Sled Calculator — Slope Physics & Friction
Find the acceleration, net force, normal force, and friction force for a sled (or any object) sliding on an inclined surface. Enter mass, slope angle, and the kinetic friction coefficient.
кг
°
N
Positive → sled accelerates downhill
- 1
Weight W = m·g
60 × 9.81 = 588,6 - 2
Normal force N = W·cos θ
588,6 × cos(15°) = 568,54 - 3
Friction force F = μ·N
0,05 × 568,54 = 28,43 - 4
Net force along slope
152,34 + 0 − 28,43 = 123,91Downhill gravity component plus any push, minus kinetic friction. - 5
Acceleration a = F_net / m
123,91 ÷ 60 = 2,07
Як працює цей калькулятор?
Sled acceleration a = g·(sinθ − μ·cosθ); mass cancels. Normal force N = mg·cosθ, friction F = μN. At slope angle θ < arctan(μ) the sled stays still. Use g = 9.81 m/s². A push force adds directly to the downhill component.
Формула
How this is calculated
A sled on a slope experiences three main forces: gravity (mg, vertically downward), the normal force perpendicular to the slope surface (N = mg·cos θ), and kinetic friction opposing motion along the slope (F_f = μ·N = μ·mg·cos θ). Splitting gravity into components: mg·sin θ acts along the slope (downhill) and mg·cos θ acts into the slope (balanced by N). The net force along the slope is mg·sin θ − F_f, and by Newton's second law a = F_net/m = g·(sin θ − μ·cos θ).
A remarkable result is that mass cancels: acceleration depends only on the slope angle and the friction coefficient, not on how heavy the sled is. This is analogous to Galileo's result for free-fall. The critical angle where the sled just begins to slide is arctan(μ) — below that angle, static friction can hold the sled stationary. This calculator uses kinetic (sliding) friction μk, which is typically slightly lower than the static coefficient μs.
An optional push force (directed down the slope) can model a running start or a parent giving a push. Air resistance is not modelled. g is taken as 9.81 m/s². For ski runs replace the sled with skis; for a box on a ramp the physics is identical.
Поширені запитання
A well-waxed plastic sled on packed snow is around μ = 0.03–0.05; a wooden sled on snow is closer to 0.07–0.10. Wet or slushy snow is higher (0.10–0.15). Rough grass or gravel is 0.20–0.40. These are estimates — measure or look up values for your specific surface.
Both the gravitational pull and the friction force are proportional to mass (F_net = m·g·sinθ − μ·m·g·cosθ). Dividing by m to get acceleration gives a = g·(sinθ − μcosθ), independent of mass. A 10 kg sled and a 100 kg sled accelerate identically on the same slope.
The sled starts sliding when the slope component of gravity exceeds maximum static friction: tanθ > μ_s (static friction coefficient). For μ = 0.05 that is arctan(0.05) ≈ 2.9°. The calculator shows this critical angle in the stats grid.
Також відомий як
TG we-Calculate Editorial Team. (2026). Sled Calculator — Slope Physics & Friction [Online calculator]. TG we-Calculate. https://we-calculate.com/uk/calculator/sled-calculator
TG we-Calculate Editorial Team. "Sled Calculator — Slope Physics & Friction." TG we-Calculate. 2026. https://we-calculate.com/uk/calculator/sled-calculator.
TG we-Calculate Editorial Team, "Sled Calculator — Slope Physics & Friction," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/uk/calculator/sled-calculator
@misc{wecalculate_sled_calculator, title = {Sled Calculator — Slope Physics & Friction}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/uk/calculator/sled-calculator}}, year = {2026}, note = {TG we-Calculate} }
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