Motion Lab · Speeding Up on a Ramp
Change how high the ramp is and how heavy the cart is. Put two photogates anywhere on the ramp, then use the speeds they measure to find the cart's acceleration — part by part.
No friction here: this ramp is a simplified model with zero friction, so nothing slows the cart down as it slides. In real life, ramps, wheels, and air always add a little friction — but leaving it out here makes the math easier while you learn about acceleration.
Drag the two gate posts on the ramp, or use the sliders below, to put them anywhere you want.
Readings show up here the moment the cart passes each gate.
Save each run so you can compare acceleration for different spots on the ramp, different heights, and different masses.
| # | Height (cm) | Mass (g) | Gate A (cm) | Gate B (cm) | Δx (cm) | v₁ (cm/s) | v₂ (cm/s) | t₁ (s) | t₂ (s) | a = Δv/Δt |
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Tap to open the step-by-step directions.
Tap to open the formulas and the science behind them.
The ramp is always L = 100 cm long. When you raise the release point to height h, you make the ramp steeper. A steeper ramp pulls the cart down faster, so a taller ramp always means a bigger acceleration — and that acceleration stays the same all the way down that ramp.
Each photogate gives you a speed and a time. It shouldn't matter which two spots you pick — near the top, near the bottom, or in the middle — this formula should give you close to the same number every time, because the ramp speeds up the cart by the same amount everywhere along it.
Try the same ramp height with no extra mass, then with 200 g added, using the same two gates. Since there's no friction, gravity speeds up every part of the cart by the same amount. So the acceleration should come out about the same, even though the cart is heavier. Extra mass makes the cart harder to stop — it doesn't make it speed up faster.
This is a simplified, friction-free model · positions are measured from the fixed release point at the top of the ramp · g = 980 cm/s²