Simulate objects on inclined planes with friction. Decompose forces, calculate acceleration, and animate motion up and down slopes.
Model an object moving on a sloped surface by setting its mass, incline angle, friction, and starting motion. The Inclined Plane Simulator separates weight into components parallel and perpendicular to the plane, determines the frictional contribution, calculates net acceleration, and visualizes motion uphill or downhill. The most common surprise is that friction does not always point uphill. It opposes the object's current motion or tendency to move, so an object launched uphill experiences both gravity and kinetic friction acting downhill.
A concrete input and expected output from the current implementation.
Input
Mass = 1 kg; angle = 45 degrees; friction coefficient = 1.00; initial velocity = 1.00 m/s downhill
Expected output
Net force along plane = 0 N; acceleration = 0 m/s^2; velocity remains 1.00 m/s downhill while the object stays on the plane.
At 45 degrees, sin(45 degrees) and cos(45 degrees) are equal. The downhill weight component is exactly matched by kinetic friction when the coefficient is 1.00, producing zero net force and therefore zero acceleration.
The object's weight, mg, separates into mg sin(angle) parallel to the surface and mg cos(angle) perpendicular to it. With no other perpendicular force, the normal force matches the perpendicular component. The parallel component points downhill. Changing mass changes these force magnitudes, but mass cancels from the basic acceleration because gravity and coefficient-based sliding friction both scale with mass.
During sliding, kinetic friction has magnitude mu times the normal force and points opposite the velocity. Taking downhill as positive gives a = g[sin(angle) - mu cos(angle)] while the object slides downhill. If it moves uphill, gravity and friction both point downhill. The motion display uses the resulting acceleration to show changes in position, speed, and direction.
Gravity's component parallel to the plane points downhill, and kinetic friction also points downhill because it opposes the uphill velocity. Their effects add until the object stops. What happens afterward depends on the downhill component and static friction. Reaching zero velocity does not by itself guarantee that the object will reverse and slide downhill.
No, not in the ideal sliding-block calculation represented by these force equations. The downhill weight component and coefficient-based friction both increase in direct proportion to mass, so mass cancels when net force is divided by mass. Holding angle, coefficient, and initial motion fixed changes the force values, but not the calculated acceleration.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
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