Physics and Engineering: Key Variables, Relationships, and Graphs

What is an independent variable?

The factor being manipulated in an experiment.

What is a dependent variable?

The variable that depends on the independent variable for its outcome.

What is a line of best fit?

A model used to make predictions from data.

What is a linear relationship?

A relationship where a scatter plot forms a straight line.

What is a nonlinear relationship?

A relationship that does not form a straight line.

What is a quadratic relationship?

A nonlinear relationship where the variable depends on x².

What is an inverse relationship?

When one variable depends on the inverse of another (y = a/x).

Why do scientists use relationships?

To make predictions about values.

What is the main goal of experiments?

To discover a pattern.

What does a circle graph show?

Parts of a whole.

What does a bar graph show?

How a quantity varies with different factors.

What is percent error a measure of?

How precise your measurements are.

What is the percent error formula?

(True value - Measured value) / True value.

What does negative percent error mean?

Measured value is short of true value.

What does positive percent error mean?

Measured value is above true value.

What is interpolation?

Reading data between measured points.

What is extrapolation?

Extending a line beyond plotted data to estimate values.

What is the first step in the engineering process?

Define the problem.

What are the steps in the engineering process?

Define, Research, Brainstorm, Design, Choose, Build, Test, Redesign.

What questions define an engineering goal?

Who, What, Why.

What is the difference between defining a problem and recognizing a need?

Defining is specific and addresses a real need; recognizing is realizing something could be improved.

What must engineering goals be?

Specific but broad enough to allow solutions.

In what point of view should engineering documentation be written?

Third person.

What are the types of technical drawings?

Freehand, CAD, Instrument.

What is the important face in a basic diagram?

The face that faces you.

What angle is used in isometric drawing?

30 degrees.

What does orthographic projection show?

Top, front, and side views.

How many principal views exist?

Six: top, bottom, left, right, front, back.

What do visible lines represent?

Edges you can see; they outrank all others.

What do hidden lines represent?

Edges you cannot see.

What do center lines represent?

Centers of circles only.

What is the engineering definition of scaling?

Representing a life-sized object by proportionally adjusting its size on paper.

What should you always give when scaling?

Real measurements.

How many miles is 1 km?

0.62 miles.

What does tolerance mean?

How close values must be for the system to work properly.

What happens to corresponding sides when scaling?

They change by the same factor.

What happens to corresponding angles when scaling?

They remain unchanged.

What is a motion diagram?

A series of images showing position at equal time intervals.

How are coordinate systems imagined?

As local to the observer.

What is the displacement formula?

d = d_final - d_initial.

What is the average velocity formula?

v = displacement / time.

What is the time interval formula?

t = t₁ - t₀.

What does a position-time graph show?

d on y-axis, t on x-axis.

What is the average acceleration formula?

a = change in velocity / time.

What does the area under a velocity-time graph give?

Displacement.

What is instantaneous velocity?

Velocity at a specific moment.

What is kinematics?

Study of motion without considering causes.

What is the first kinematic equation?

d = ((vf + vi)/2) t.

What are the variables in the first kinematic equation?

d, t, vf, vi.

What is the second kinematic equation?

vf = vi + at.

What are the variables in the second kinematic equation?

vi, vf, a, t.

What is the third kinematic equation?

d = vit + (1/2)at².

What are the variables in the third kinematic equation?

d, vi, t, a.

What is the fourth kinematic equation?

vf² = vi² + 2ad.

What are the variables in the fourth kinematic equation?

vi, vf, a, d.

What is the velocity in circular motion formula?

v = 2πr / T.

What is the period?

Time for one complete revolution.

What does constant velocity mean?

vf = vi and a = 0.

What is a projectile?

Object under the influence of gravity only.

What is the horizontal motion acceleration?

Zero.

What is the vertical motion acceleration?

9.8 m/s² downward.

What is the horizontal displacement formula?

x = vix t.

What is the vertical displacement formula?

y = viy t + ½ g t².

What is the horizontal velocity?

Constant.

What is the vertical velocity?

Changes by 9.8 m/s each second.

What is the vix formula?

vi cosθ.

What is the viy formula?

vi sinθ.

What is the time to peak height formula?

t = viy / g.

What is the hang time formula?

2 × time to peak.

What is the maximum height formula?

y = viy t + ½ g t².

What is the range formula?

dx = vx × hang time.

How is force measured?

In Newtons.

What is Newton's First Law?

Objects remain at rest or constant velocity unless acted on by net force.

What is Newton's Second Law?

F = ma.

What is Newton's Third Law?

Every action has an equal and opposite reaction.

What is torque?

Ability of a force to rotate an object.

What is the torque formula?

T = Fd sinθ.

What are the units of torque?

Newton-meters (Nm).

What is the sign of clockwise torque?

Positive.

What is the sign of counterclockwise torque?

Negative.

What are the types of forces?

Friction, tension, normal, air resistance, applied, spring, gravitational.

What is static friction?

Opposes start of motion.

What is kinetic friction?

Opposes motion in progress.

What is the kinetic friction formula?

Fₖ = μₖ Fₙ.

What is the static friction limit?

0 < Fₛ ≤ μₛ Fₙ.

What is the direction of normal force?

Perpendicular to surface.

What is Fgx always?

Parallel to incline.

What is Fgy always?

Perpendicular to incline.

What did Mesopotamians engineer?

First canals.

What did Assyrians engineer?

Iron weapons.

What did Egyptians engineer using?

Accuracy, limestone, massive labor.

What did Greeks contribute?

Hydrostatics, mechanical advantage, screws/fasteners.

What did Romans develop?

Roads, bridges, cement, water wheels, sewers, trusses.

What were Asian engineering contributions?

Curved roofs, irrigation canals, bamboo bridges, wheelbarrow.

What did European medieval engineering focus on?

Statics, forces in walls, trusses, water-powered machinery.

What were Renaissance contributions?

Engineering schools and formal disciplines.

What were the contributions of the Second Industrial Revolution?

Telegraph, railroads, gas/water, sewage, phones, electricity, assembly line.

What is the universal gravitation formula?

F = G(m₁m₂) / d².

What is the value of G?

6.67 × 10⁻¹¹ N·m²/kg².

What happens to gravity when distance doubles?

Becomes 1/4 as strong.