1. The problem statement, all variables and given/known data To avoid this stress, vertical loops are teardrop-shaped rather than circular, designed so that the centripetal acceleration is constant all around the loop. How must the radius of curvature R change as the car's height h above the ground increases in order to have this constant centripetal acceleration? Express your answer as a function: R=R(h). Given variables: Initial radius R0 Initial velocity v0 2. Relevant equations a_c = v2/r v = r*ω ΔPE = -ΔKErotational -ΔKEtranslational 3. The attempt at a solution ΔPE = mgh -ΔKEtranslational = (1/2)m(v02 - vf2) -ΔKErotational = (1/2)m(r02ω02 - rf2ωf2) if v=r*ω, then unless I'm mistaken, ΔKErotational = ΔKEtranslational (substitution), and therefore: mgh = m(v02 - vf2) Mass cancels out. Since centripetal acceleration is constant, I know that a_c initial = a_c final, therefore: vf2 = (v02*rf)/r0 Substituting this back into the energy equation and then doing algebra, rf = r0((v02 - gh)/v02) This is incorrect, and I can't figure out where I've gone wrong?