Conservation of Energy and Energy Storage Methods

Law of Conservation of Energy

Energy in a closed system remains constant.

Isolated System

A system where no energy enters or leaves.

Energy Storage

Energy can change forms but total remains constant.

Energy Accounts

Different modes of energy storage in a system.

Feynman's Analogy

Blocks represent energy in a system.

Kinetic Energy

Energy due to motion of parts in a system.

Translational Kinetic Energy

Energy of motion along a path.

Rotational Kinetic Energy

Energy of rotation around an axis.

Thermal Energy

Energy from motion of particles in matter.

Potential Energy

Energy stored due to position or configuration.

Gravitational Energy

Energy due to an object's vertical position.

Elastic Energy

Energy stored from distortion of an object.

Chemical Energy

Energy from arrangement of atoms in molecules.

Energy Fields

Areas where energy is stored due to configuration.

Internal Energy

Total energy in an object, kinetic plus potential.

Force Field

An area of energy covering a specific place.

Energy Bar Graphs

Visual representation of energy distribution in a system.

Energy Transfer

Movement of energy into or out of a system.

Energy Conservation Principle

Energy cannot be created or destroyed.

Energy Change

Energy can change forms but total remains unchanged.

MARK ZRL

Method for analyzing energy in systems.

Independent variables

Cause, variable manipulated by researcher.

Dependent variables

Effect.

Hypotheses

Writing a hypothesis in proper form, make a prediction which describes how changing the independent variable will affect the dependent variable.

Running a controlled experiment

Change 1 thing at a time, important so you can identify what's influencing the results.

Constructing a proper data table

Titles, rulers, positions of independent and dependent variables, labeled columns with quantity (variable) and units.

Making Graphs

Titles (dependent vs. independent variable), rulers, positions of variables on axes, labeling axes with quantity (variable) and units, scaling axes correctly, point protectors, line of best fit, recognizing linear vs. curved graphs.

Analyzing and interpreting graphs

Is the graph linear or curved? Is the relationship between the variables direct, inverse, or is there no relationship? What does the graph show about the relationship between the variables? What does the graph mean?

Slopes

Calculating constants of proportionality (slopes) for linear graphs. Defining symbols for variables, writing the slope equation using delta (!) notation, marking points used for slope calculations, substituting values into slope equations including units, calculating the value of the slope including units.

Slope intercept

y = mx + b.

Linear, no go through origin

y = mx + b.

Direct proportion

Go through origin, y = mx.

Constant of proportionality

Tells you the fixed ratio between 2 variables in a proportional relationship.

Conclusions

Writing conclusions for experiments. What does the experiment show? How can you support your conclusions? Provide specific evidence for your conclusions.

Using graphs to predict the behavior of a system

Given a value for the independent variable, determine the value of the dependent variable using a graph.

Using equations to predict the behavior of a system

Given a value for the independent variable, determine the value of the dependent variable using an equation.

Graphs which show no relationship

Scatter plots + line graphs no relationship because uncorrelated variables, constant output, etc.

Inverse relationship

If x increases as y decreases proportionally.

Negative slope

Line / curve that slopes downwards.

Direct proportions

Straight line, goes through origin.

Direct proportion

Means that both variables change in the same direction at a constant rate.

y = kx

Equation representing direct proportion.

Position

Vector quantity of location of object relative to point / origin, most common unit meters.

Change in position

Displacement, x - xo, delta x with arrow over, distance away from origin / point, most common unit is meters.

Displacement

Vector, shortest straight line distance between starting + ending point of object.

Distance

Scalar, total length of path traveled by object.

Average velocity

v with line + arrow over it, total displacement / total time.

Vector

Change in position / change in time, measured in m/s.

Average speed

V with just line over it, total distance / total time.

Scalar

Just magnitude, examples include distance, speed, temperature.

Instantaneous velocity

v with arrow over it, velocity of object at specific time, found with tangent line or t mid + v, measured in m/s.

Uniform motion

Must have constant velocity + 0 acceleration + straight line graph.

Position vs. time graphs

Tells you position of object change over time, uniform motion, direction, velocity; slope means velocity.

Velocity vs. time graphs

Tells you velocity per unit of time, direction, type, acceleration; slope means acceleration.

Area under graph

Represents displacement.

Motion maps

Can you make a motion map for an object with uniform motion? Yes, dots cover equal distances in equal time intervals.

Stroboscopic photographs

Given a stroboscopic photograph can you collect position and time data to create a position vs. time graph and a velocity vs. time graph?

Proper format for problem solutions

Be sure that you know all of the required steps for solving physics problems including the diagram, given, find, equations, algebraic rearrangement of equations, substitution of values (including units) into equations and determining the final answer.

y = mx + b

Equation of a line in slope-intercept form.

x = vt + xo

Equation representing position as a function of time.

v = at + vo

Equation representing velocity as a function of time.

Acceleration

Rate of change of velocity per time, m/s².

Average acceleration

Change in velocity over time interval, m/s².

Instantaneous velocity

Velocity at a specific time, m/s.

Uniform acceleration

Constant rate of change in velocity.

Acceleration vs. time graph

Shows acceleration per unit time.

Slope of v vs. t graph

Indicates acceleration of the object.

Displacement

Area under velocity vs. time graph.

Motion maps

Visual representation of motion parameters.

Graph transformation

Convert between x vs. t, v vs. t, a vs. t.

Galileo's perfect squares

Distance increases quadratically with time.

Odd integer idea

Distance changes proportional to odd integers.

Aristotle's theory

Falling speed proportional to object's weight.

Galileo's theory

All objects fall at same rate.

x = xo + vot + ½ at²

Equation for position with uniform acceleration.

Slope of x vs. t² graph

Equals ½ of acceleration.

Acceleration

a = change in velocity / change in time.

Velocity vs. time graph

Used to determine change in position.

Transition points

Key points in graph transformations.

Uniformly accelerated motion

Straight line motion with constant acceleration.

Area under a vs. t graph

Represents change in velocity over time.

Significant Figures

Digits indicating measurement accuracy and precision.

Precision

Clarity and exactness of a measurement.

Accuracy

How close a measurement is to the true value.

Leading Zeros

Zeros before the first nonzero digit; not significant.

Trailing Zeros

Zeros after a decimal point; significant only if nonzero.

Addition/Subtraction Rule

Match to least precise decimal place.

Multiplication/Division Rule

Match to least precise significant figures.

Scientific Notation

Method to express large/small numbers using exponents.

Metric Prefixes

Standardized units: TERA, GIGA, MEGA, etc.

International System of Units (SI)

Global standard for measurements based on 7 units.

Fundamental Units

Base units: meter, kilogram, second, etc.

Derived Quantities

Units derived from fundamental units, e.g., newtons.

Physical Quantity

Measurable and quantifiable attribute.

Unit

Standardized quantity for expressing physical quantities.

Dimensional Analysis

Technique for converting between units.

Unit Conversion

Changing units using dimensional analysis.

Metric Conversions

Adjusting scale of units within the metric system.

SOHCAHTOA

Mnemonic for right triangle trigonometry ratios.

Exponent

Power to which a number is raised in notation.