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a7_cee3804_2011_sol - CEE 3804 Computer Applications in...

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CEE 3804: Computer Applications in Civil Engineering Spring 2011 Assignment 7: Simulink and Modeling Systems Solution Instructor: Trani Problem 1 Your task is design an emergency exit ramp for a runaway truck. Figure 1 illustrates the situation. Figure 1. Emergency Exit Ramp. The truck has a mass of 40,000 kg. and enters the ramp at a speed of 42 m/s (~80 mph) while on a -5% grade. The ramp is constructed in two segments: a) curved section with a radius of 1000 meters and b) straight section with a grade of 15%. neglecting the aerodynamic drag acting on the truck, a free-body diagram showing the forces acting on the truck are shown in Figure 2. Figure 2. Free Body Diagram of Truck. CEE 3804 Trani Page 1 of 9
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Define a common set notation to solve the problem. When the truck is going downhill, the gravity force helps accelerate the truck. When is going uphill the gravity force helps slow down the motion. The fundamental equation of motion to describe the deceleration of the truck on the exit ramp is: m dV dt = mg cos( δ ) μ + mg sin( δ ) Here we adopt the nomenclature that when angle δ is positive (i,e., downhill) the term mg sin( δ ) will be positive and thus opposite to the friction term. In this case, the gravity helps accelerate the truck. When going uphill δ is negative and the term mg sin( δ ) is negative helping decelerate the truck. Task 1 Model the curved section of the road as either a series of line segments or by deriving an equation that relates the local grade of the curve as a function of the path length along the curve.
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