What is the work done by a conservative force equal to?

The negative change in potential energy

What happens to light when it enters a medium with a higher refractive index?

It slows down and bends toward the normal

Work, Energy, and Waves Cheat Sheet

This cheat sheet covers fundamental concepts in physics, including the principles of work and energy conservation, the behavior of waves, and the physics of collisions and light refraction. It provides formulas, definitions, and examples to solidify understanding.

Core Principles

Energy is conserved; it can only be transferred or transformed.
Work is the transfer of energy by a force acting over a displacement.
Conservative forces result in changes in potential energy.
Non-conservative forces change the total mechanical energy.
The net work done on a system equals its change in kinetic energy.
Momentum is conserved in collisions if no external forces act.
Waves transfer energy through a medium or vacuum.
Interference occurs when waves overlap, leading to constructive or destructive effects.
Refraction is the bending of light as it passes between media with different refractive indices.
Total internal reflection occurs when light strikes a boundary at a critical angle or greater.

Action Steps

Identify the forces acting on the system.
Determine if forces are conservative or non-conservative.
Calculate work done by each force.
Apply the work-energy theorem ($W_{net} = \Delta K$).
Analyze momentum before and after collisions ($p_i = p_f$).
Identify wave properties: amplitude, frequency, wavelength, speed.
Determine the type of interference based on path difference.
Use Snell's Law to calculate angles of refraction.
Check for total internal reflection conditions.

Formulas

$W_c = -\Delta U$
$W = F \cdot \Delta r = F \Delta r \cos(\theta)$
$W_{net} = \Delta K$
$p = mv$
$F_{net} = m a$
$J = \Delta p = F_{net} \Delta t$
$y(x, t) = A \sin(kx \pm \omega t)$
$c = f \lambda$
$n = c/v$
$n_1 \sin(\theta_1) = n_2 \sin(\theta_2)$

Key Terms

Work: Energy transferred by a force acting over a displacement.
Conservative Force: A force for which the work done is independent of the path taken (e.g., gravity, spring force).
Non-conservative Force: A force for which the work done depends on the path taken (e.g., friction).
Kinetic Energy: The energy an object possesses due to its motion ($K = 1/2 mv^2$).
Potential Energy: Stored energy due to position or configuration (e.g., gravitational, elastic).
Momentum: A measure of an object's motion, calculated as mass times velocity ($p = mv$).
Impulse: The change in momentum of an object, equal to the net force multiplied by the time interval ($J = F_{net} \Delta t$).
Wave: A disturbance that transfers energy through a medium or space.
Interference: The superposition of two or more waves, resulting in constructive or destructive effects.
Refraction: The bending of light as it passes from one medium to another.
Refractive Index: A measure of how much light slows down in a medium ($n = c/v$).
Total Internal Reflection: The complete reflection of light within a medium when it strikes the boundary at an angle greater than or equal to the critical angle.

Timeline

Ancient Greece: Early concepts of energy and motion explored by philosophers.
17th Century: Newton develops laws of motion and universal gravitation, laying groundwork for work and energy.
18th-19th Century: Development of the concept of energy conservation and the definition of work by scientists like Coriolis and Joule.
19th Century: Maxwell unifies electricity and magnetism, describing electromagnetic waves.
Late 19th Century: Huygens' principle and wave phenomena like interference and diffraction are studied.
Early 20th Century: Einstein's theories of relativity and quantum mechanics revolutionize understanding of energy and matter.

People

Isaac Newton: Formulated laws of motion and universal gravitation, fundamental to work and energy calculations.
James Prescott Joule: Conducted experiments establishing the conservation of energy and the mechanical equivalent of heat.
Christiaan Huygens: Proposed a wave theory of light and described wave phenomena.
Willard Gibbs: Developed concepts of thermodynamic potential and statistical mechanics.
Willem Snellius: Discovered the law of refraction (Snell's Law).

Quiz

What is the work done by a conservative force equal to?: The negative change in potential energy
In an inelastic collision, which quantity is conserved?: Momentum
What happens to light when it enters a medium with a higher refractive index?: It slows down and bends toward the normal