1. A Banked Curve

2. Banked Curve Train in Philadelphia was going to fast Banking too little Example 5.42 pg 157 For a car traveling at a certain speed, it is possible to bank a curve at just the right angle so that no friction at all is needed to maintain the car’s turning radius. Then a car can safely round the curve even on wet ice. Forces on Car Gravity Road (normal) No Friction n = n sinβ i + n cosβ j

3. Horizontal & Vertical Components The acceleration in the x-direction is the centripetal acceleration: a rad = v 2 /R ΣF x = ma rad = mv 2 /R = n x = n sinβ There is no acceleration in the y-direction ΣF y = 0 = −mg + n cosβ mv 2 /R = n sinβ mg = n cosβ Divide the equations: v 2 /Rg = sinβ/cosβ sin = opp/hyp cos = adj/hyp sin / cos = opp/adj = tan

4. Final Result mv 2 /Rg = sinβ/cosβ = tan β β = tan -1 (v 2 /Rg)