## Simulation documentation

A computer simulation of a particle obeying Newton's laws of motion, on a ramp with dry friction, acting under gravity.

The user-controlled options in the simulation are:

• Ramp shape (e.g. linear, quadratic, etc.)
• Ramp steepness (from 0 to 100)
• Ramp y-intercept (from 0.00 m to 3.00 m)
• Particle's initial x co-ordinate (X0) (from 0.00 m to 6.00 m).
• Particle's initial velocity (V0) tangential to the ramp (from −99.99 m/s to 99.99 m/s).
If the particle's speed is too large, it will fly off the ramp and the simulation will end.
• Co-efficient of friction (μ) between the particle and the ramp (from 0.000 to 1.000).
If this is too large, the particle may not move at all.
• Time increment (dt) used to iteratively calculate the particle's motion (from 0.000001 s to 0.000100 s).
The smaller the value, the more accurate the simulation, but the slower it will run. A higher value leads to a less accurate simulation that runs faster. It should not normally be necessary to change the default value of dt unless you are using a very slow or very fast computer.

The mass of the particle and the gravitational field strength are fixed at 1.00 kg and 9.81 N/kg respectively.

When the “Start Simulation” button is pressed, the ramp is drawn and the particle's motion plotted. Whilst moving from left to right, the particle's path is plotted in blue. Whilst moving from right to left, its path is plotted in red.

The simulation will automatically end if the particle reaches one end of the ramp or if it is going too fast to stay on the ramp's surface. The simulation will also end automatically if the particle does not have enough speed to move. At other times it is necessary to end the simulation manually using the “Stop Simulation” button.

Whilst the simulation is running, the particle's x and y co-ordinates are displayed at the top right of the screen, next to the time counter. The particle's kinetic energy (KE), its change in gravitational potential energy (PE) and the work it has done against friction are also displayed.

When the simulation ends, a brown line is drawn between the particle's initial and final positions. This represents the path the particle would have taken were it to have travelled along a linear ramp between those points. The work it would have done against friction on this ramp is then also displayed at the top right of the screen, underneath the actual work done against friction by the particle during the simulation. This allows for easy comparison between the two values.

The particle's initial conditions can be changed between simulations using the boxes at the top right of the screen. To change the ramp settings, simply press the “Choose a different ramp” button.