Working Model 2D Exercise Problem ME 114 Vehicle Design Dr. Jose Granda. Performed By Jeffrey H. Cho

Transcription

1 Working Model 2D Exercise Problem ME 114 Vehicle Design Dr. Jose Granda Performed By Jeffrey H. Cho

2 Table of Contents Problem Statement... 1 Simulation Set-Up...2 World Settings... 2 Gravity... 2 Accuracy... 2 Pause Control... 2 Vehicle Settings... 3 Meters... 3 Results... 7 Appendix... 7 References... 7 Table of Figures Figure 1: Velocity of Car A... 4 Figure 2: Position of Car C... 5 Figure 3: Pole Collision... 6 i

3 Problem Statement Problem Given: Mass: Initial velocities: Car A = 1500 kg Car B = 1300 kg Car C = 1200 kg Car B = 72 km/h (north) = 20 m/s Car C = 90 km/h (west) = 25m/s Position: (x, y) Utility pole = (18, 13.9) m from center of intersection. Car C when Car A & Car B collide = (10, 3) m from center of intersection. *All vehicles stick together upon impact (perfect plastic collision). *Vehicles slide across wet road surface. Find: a. Time elapsed from the first collision (Car A & Car B) to the impact with utility pole. b. Speed of Car A. 1

4 Simulation Set-Up World Settings Gravity Due to the plan view perspective of this simulation and the 2D limitations of the program, gravity had to be turned off. Neglecting gravity results with no normal forces acting on the tires from the road surface, hence, there are also no frictional forces: f = μ N = μ mg ( ) = 0 Accuracy In order to produce a smooth simulation and create more points of reference, the animation step was increased to 200 frames per second. While running the simulation the vehicles had a tendency of separating upon impact although the coefficient of restitution was zero. To surmount this, the overlap error was set to 0.3 meters, allowing the vehicles to deform during impact. Pause Control Three pause controls were used to identify the three main phases of this collision simulation. The first pause control takes effect after 0.5 seconds (Figure 1). At this time, one can observe the velocity meter (40 m/s) of Car A without manually stopping the program to rewind to the appropriate step frame. To resume the simulation, press the run button. The second pause occurs after seconds. This is the point of collision between Car A and Car B. At this point, the Car C position-meter can verify that Car C is located (10, 3) m from the intersection (Figure 2). To resume the simulation, press the run button. The last pause control stops the simulation after the vehicles collide with the pole, 2 seconds after Car A and Car B collide (Figure 3). 2

5 Vehicle Settings Vehicle dimensions: 2m x 4.5m 1. Mass Car A = 1500 kg Car B = 1300 kg Car C = 1200 kg 2. Initial velocities Car A = 144 km/h (east) = 40 m/s from simulation Car B = 72 km/h (north) = 20 m/s given Car C = 90 km/h (west) = 25 m/s given 3. Position: Utility pole = (18, 13.9) m from center of intersection. (x, y) Car C when Car A & Car B collide = (10, 3) m from center of intersection. 4. Coefficient of restitution = 0 (perfect plastic) 5. Moment of inertia, I = excessively high to resist rotation = kg*m 2 *All vehicles stick together upon impact (perfect plastic collision, e = 0). *Vehicles slide across wet road surface (μ = 0). Meters A position meter was used to verify the location, according to the problem statement, of Car C when Car A and Car B collide. To determine the instant of impact between Car A and Car B, a total force meter was applied to Car B. When the total force meter displays a value, Car C should be at it prescribed location and at this time, the time meter will offer a time display. This is necessary to determine the time it takes for all three cars to crash into the pole after Car A and Car B collide (part a. of the problem analysis). After the correct conditions have been met, a velocity meter was applied to Car A to determine its initial velocity. 3

6 Figure 1: Velocity of Car A 4

7 Figure 2: Position of Car C 5

8 Figure 3: Pole Collision 6

9 Results After careful manipulation of the world and vehicle setting, the following values were determined: a. Time elapsed from the first collision (Car A & Car B) to the impact with utility pole = 2 seconds b. Speed of Car A = 40 m/s (east) Appendix References Beer, F., Johnston E., Clausen W., Vector Mechanics for Engineers: Dynamics 7 th Edition (New York, New York: McGraw-Hill Companies, Inc., 2004). 7