Simulation · Dynamics

Forces, friction, and motion

Explore how applied force, surface angle, and static or kinetic friction determine whether a block remains at rest, begins to slide, or changes its motion.

Physical model

Tangential forces, contact, and two friction regimes

A block moves along a rigid surface. Static friction takes the required value up to its limit; while sliding, kinetic friction opposes velocity.

N=mgcosβ−FsinαFdrive=Fcosα−mgsinβ|fs|≤μsN·|fk|=μkN∑F∥=ma∥

The expression for N assumes maintained contact and zero perpendicular acceleration.

2D Canvas · tracking view

Motion and forces along the surface

The block remains near the center while surface marks record its displacement.

StateStatic · at rest

The scene shows only the block, surface, and selected vectors. The accessible FBD, equations, and graphs sit outside the Canvas.

Display

F, W, N, and f are forces; v [m/s] and a [m/s²] use dashed lines and independent visual scales.

Force analysis

Free-body diagram

Isolated block with weight, normal force, applied force, and friction, oriented relative to the surface.WNFf

The components are projections of weight, not additional forces.

Current substitution

Live equations

N=mgcosβ−Fsinα={display(readings.normal)} NFdrive=Fcosα−mgsinβ={display(-Number(readings.requiredStatic))} N
fs=−Fdrive={display(readings.friction)} N|fs|≤μsN·∑F∥=0·a=0
Graphs

Last ten seconds

Time evolution

v(t)

Graph of velocity along the surface over time, preserving sign and showing the current point.

ΣF∥(t)

Graph of net parallel force over time, preserving sign and showing the current point.

Regime comparison

Friction and threshold versus applied force

Relationships with applied F

Compares friction required for rest, the static maximum, and kinetic friction as F varies while other parameters remain fixed.
  • Friction required for rest
  • Static maximum μ_sN
  • Kinetic μ_kN

Current state: rest is possible.

Static threshold

Required and available friction

Required
20 N
Maximum
49 N
Current friction
20 N
Required / static maximum
40.82 %

Rest is compatible with the static limit.

Live readings

Physical state

Instant t
0 s
Position along the surface s
0 m
Velocity v
0 m/s
Acceleration a
0 m/s²
Normal force N
98 N
Friction force f
-20 N
Net parallel force ΣF∥
0 N

Paused

Exploration guide

What to observe

  1. 01

    Use the “Friction and threshold” graph while increasing F. Notice that f_s matches the required force before reaching its maximum.

  2. 02

    Cross the static threshold and compare μ_sN with the kinetic friction that follows.

  3. 03

    Compare the inclined-plane presets: the weight component may be smaller or larger than the maximum static friction.

  4. 04

    In “Pulling reduces the normal force”, change alpha and observe how N changes and shifts both the static-maximum and kinetic curves.

  5. 05

    Give the block a positive initial velocity and configure a negative net force: velocity and acceleration can point in opposite directions while the block slows down.

Scope

Model limits

Particle model constrained to a rigid surface. It uses a Coulomb dry-friction law and ignores air resistance, deformation, rolling, and block rotation. If the parameters would require N ≤ 0, the simulation stops the contact model instead of inventing a negative normal force.