Why are Curved Roads BANKED? 🛣️ Banking of Roads

Scenario: A vehicle test facility has two curves that share the same radius, R = 50 m. Curve A is flat (unbanked) and relies entirely on friction; on the dry track, the tires have a coefficient of static friction μₛ = 0.80 with the surface. Curve B is banked at θ = 25° and is built to need no friction. The same 1500 kg car is driven on both. Take g = 10 m/s².

Use the ground reference frame. Take the direction toward the center of each curve as positive for horizontal forces and “up” as positive for vertical forces. Both circular paths lie in horizontal planes; treat the car as a point particle.

(a) For the car rounding each curve at its maximum safe speed, describe the free-body diagram and state which force provides the centripetal force on Curve A and on Curve B.

(b) Determine the maximum speed on the flat Curve A and the design speed on the banked Curve B.

(c) Explain, in terms of the direction of the forces involved, why Curve B can be rounded with no friction at all but Curve A cannot.

(d) A sudden downpour makes both surfaces essentially frictionless (μ → 0). Predict what happens to a car traveling at 15 m/s on each curve, and justify each prediction.

🚨 The Conical Pendulum Trap
Does a wider conical pendulum take longer to swing? Most students guess "yes"—but physics says otherwise. Download this slide deck to see exactly why that intuition fails.

Key takeaways:
• Mass and speed never dictate the period.
• T is strictly determined by vertical height (h = L cos θ), so T = 2π√(h / g).
• A wider cone always results in a shorter period.
• Why the conical pendulum fails as a clock.

Don't lose easy FRQ points on this standard problem.

You can find more free resources including physics simulations on my website https://www.thesciencecube.com/

The Circle Always Wins: The physics behind the Conical vs. Simple Pendulum race