For the exit ramp if a typical car rounds it at a R = 100.0(m) radius and a spee

Question

For the exit ramp if a typical car rounds it at a R = 100.0(m) radius and a speed of 15 m/s. a) Find the angle at which the curve should be basked. b) Find the necessary centripetal acceleration on this basked curve so the car won't slip down or slide up the incline. F_ = mv^/r, F =ma_c (a) What is the tangential acceleration of a bug on the rim of a 5 cm radius disk if the disk moves from rest to an angular speed of 31.4 rad/s in 3.0 s? (b) When the disk is at its final speed, what is the tangential velocity of the bug? (c) One second after the bug starts from rest, what are its tangential acceleration, centripetal acceleration, and total acceleration? (d) Through what angle does the disc turn while coming up to speed of 20 rad/s?

Explanation / Answer

5a ] angle of banking is given by : theta = arctan(v^2/rg) = arctan(15^2/(100*9.8)) =12.93 degree

b] ac = v^2/r = 15^2/100 = 2.25 m/s^2

6a] a = r*alpha = r dw/dt = 0.05*31.4/3 = 0.523 m/s^2

b] v = wr = 31.4*0.05 = 1.57 m/s

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