QLine Momentum & Braking Lab
Momentum, braking force, and stopping distance — using Detroit's QLine streetcar as a real system.
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Standards
HS-PS2-1 — Analyze data to support the claim that Newton's second law describes the mathematical relationship among the net force on an object, its mass, and its acceleration.
Why Does This Matter?
Detroit's QLine streetcar runs along a 3.3-mile route on Woodward Avenue, sharing the street with cars, cyclists, and pedestrians. Operators have to judge safe stopping distances at every stop — a real, everyday application of momentum and braking force.
Objective
Calculate momentum and stopping distance for a model streetcar at different speeds and braking forces, then recommend a safe operating speed near a crowded stop.
Materials
- Data sheet: qline_braking_model.csv (assumed teaching values for streetcar mass, braking force, and speeds — not manufacturer specifications)
- Calculator
- Optional: toy cart/vehicle, ramp, and stopwatch for a physical stopping-distance demonstration
Safety: If using a physical cart demonstration, keep the stopping area clear of people and materials.
Procedure
- Using the provided mass of a loaded QLine streetcar and a range of typical operating speeds (in m/s), calculate the momentum (p = mv) at each speed.
- Using the provided braking force value, calculate the time to stop at each speed (t = m·Δv / F).
- Calculate the approximate stopping distance at each speed using your time and an average velocity estimate.
- Plot stopping distance (y-axis) vs. initial speed (x-axis).
- Identify the speed at which stopping distance exceeds a safe buffer zone (provided by your teacher) near a crowded stop.
- If using a physical cart: build a small ramp, time a cart's deceleration under a fixed friction/braking setup at two different starting speeds, and compare to your calculated trend.
Data Table
| Speed (m/s) | Momentum (kg·m/s) | Stopping time (s) | Estimated stopping distance (m) |
|---|---|---|---|
Analysis Questions
- How does stopping distance change as speed increases? Is the relationship linear? Explain using your graph.
- Based on your data, what is the maximum safe operating speed near a crowded stop, given the buffer zone your teacher provided?
- Why does a loaded streetcar (full of passengers) need a longer stopping distance than an empty one, even at the same speed and braking force?
- How might this same momentum analysis apply to a school bus or a delivery truck driving through a Detroit neighborhood?