How to Use the Systems of Masses Simulator
 

View & Playback

• Use the view options to set the simulator to Dark, Light, or Landscape mode. Dark and Light are simplified "scientific" views, while Landscape gives a less abstract picture of what's happening.

• Use Play to start the simulation and Reset to return the blocks to the start.

• The speed buttons (0.1× to 4×) control how fast the simulation runs, which makes it easier to see what's happening.
   

Number of Objects

• Choose how many blocks are tied together, from 1 to 5. Each block gets its own mass slider, and a tension readout appears for each string between them.
   

Parameters

• Set the mass of each block (m1, m2, and so on) in kilograms.

• Applied Force (Fₐ) pulls on the front of the train.

• Gravity (g) sets the gravitational field strength, which affects the weight, the normal force, and friction.
   

Friction

• Turn on Enable Friction to make the surface rough, then set the coefficient of friction.
  Note for teachers: With friction on, the net force is the applied force minus the total friction on all the blocks. This is a good place to check whether students are treating the system as a whole.
   

Calculated Forces

• This section gives a live readout of the Total mass (Σm), Weight (Fg), Normal force (Fn), each string Tension, Net Force (Fnet), and Acceleration (a). Net force and acceleration appear once you hit Play.
  Mastery tip: Look at the tensions from front to back. Each string only has to accelerate the blocks behind it, so the tension drops the farther back you go.
   

Display

• Force Arrows lets you choose which forces to draw: on m1 only, on All blocks individually, or on the whole System as one object.

• Switch between All and System to compare the two ways of drawing the same situation. In the System view, the tensions disappear because they are internal forces.

• Motion Graphs adds live position, velocity, and acceleration graphs.
  Note for teachers: The m1, All, and System options make a great discussion about choosing a system. Ask students which forces disappear when you draw the whole train as one object, and why.
   

Live Readout

• Net Force, Acceleration, Velocity, Position, and Time update live while the simulation plays.
   

System Challenge (Test your understanding!)

• Difficulty: Easy, Medium, or Hard.

• The Given panel lists the known values, such as the masses and the target acceleration. Your task is to find the missing value, for example the applied force needed to produce that acceleration.

• Solve the challenge and click Check. Play stays locked until you check your answer, so you can't just run the simulation to find it.

• If you're stuck, use Get a Hint. Use New Challenge for another problem.
  Mastery tip: If you need hints, use them! Just keep working new challenges until you can solve them without the hints.
   

Tension Challenge

• This challenge needs at least two blocks.

• Step 1 asks for the acceleration of the whole system. Once that is correct, you solve for each tension in turn.

• Complete Step 1 and all of the tensions to unlock Play and watch your answers in action.
  Mastery tip: For each tension, draw a system that includes only the blocks behind that string. The tension is the only horizontal force pulling that smaller system forward.
   

Lab

• Choose a lab to investigate. Data is recorded instantly from the parameters, so you don't need to run the simulation.

  • a vs F (find total mass): the masses are locked. Vary the applied force and record the acceleration each time. Force is your independent variable, acceleration is your dependent variable, and the total mass is your constant variable.

  • a vs Σm (find applied force): the applied force is locked. Vary the total mass and record the acceleration. Mass is your independent variable, acceleration is your dependent variable, and the applied force is your constant variable. This graph is not linear, so plot a vs 1/Σm to linearize it.

• Click Record Data Point after each change. Your data appears in a table, and you need at least five points before you can submit.

• Use the slope of your graph to find the hidden value, total mass in the first lab and applied force in the second.

• Use the Copy buttons to paste your data table and graph into a document for your teacher, and New lab (different setup) to start over.