Inclined Plane Simulator
Watch a block on a ramp slide or hold still. Set the angle, mass, and friction and see the force components and acceleration a = g(sinθ - μcosθ) live.
Offline ● Works without internet after loading After the first page load, no network connection is needed.Drag up or down to change the ramp angle
This simulation needs a modern browser with canvas support. The measurements and formula below still describe the physics.
Controls
Live measurements
Graph
Formula
a = g(sinθ - μcosθ)
Type your own values to solve the formula. The simulation follows along.
- a Acceleration
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Observations
What's happening
Real-world examples
Frictionless slope
With no friction the block accelerates at g sinθ, the same for any mass.
Friction holds it
On a shallow ramp with grippy contact the block stays static because tanθ is less than μ.
Steep and slippery
A steep, low-friction ramp lets the block accelerate quickly down the slope.
Wheelchair ramp
A gentle angle keeps the driving force small, which is why accessibility ramps are long and shallow.
Common Questions
What is the acceleration of a block on an inclined plane?
For a block sliding down a ramp, the acceleration is a = g(sinθ - μcosθ), where θ is the ramp angle, μ is the coefficient of friction, and g is gravity. The weight component along the incline, g sinθ, drives it down while friction, μg cosθ, resists. Notice the mass cancels out, so a heavy and a light block slide with the same acceleration. The simulator shows this value updating as you change the angle or friction.
How do I find the normal force on a ramp?
The normal force is N = mg cosθ, not the full weight mg. On a slope the surface only has to support the component of gravity perpendicular to it, which shrinks as the ramp gets steeper. To find the normal force, multiply the weight by the cosine of the ramp angle. Friction is then μN = μmg cosθ, which is why steeper ramps have less friction to fight.
Why does the block sometimes stay still?
When the ramp is shallow enough, the maximum friction force μmg cosθ is larger than the weight component mg sinθ trying to pull the block down, so it stays static. This happens whenever tanθ is less than μ. Raise the angle past that point in the simulator and the block breaks free and begins to slide. The status label tells you which regime you are in.
Does a heavier block slide faster?
No. The acceleration a = g(sinθ - μcosθ) has no mass in it, because both the driving force and the friction force scale with the mass and cancel. A heavier block feels a bigger pull but also a bigger friction force, so it slides with exactly the same acceleration as a light one. Change the mass slider in the simulator and the acceleration reading does not move.
How does the ramp angle change the motion?
A steeper ramp increases the weight component along the incline (mg sinθ) and reduces the normal force and friction (mg cosθ), so the block accelerates faster. A shallower ramp does the reverse and may let friction hold the block still. Comparing a steep vs shallow ramp in the simulator shows the acceleration and force arrows change together.
Does the simulator send my data anywhere?
No. Everything runs in your browser with a canvas and simple arithmetic. Nothing is uploaded or stored remotely, and the simulator keeps working offline after the page loads.