Two banked curves have the same radius. Curve A is banked at14.0 °, and curve B is banked at an angle of 17.9 °. A carcan travel around curve A without relying on friction at a speed of11.5 m/s. At what speed can this car travel around curve B withoutrelying on friction? for the set up how do we know thattan=v(squared)/rg and then we go to tanA/tanB = v(sq)A/v(sq) B How do we get those relationships? Two banked curves have the same radius. Curve A is banked at14.0 °, and curve B is banked at an angle of 17.9 °. A carcan travel around curve A without relying on friction at a speed of11.5 m/s. At what speed can this car travel around curve B withoutrelying on friction? for the set up how do we know thattan=v(squared)/rg and then we go to tanA/tanB = v(sq)A/v(sq) B How do we get those relationships?
Explanation / Answer
it is a formula a vehicle can negotiate a circular turn with outrelying on static friction to provide centripetal force providedthe turn is banked at angle relative to horizontal the angle at which a friction freecurve must be banked is related to the speed v of the vehicle theradius of curve is r and magnitude of accleration due to gravity isg then tan = v2/rg here two banked curves tan1 = v2A/rg tan2 =v2B/rg diving we get tanA/tanB = v(sq)A/v(sq)B