🧭 Plot Summary
A fire marshal needs an emergency way down from a second-floor balcony, and the rule is simple: riders must leave the slide at a safe speed. Drop someone 3.0 m with no friction and they would hit the ground at nearly 8 m/s. That’s far too fast. Friction is your brake, and every choice you make decides how much of the balcony’s energy it takes.
Your job is to design a slide from a real materials list and a real budget, check with an energy budget that it meets the speed limit for any rider, and test your friction numbers so the design doesn’t rest on a guess.
What you will do in this problem
- Budget the energy of a ride down from a 3.0 m balcony: how much becomes speed, and how much friction can take.
- Choose a slide length, surfaces, and a runout from a real materials list with real prices.
- Check that your slide keeps a rider moving but under the speed limit, for a 40 kg rider and a 100 kg rider.
- Validate your friction numbers with a drag test or a scale model, and calculate your percent error.
- Explain the tradeoffs you made and the tempting designs you rejected.
Why it matters
This is the payoff for the whole unit. The work and energy tools from 4-1, the friction budget and efficiency ideas from 4-2, and the predict-then-test method from the foam coaster all feed into designing something that has to be safe, not just clever.
✅ Self-Check Before You Roll On
Check off each item as you get there. These are not grades — they are your own signal.