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Vector Addition - model description

This document is a high-level description of the model used in PhET's Vector Addition simulation.

Explore 1D screen

The Explore 1D screen facilitates exploration of vectors in 1 dimension. Vectors are constrained to either horizontal or vertical orientation.

To manipulate vectors:

  • add/remove vectors by dragging them between the toolbox and the graph
  • move a vector by dragging its tail (constrained to the graph's grid)
  • scale a vector by dragging its tip (constrained to the graph's grid)

Selection of the orientation is controlled by the radio buttons at the lower-right of the screen.

In the horizontal orientation:

  • 3 vectors can be created, labeled a⃗, b⃗, and c⃗
  • the y component of all vectors is zero
  • the sum is a⃗ + b⃗ + c⃗ = s⃗

In the vertical orientation:

  • 3 vectors can be created, labeled d⃗, e⃗, and f⃗
  • the x component of all vectors is zero
  • the sum is d⃗ + e⃗ + f⃗ = s⃗

Explore 2D screen

The Explore 2D screen facilitates exploration of vectors in 2 dimensions, and introduces component vectors (and their various representations).

To manipulate vectors:

  • add/remove vectors by dragging them between the toolbox and the graph
  • move a vector by dragging its tail (constrained to the graph's grid)
  • scale or rotate a vector by dragging its tip (constrained to the graph's grid)
  • component vectors cannot be directly manipulated

There are 2 "snap modes" that determine which vector quantities snap to integer values. Selection of the snap mode is controlled by the radio buttons at the lower-right of the screen.

In Cartesian snap mode:

  • 3 vectors can be created, labeled a⃗, b⃗, and c⃗
  • vector x and y components snap to integer values
  • the sum is a⃗ + b⃗ + c⃗ = s⃗

In Polar snap mode:

  • 3 vectors can be created, labeled d⃗, e⃗, and f⃗
  • vector magnitude snaps to integer values
  • vector angle snaps to 5-degree intervals
  • the sum is d⃗ + e⃗ + f⃗ = s⃗

Lab screen

The Lab screen is similar to the Explore 2D screen, with these differences:

  • each snap mode has 2 sets of vectors (blue and red for Cartesian, purple and green for Polar)
  • 10 vectors can be created for each set of vectors
  • the sum for a set of n vectors is v⃗1 + v⃗2 + ... + v⃗n = s⃗

Equations screen

The Equations screen introduces the concepts of base vectors, equations, and coefficients. Like the Explore 2D and Lab screens, it has Cartesian and Polar "snap modes" that determine which vector quantities snap to integer values.

The Equations screen has a couple of differences in how the student manipulates vectors:

  • Vectors are pre-populated on the graph; the student does not add and remove vectors.
  • Vectors can be moved directly on the graph, but their other properties must be changed using spinners.

In Cartesian snap mode:

  • the graph shows vectors labeled a⃗, b⃗, and c⃗
  • base vectors are provided for a⃗ and b⃗
  • x and y components can be changed for base vectors; range is [-10,10], integers
  • coefficients can be changed for a⃗ and b⃗; range is [-5,5], integers
  • vector c⃗ is derived based on the selection of one of these equations:
    • a⃗ + b⃗ = c⃗
    • a⃗ - b⃗ = c⃗
    • a⃗ + b⃗ + c⃗ = 0

In Polar snap mode:

  • the graph shows vectors labeled d⃗, e⃗, and f⃗
  • base vectors are provided for d⃗ and e⃗
  • magnitude and angle can be changed for base vectors
  • base vector magnitude range is [-10,10], integers
  • base vector angle range is [-180,180] degrees, in 5-degree intervals
  • coefficients can be changed for d⃗ and e⃗; range is [-5,5], integers
  • vector f⃗ is derived based on the selection of one of these equations:
    • d⃗ + e⃗ = f⃗
    • d⃗ - e⃗ = f⃗
    • d⃗ + e⃗ + f⃗ = 0