Conservation of Energy — Revision Notes

⚡ 30-Second Revision

Conservation of Total Energy — Total energy of an isolated system is constant. Energy is transformed, not created/destroyed.
Kinetic Energy — $E_k = \frac{1}{2}mv^2$
Gravitational Potential Energy — $U_g = mgh$
Elastic Potential Energy — $U_s = \frac{1}{2}kx^2$
Mechanical Energy — $E_M = E_k + E_p$
Conservation of Mechanical Energy — $E_{k,i} + U_{i} = E_{k,f} + U_{f}$ (only if $W_{nc}=0$)
Work-Energy Theorem (General) — $W_{net} = \Delta E_k$
Work by Non-Conservative Forces — $W_{nc} = \Delta E_M = (E_{k,f} + U_{f}) - (E_{k,i} + U_{i})$
Conservative Forces — Work is path-independent, potential energy defined (e.g., gravity, spring).
Non-Conservative Forces — Work is path-dependent, dissipate mechanical energy (e.g., friction, air resistance).

2-Minute Revision

The core idea of Conservation of Energy is that the total energy in a closed system remains constant, merely changing forms. For NEET, the most frequently tested aspect is the Conservation of Mechanical Energy, which states that if only conservative forces (like gravity or spring force) do work, the sum of kinetic energy ($E_k = \frac{1}{2}mv^2$) and potential energy ($U_g = mgh$ or $U_s = \frac{1}{2}kx^2$) remains constant: $E_{k,i} + U_{i} = E_{k,f} + U_{f}$.

Remember to choose a consistent reference point for potential energy. If non-conservative forces like friction or air resistance are present, mechanical energy is *not* conserved. Instead, the work done by these non-conservative forces ($W_{nc}$) equals the change in mechanical energy: $W_{nc} = (E_{k,f} + U_{f}) - (E_{k,i} + U_{i})$.

This work done by non-conservative forces is typically negative, indicating a conversion of mechanical energy into heat or sound. Always identify the forces acting and the initial/final states of the system to correctly apply these principles.

5-Minute Revision

Conservation of Energy is a cornerstone of physics, asserting that energy cannot be created or destroyed, only transformed. For NEET, focus primarily on mechanical energy, which is the sum of kinetic energy ($E_k = \frac{1}{2}mv^2$) and potential energy ($U$). Potential energy can be gravitational ($U_g = mgh$) or elastic ($U_s = \frac{1}{2}kx^2$).

Key Principle 1: Conservation of Mechanical Energy

This applies when *only conservative forces* (gravity, spring force) do work. In such cases, the total mechanical energy remains constant:

$$E_{k,i} + U_{i} = E_{k,f} + U_{f}$$

Example: A ball dropped from height $H$. Initial: $E_k=0, U_g=mgH$. Final (just before hitting ground): $E_k=\frac{1}{2}mv^2, U_g=0$. So, $mgH = \frac{1}{2}mv^2$, leading to $v=sqrt{2gH}$.

Key Principle 2: Work-Energy Theorem with Non-Conservative Forces

When *non-conservative forces* (friction, air resistance) do work, mechanical energy is *not* conserved. Instead, the work done by these forces ($W_{nc}$) equals the change in mechanical energy:

$$W_{nc} = (E_{k,f} + U_{f}) - (E_{k,i} + U_{i})$$

Work done by friction is typically negative ($W_f = -f_k d$), indicating a loss of mechanical energy, which is converted into heat.

Example: A block slides down a rough incline. Initial: $E_{k,i}=0, U_{g,i}=mgh$. Final: $E_{k,f}=\frac{1}{2}mv^2, U_{g,f}=0$. The work done by friction is $W_f$. Then, $W_f = (\frac{1}{2}mv^2 + 0) - (0 + mgh)$.

Important Tips for NEET:

1
Identify forces — Determine if conservative, non-conservative, or both are acting.
2
Reference point — Choose $h=0$ strategically (e.g., lowest point of motion).
3
Units — Ensure consistency (SI units).
4
Initial/Final states — Clearly define $E_k$ and $U$ at the start and end points.
5
Springs — Remember $x$ is displacement from equilibrium.

Mastering these concepts allows you to solve a wide range of problems efficiently.

Prelims Revision Notes

1
Law of Conservation of Energy — Total energy of an isolated system is constant. Energy transforms, but is never created or destroyed.
2
Kinetic Energy ($E_k$) — Energy of motion. $E_k = \frac{1}{2}mv^2$. Always positive.
3
Potential Energy ($U$) — Stored energy due to position or configuration.

* **Gravitational Potential Energy ($U_g$)**: $U_g = mgh$. $h$ is height above a chosen reference level ($U_g=0$). * **Elastic Potential Energy ($U_s$)**: $U_s = \frac{1}{2}kx^2$. $k$ is spring constant, $x$ is displacement from equilibrium.

1
Mechanical Energy ($E_M$) — Sum of kinetic and potential energy: $E_M = E_k + U$.
2
Conservative Forces — Forces for which work done is path-independent (e.g., gravity, spring force). A potential energy function can be defined. Mechanical energy is conserved if only conservative forces do work.
3
Non-Conservative Forces — Forces for which work done is path-dependent (e.g., friction, air resistance). They dissipate mechanical energy, usually as heat or sound.
4
Conservation of Mechanical Energy — If only conservative forces do work, then $E_{M,i} = E_{M,f}$, or $E_{k,i} + U_{i} = E_{k,f} + U_{f}$.
5
Work-Energy Theorem (General) — The net work done on an object equals its change in kinetic energy: $W_{net} = \Delta E_k$.
6
Work Done by Non-Conservative Forces — If non-conservative forces are present, $W_{nc} = \Delta E_M = (E_{k,f} + U_{f}) - (E_{k,i} + U_{i})$. $W_{nc}$ is typically negative for dissipative forces.
7
Problem-Solving Steps

* Identify initial and final states (position, velocity, spring compression/extension). * Choose a convenient reference level for potential energy ($h=0$). * Determine if non-conservative forces are present. * Apply the appropriate energy conservation equation. * Solve for the unknown quantity.

1
Common Scenarios — Pendulum, free fall, inclined planes (with/without friction), spring-mass systems, roller coasters. Always convert units to SI (e.g., cm to m).

Vyyuha Quick Recall

MECH-E: Mechanical Energy Conserved Happily, Except for Non-Conservative Forces (NCF)!