a civi engineer wishes to design an expressway so that a minima amount of breaki

Question

a civi engineer wishes to design an expressway so that a minima amount of breaking and accerlating (via the gas pedal) is required by the motorist. use what you know abouth the conservation and potential and kinetic energy to determin the optimal depth for expressway.
the speed limit on the freeway is 30 m/s, and the speed limit on the service drive is 10 m/s. mr boman. red pick up truck has a mass of 1,000kg.
since friction depends on so many factors such as the condition of the vehicle and the direction of the wind, the civil engineer neglects it.

A- how deep should the freeway be so that a car that is going the speed limit at the top of the entrance ramp will be going the speed limit when it reaches the bottom (without touching the gas pedal)

B- how deep should the freeway be so that a car going the speed limit at the bottom of the exit ramp will be going at the speed limit when it reaches the top.

C- compare the result for the exit and entrance ramps. which height is better in general?

D- the freeway will be used for both honda civics and mack trucks. how will the different masses effect ones choice of an ideal depth for the freeway.

Explanation / Answer

a) Ui + Ki = Uf + Kf mgh + 1/2m*vi^2 = 0 + 1/2m*vf^2 h = 2(vf^2-vi^2)/g = 2(30^2-10^2)/9.8 = 163m b) Ui + Ki = Uf + Kf 0 + 1/2m*vi^2 = mgh + 1/2m*vf^2 h = 2(vi^2-vf^2)/g = 2(30^2-10^2)/9.8 = 163m c) They are the same. d) According to our results, the ideal depth is not related to the mass.

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