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Malti📐 Static vs Kinetic Friction — Block on an Incline
Adjust the incline angle, applied force, and static/kinetic friction coefficients to see exactly when a block stays put and when it slides, with a full force diagram and the critical angle computed live.
About Static vs Kinetic Friction — Block on an Incline
This simulation places a block on a ramp whose angle you control (0–60°) and lets you push or pull it along the surface with an adjustable applied force. Gravity mg is resolved into two components: mg sinθ along the slope, pulling the block down-hill, and mg cosθ into the surface, which the surface pushes back against as the normal force N = mg cosθ. Friction is modelled with the classic Coulomb law: while the block is at rest, static friction can take on any value up to a maximum of μs·N, in whatever direction is needed to cancel the net driving force. If the net driving force (applied force minus the down-slope weight component) would exceed that maximum, static friction can no longer hold the block, and it begins to slide.
Once sliding starts, friction switches to the kinetic regime: it has a fixed magnitude μk·N and always opposes the direction of motion, so the block's acceleration follows Newton's second law with that fixed friction force subtracted from the net driving force. Physically μs is always at least as large as μk, because breaking the microscopic contact points that hold a stationary surface together takes more force than sustaining sliding once those contacts are already shearing — this is why a stalled car is harder to start pushing than to keep rolling. A special case is the critical angle, θc = arctan(μs): tilt an unpushed ramp beyond this angle and the block's own weight is enough to overcome static friction on its own, so it starts to slide with no applied force at all.
Frequently Asked Questions
What does this simulation actually show?
It shows a block on a tiltable ramp with a full force diagram: gravity, the normal force, friction, and any applied force you dial in. As you change the angle, applied force, mass, or the two friction coefficients, the simulator recomputes whether the block is held in place by static friction or is sliding, and animates the block's motion along the incline accordingly.
Why doesn't the applied force change the normal force?
The applied force in this simulation acts parallel to the incline surface, like someone pushing or pulling the block up or down the slope rather than into it. Because it has no component perpendicular to the surface, it does not add to or subtract from the normal force, which stays equal to mg cosθ regardless of how hard you push along the ramp.
What is the difference between static and kinetic friction?
Static friction acts on a block that is not moving relative to the surface; it adjusts itself up to a maximum of μs·N to exactly cancel whatever net force is trying to move the block. Kinetic friction acts once the block is actually sliding; it has a fixed magnitude μk·N and always points opposite to the direction of sliding. Both are captured by the Coulomb friction model used here.
What do the controls change?
The angle slider tilts the ramp from flat (0°) to steep (60°). The static (μs) and kinetic (μk) sliders set the two friction coefficients — μk is capped so it can never exceed μs, since kinetic friction is never larger than static friction for a given pair of surfaces. The applied-force slider pushes the block up-slope (positive) or down-slope (negative), and the mass slider changes how heavy the block is. A reset button returns the block to the middle of the ramp.
What is the critical angle, and why does it matter?
The critical angle is θc = arctan(μs), the steepest angle at which an unpushed block can still rest motionless on the ramp under its own weight. Beyond θc, the down-slope component of gravity, mg sinθ, exceeds the maximum static friction μs·mg cosθ, so the block slides on its own. This angle is a quick, purely geometric way to measure a surface's static friction coefficient — it's the same idea used in tilt-table friction experiments.
Why must μk be less than or equal to μs?
Static friction comes from countless microscopic contact points that have had time to settle, deform slightly and even micro-weld together, which takes real force to break. Once the surfaces are sliding, those contacts are constantly forming and breaking too quickly to fully bond, so on average less force is needed to sustain the motion. That is why μk ≤ μs almost always holds, and why it takes a harder shove to start pushing a heavy crate than to keep it moving.
How is the block's motion animated?
When the sliding condition is met, the simulator computes the acceleration a = (F_drive − sign(F_drive)·μk·N) / m from Newton's second law and integrates it forward in time to update the block's velocity and position along the incline on every frame. The block's position is clamped between the bottom and top of the ramp — it stops cleanly if it reaches either end, and the reset button brings it back to the middle.
What happens if I push the block hard enough up the slope?
If the applied force is strong enough that the net driving force up-slope exceeds the maximum static friction, the block starts sliding up-slope. Kinetic friction then acts down-slope, opposing the upward motion, and combines with the down-slope pull of gravity to decelerate the block. The state readout switches to "Sliding up" and the friction arrow flips to point down the ramp.
Where does this friction model apply in the real world?
The same static-versus-kinetic distinction governs why a parked car's brakes can hold it on a hill up to a certain slope but not beyond, why climbers and hikers judge how steep a slope they can stand on safely, why anti-lock brakes try to keep tyres in the higher-friction static/rolling regime instead of sliding, and why engineers choosing materials for conveyor belts, ramps, or gripping surfaces care about both friction coefficients, not just one.
Adjust the incline angle, applied force, and static/kinetic friction coefficients to see exactly when a block stays put and when it slides, with a full force diagram and the critical angle computed live.
2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install