DYNAMICS · NEWTON’S SECOND LAW
Inclined Plane
Explore the forces acting on a block: weight, normal reaction, static and kinetic friction, and applied force. Observe equilibrium, upward and downward motion, stopping and restarting, with analytical calculations for each phase.
Physical Parameters
Controls
Examples: frictionless · static equilibrium · sliding · ascent and stop · reversal · applied force.
Force Diagram and Motion
True Geometric Scale 1:1: Horizontal and vertical distances use the same scale. Force-arrow lengths use a separate scale, independent of meters.
Arrows show the actual force directions; their relative lengths are illustrative. The weight components are dashed: they are not additional forces. A collision with a boundary is inelastic, with no rebound. On phones, scroll horizontally to see the full plane and read the arrows.
Results and Physical Conditions
Synchronized Graphs
Coordinate s follows the plane: s = 0 at the bottom, s = L at the top. Acceleration jumps correspond to actual changes in the motion regime; at a boundary the velocity becomes zero after an inelastic impact. Select a point on a graph or enter an exact time.
Position s(t)
Velocity v(t)
Acceleration a(t)
Net Force F(t)
Values Table
| t (s) | s (m) | v (m/s) | a (m/s²) | F (N) | Motion Regime |
|---|
Stopping events and boundary contacts are included.
SI units; decimal point and comma-separated values.
Physical Model
Apply Newton's second law along the plane: the sum of the parallel forces equals mass times acceleration.
At Rest: Static friction adjusts to balance the driving force up to its maximum μₛN. It is not always equal to its maximum.
In Motion: Kinetic friction has magnitude μₖN and acts opposite to velocity. When velocity reaches zero, the static-equilibrium condition is checked again before deciding whether the block restarts.
At the Boundaries: The block hits a rigid stop; its velocity becomes zero instantly without rebound. If the forces later allow motion back into the plane, it starts moving again. The boundary reaction is separate from friction.
Assumptions: point-mass translational dynamics, rigid straight plane, constant gravity, no air resistance, constant μₖ ≤ μₛ, constant applied parallel force. Rolling, tipping and deformation are excluded. Check the assumptions before applying this model to real bodies.
FROM FORCES TO MOTION
Step-by-Step Calculations
Every substitution includes measurement units. Calculations refer to the selected time and the current dynamical phase.
Values are calculated at full precision and rounded only for display. At transitions, the solution is computed piecewise: no equation of motion is incorrectly extended across a change of regime.
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