Please be detailed A civil engineer wishes to design an expressway so that a min
ID: 2118868 • Letter: P
Question
Please be detailed
A civil engineer wishes to design an expressway so that a minimal amount of breaking and accelerating (via the gas pedal) is required by the motorist. Use what you know about the conservation and potential and kinetic energy to determine the optimal depth for the expressway.
The speed limit on the Freeway is 30 m/s and the speed limit on the service drive is 10m/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.
1) 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)
2)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.
3) Compare the results for the exit and entrance ramps. Which height is better in general?
4) 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?
1) A car travels counterclockwise around a flat circle of radius 0.5 km at a constant speed of 30 m/s. When the car is at a point A point where the instantaneous belocity is due north, what is the car's acceleration?
2) An Airplane moves 100 m/s as it travels around a vertical circular loop which has a 1.0-km radius. What is the magnitude of the resultant force on the 50 kg pilot of this plane at the bottom of this loop?
3) A 4.0 kg block sliding on a horizontal frictionless surface is attached to one end of a horizontal spring (k = 200 N/m) which has its other end fixed. If the block has a speed of 4.0 m/s as it passes through the equilibrium position, what is its speed when it is 20 cm from the equilibrium position?
4) A 2.0 kg block slides down a plane (inclined at 25 degree with the horizontal) at a constant speed of 2.0 m/s. At what rate is the frictional force changing the mechanical energy of the block?
5) Each of two vector D1 and D2, lies along a coordinate axis in the xy plane. Each vector has its tail at the orgin, and the dot product of the two vectors is D1XD2 = 1. Which angles are possible?
Explanation / Answer
1)0.5(20*20-10*10)=10*h
h=15m