Cart Motion Lab: Change Force, Mass, and Friction
Simulate a cart on a level surface. Change force, mass, and friction, then compare position, velocity, and acceleration graphs.
Free, with no sign-up.
For High school students and adults reviewing the topic.
About 8 minutes.
How does it work?
- Change a control or choose a preset. All three graphs use the same time axis.
- Move the time control to inspect the cart and the three graphs at the same instant.
- Adjust the controls, then check a challenge.
What will you get?
Compare ten seconds of motion and solve two force challenges.
What does the model assume?
- The cart moves in one dimension on a level surface. Right is positive; initial position is zero.
- Gravity is 9.8 m/s². Mass and applied force stay constant for each ten-second run.
- Sliding friction has magnitude μmg and opposes velocity. The symbol μ is the friction coefficient.
- At rest, static friction balances the applied force up to μmg. This simplified model uses the same coefficient for static and kinetic friction.
- At a stop, the cart stays still unless the applied force exceeds the friction limit. Air resistance and wheel rotation are omitted.
Which setup would you like to try?
What can you change?
Range: -20 to 20 N.
Range: 0.5 to 10 kg.
Range: 0 to 0.6 .
Range: -5 to 5 m/s.
What does the model predict?
| Quantity | Value | Unit |
|---|---|---|
| Position after 10 s | 100 | m |
| Velocity after 10 s | 20 | m/s |
| Initial acceleration | 2 | m/s² |
| Time (s) | Position (m) | Velocity (m/s) | Acceleration (m/s²) |
|---|---|---|---|
| 0 | 0 | 0 | 2 |
Read the motion as a table
| Time (s) | Position (m) | Velocity (m/s) | Acceleration (m/s²) |
|---|---|---|---|
| 0 | 0 | 0 | 2 |
| 1 | 1 | 2 | 2 |
| 2 | 4 | 4 | 2 |
| 3 | 9 | 6 | 2 |
| 4 | 16 | 8 | 2 |
| 5 | 25 | 10 | 2 |
| 6 | 36 | 12 | 2 |
| 7 | 49 | 14 | 2 |
| 8 | 64 | 16 | 2 |
| 9 | 81 | 18 | 2 |
| 10 | 100 | 20 | 2 |
Can you reach these targets?
Start from rest with a 2 kg cart and no friction. Reach 20 m/s after 10 s.
- Target: Cart mass = 2 kg; tolerance 0 kg.
- Target: Friction coefficient = 0 ; tolerance 0 .
- Target: Initial velocity = 0 m/s; tolerance 0 m/s.
- Target: Velocity after 10 s = 20 m/s; tolerance 0.05 m/s.
Keep a 5 kg cart moving at 2 m/s for 10 s with μ = 0.20.
- Target: Cart mass = 5 kg; tolerance 0 kg.
- Target: Friction coefficient = 0.2 ; tolerance 0 .
- Target: Initial velocity = 2 m/s; tolerance 0 m/s.
- Target: Velocity after 10 s = 2 m/s; tolerance 0.02 m/s.
- Target: Position after 10 s = 20 m; tolerance 0.05 m.