play phryzby with physics

The Only Vector

solved Vectors

Q. Which one of these is a vector?

How it's solved

Solved with Vectors

Working
  1. temperature: a scalar, a size alone
  2. pressure: a scalar, a size alone
  3. impulse: a vector, it has a direction
  4. time: a scalar, a size alone
  5. power: a scalar, a size alone
  6. total path length: a scalar, a size alone
  7. energy: a scalar, a size alone
  8. gravitational potential: a scalar, a size alone
  9. coefficient of friction: a scalar, a size alone
  10. charge: a scalar, a size alone
Conclusion

Impulse is a force acting over a time, and it points the way the force pushes. Pressure pushes on every surface alike, whichever way it faces, so it has no direction of its own.

The web of concepts

given read from the words equation asked

The Ruby that solves it

The question and its solution are small Ruby files. The engine runs them.

question.rb
1require_relative "../physics"23question :the_only_vector do4  kind :scq5  describes "Which one of these is a vector?"67  option "temperature"8  option "pressure"9  option "impulse"10  option "time"11  option "power"12  option "total path length"13  option "energy"14  option "gravitational potential"15  option "coefficient of friction"16  option "charge"17end
solution.rb
1require_relative "../questions/the_only_vector"2require_relative "../science/motion_in_a_plane/vectors"34solve :the_only_vector, using: Vectors do5  answer options.select { |o| o.content.to_quantity.vector? }67  conclusion "Impulse is a force acting over a time, and it points the way the force pushes. " \8             "Pressure pushes on every surface alike, whichever way it faces, so it has no " \9             "direction of its own."10end
playground.rb
1require_relative "../solutions/the_only_vector"23play_with :the_only_vector do4  title "The Only Vector"5end
The laws it drew on
quantitywrittenunitswithinfrom
volumevolume——Vectors
massmass——Vectors
speedspeed——Vectors
densitydensity——Vectors
number of molesn——Vectors
angular frequencyangularfrequency——Vectors
workwork——Vectors
currentcurrent——Vectors
temperaturetemperature——Vectors
pressurepressure——Vectors
timetime——Vectors
powerpower——Vectors
total path lengths——Vectors
energyenergy——Vectors
gravitational potentialgravitationalpotential——Vectors
coefficient of frictionμ——Vectors
chargecharge——Vectors
accelerationacceleration——Vectors
velocityvelocity——Vectors
displacementdisplacement——Vectors
angular velocityangularvelocity——Vectors
forceforce——Vectors
angular momentumangularmomentum——Vectors
linear momentumplin——Vectors
electric fieldelectricfield——Vectors
average velocityaveragevelocity——Vectors
magnetic momentmagneticmoment——Vectors
relative velocityvAB——Vectors
impulseimpulse——Vectors
first vectorA—0 … ∞Vectors
second vectorB—0 … ∞Vectors
angle betweenφ—0 … 3.142Vectors
resultantR—0 … ∞Vectors
resultant directionβ—0 … 3.142Vectors
directionα—-3.142 … 3.142Vectors
x componentAx——Vectors
y componentAy——Vectors
A=Ax2+Ay2
magnitude from components
R2=A2+B2+2⋅A⋅B⋅cos⁡φ
law of cosines
R⋅sin⁡β=B⋅sin⁡φ
law of sines
R⋅cos⁡β=A+B⋅cos⁡φ
along the first
Ax=A⋅cos⁡α
resolved along x
Ay=A⋅sin⁡α
resolved along y