f' denotes the final state. Here, K is kinetic energy (½mv²) and U is potential energy (e.g., mgh for gravitational potential energy).
2. How does the conservation of mechanical energy apply to a freely falling body?
For a freely falling body, we ignore air resistance, making gravity the only force acting on it. Gravity is a conservative force. Let's consider three points in its fall:
- At Maximum Height (A): The body is momentarily at rest, so kinetic energy is zero, and potential energy is maximum (PE = mgh).
- During the Fall (B): As the body falls, its height decreases, reducing its potential energy. This lost potential energy is converted into kinetic energy, increasing its speed.
- Just Before Hitting the Ground (C): Height is nearly zero, so potential energy is minimal, and speed is maximum, making kinetic energy maximum.
At every point in the fall, the sum of kinetic and potential energy (KE + PE) remains the same, perfectly demonstrating the conservation of mechanical energy.
3. What is the key difference between conservative and non-conservative forces?
The key difference lies in their effect on a system's mechanical energy:
- Conservative Forces (e.g., gravity, elastic spring force) are path-independent. The work done by them in a closed loop is zero. They do not dissipate mechanical energy; they only convert it between kinetic and potential forms.
- Non-Conservative Forces (e.g., friction, air resistance, tension) are path-dependent. The work done by them depends on the path taken and results in the dissipation of mechanical energy, usually as heat or sound. In their presence, total mechanical energy is not conserved.
4. Can you provide some real-world examples of conservation of mechanical energy?
Yes, several real-world systems approximate the conservation of mechanical energy:
- A Roller Coaster: At the top of a hill, a coaster has maximum potential energy. As it descends, this is converted into kinetic energy, increasing its speed. This process reverses as it climbs the next hill.
- A Swinging Pendulum: At its highest points, the pendulum bob has maximum potential energy. At the lowest point of its swing, it has maximum kinetic energy.
- An Archer's Bow: The potential energy stored in the stretched bow and string is converted into the kinetic energy of the arrow upon release.
- A Bouncing Ball: In an ideal elastic collision, the ball's potential energy at its peak height converts to kinetic energy as it falls, which is then briefly stored as elastic potential energy on impact before converting back.
5. How can we derive the principle of conservation of mechanical energy using the work-energy theorem?
The derivation begins with the Work-Energy Theorem, which states that the total work done (W_total) on an object equals the change in its kinetic energy (ΔK). So, W_total = ΔK. If only conservative forces (W_c) are acting, the work done by these forces is also equal to the negative change in potential energy (ΔU). Thus, W_c = -ΔU. By equating these two expressions for work, we get:
ΔK = -ΔU
K_f - K_i = -(U_f - U_i)
K_f - K_i = -U_f + U_i
Rearranging the terms, we get:
K_f + U_f = K_i + U_i
This equation proves that the final total mechanical energy is equal to the initial total mechanical energy.
6. Why is the law of conservation of mechanical energy different from the law of conservation of energy?
This is a crucial distinction. The law of conservation of mechanical energy is a specific case that applies only when non-conservative forces like friction are absent. It deals strictly with the sum of kinetic and potential energies remaining constant. In contrast, the general law of conservation of energy is a fundamental principle of physics that is always true. It states that the total energy in an isolated system (including all forms like heat, sound, light, etc.) is always conserved; it can only be transformed from one form to another, not created or destroyed. So, when friction causes a loss of mechanical energy, that energy is simply converted into thermal energy, and the total energy is still conserved.
7. Why isn't mechanical energy conserved when a car applies its brakes and comes to a stop?
When a car brakes, a strong non-conservative force—friction—comes into play between the brake pads and the wheels, and between the tires and the road. This frictional force does negative work on the car, converting its massive kinetic energy into other forms of energy, primarily thermal energy (heat) and sound. While the car's mechanical energy decreases to zero, the total energy of the system is still conserved because it has been transformed, not destroyed.
