The ramp that turns one force into two. Rest a block on a slope and gravity splits in two: a part mg·sinθ tugging it down the incline and a part mg·cosθ pressing it into the surface. Friction can hold it — but only up to μN, so the block stays put while tanθ ≤ μ and breaks loose the moment the slope wins, sliding at a = g(sinθ − μcosθ). Tilt the ramp, change the friction and the mass, and watch the weight, normal and friction arrows rebalance. It all runs on your device.
You are in the Physics lab.
Acceleration a = g(sinθ − μcosθ) versus ramp angle. The dashed line marks the slip angle where tanθ = μ; the dot is the current angle.
What every arrow, badge and curve on the screen is telling you.
The faint red arrow is the full weight mg, pointing straight down. On a ramp it is easier to work along and across the slope, so it is drawn as two dashed components: an orange arrow mg·sinθ down the slope — the part that tries to slide the block — and a purple arrow mg·cosθ pressing into the surface. The blue arrow is the normal force N, which the ramp pushes back with to exactly cancel that purple component, so N = mg·cosθ.
The green arrow is friction f, always pointing up the slope to resist sliding. While the block holds, friction grows to match the orange driving arrow exactly, so the two cancel and nothing moves. But it can only grow so far: the Max static friction μN readout is its ceiling. Once the orange arrow would exceed that ceiling, friction gives out and a yellow net force arrow appears down the slope.
The badge reads Static while the slope is gentle and Sliding once you tilt past the tipping point. That point is the slip angle, where tanθ = μ — friction can no longer keep up. The lower plot shows the acceleration a = g(sinθ − μcosθ): it sits flat at zero through the static range, then lifts off exactly at the dashed slip-angle line and climbs as the ramp steepens.
Split gravity along and into the ramp, compare the pull with the grip, and let the block hold or slide.
The block's weight points straight down, but on a ramp it is easiest to work along and across the slope. Gravity's component along the slope is mg·sinθ — the part that wants to slide the block — and the component into the surface is mg·cosθ. The ramp answers the second with an equal normal force N = mg·cosθ.
Friction acts along the surface, opposing any tendency to slide, and it can be as large as μN but no larger. While the down-slope pull mg·sinθ stays within that budget the block does not move; the friction arrow simply matches the pull. The break-even is when mg·sinθ = μN, which reduces to tanθ = μ.
Tilt past that angle and friction can no longer hold the block. The net force along the slope is mg·sinθ − μmg·cosθ, so the block accelerates down at a = g(sinθ − μcosθ). The mass cancels, so every block on that ramp speeds up at the same rate; with no friction it is just g·sinθ, and at 90° it becomes free fall.
Teaching or blogging about mechanics? You can embed this simulator on your own site free — one line of code, no sign-up.