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Assuming that drag is proportional to the square of velocity, we can model the velocity of a falling object like a parachutist with the following
where v is velocity (m/s),
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- HW4 EX1: An automobile moving over a rough road (Fig. 1.64) can be modeled considering (a) weight of the car body, passengers, seats, front wheels, and rear wheels; (b) elasticity of tires (suspension), main springs, and seats; and (c) damping of the seats, shock absorbers, and tires. Develop three mathematical models of the system using a gradual refinement in the modeling process. FIGURE 1.64 An automobile moving on a rough road. EX2 1.5* The consequences of a head-on collision of two automobiles can be studied by considering the impact of the automobile on a barrier, as shown in Fig. 1.65. Construct a mathematical model by considering the masses of the automobile body, engine, transmission, and suspen- sion and the elasticity of the bumpers, radiator, sheet metal body, driveline, and engine mounts. FIGURE 1.65 An automobile colliding with a barrier.arrow_forwardUsing Newton's second law, the movement of a body in a viscous fluid can be modeled. For this case it will be a one-dimensional movement. ec.1) F -FR = ma F: Force applied to the body. FR: Resistance that opposes the fluid to the movement. m: body mass a: body acceleration For a sphere with initial radius R0 = 1 meter and density 8960 kg/m^3 to which a constant force of 3 Kilo Newtons is applied, it is requested: Using Euler's method, find the velocity as a function of time for the first 5 seconds of movement, considering that v(0) = 10 m/s. Use a 1 second step. For this case use: ec.2) FR = 210Rv R: Radius of the sphere. v: velocity Where, in addition, the sphere disintegrates as time passes in this fluid, so its radius is given by the following function: ec.3) R = R0*e^(-t/250)arrow_forwardThermodynamics Answer the following problem with complete solutions. Write legibly A gas goes through the following thermodynamic processes: A to B: constant-temperature compression; B to C: constant-volume cooling; C to A: constant-pressure expansion. The pressure and volume at state C are 1.4 bars and 0.028 m^3, respectively. The net work during the C-to-A process is 10.5 kJ. What net work is derived from one complete A-B-C cycle?arrow_forward
- Energy of a Roller Coaster Car 500 450 400 350 --- 3 300 250 E 200 150 100 50 6 8 10 Time (s) Mechanical Energy ....... Potential Energy -- Kinetic Energy This graph shows different types of energy for a roller coaster car that starts at the top of a large hill and goes down to its lowest point at 6 s. According to the graph, what is the most likely relationship between height and potential energy? Your answer: They are directly related. They are inversely related. There is no relationship between the two. There is not enough information for a conclusion.arrow_forwardIn medical literatures, local blood perfusion rate is typically presented as xx ml/(min 100g tissue), in another word, it represents xx ml of blood supplied to a tissue mass of 100 g per minute to satisfy its nutritional needs. As we learned from the course lectures, the local blood perfusion rate appearing in the Pennes bioheat equation is in a unit of 1/s, or can be interpreted as xx ml of blood supplied to a tissue volume of 1 ml per second. The following lists the blood perfusion rates in various organs or structures in a human body from medical textbooks: brain (50 ml/(min 100g tissue)), kidney (35 ml/(min 100g tissue)), and muscle at rest (3 ml/(min 100g tissue)). Please convert the above local blood perfusion rates into values with the unit of 1/s, therefore, they can be used in the Pennes bioheat equation. The tissue density in a human body is 1050 kg/m³.arrow_forwardThermodynamics Answer the following problem with complete solutions. Write legibly A balloon is filled with pure oxygen at 10 ℃. The balloon is released from the bottom of a water-filled testing pool and floats 30 m to the water surface (where the atmospheric pressure is standard). The volume of the balloon is 3,000 cm^3. The temperature is 25 ℃ at the surface of the water, and the water temperature at the bottom of the pool is 10 ℃. What is the volume of the balloon at the surface after it has come into thermal equilibrium with the surroundingsarrow_forward
- fluid mechanics A pipe 200 (mm) diameter carries Oil at a flow rate of 0.030 (m³/s). The pipe diameter reduces from 200 (mm) to 150 (mm). Point 1 is located at the beginning of the pipe and point 2 is located at the end of the pipe. Elevation of point 1 is 165 (m) lower than elevation of point 2. Water pressure at point 2 is atmospheric pressure. Water flow in the pipe ascending from point 1 to point 2. Total head losses of flow in the pipe equals to 15 (m). 1- Find the value of pressure head of Oil at point 1. 2- Draw the H.G.L. of flow in the pipe.arrow_forward62. •A 5-kg object is constrained to move along a straight line. Its initial speed is 12 m/s in one direction, and its final speed is 8 m/s in the opposite Complete the graph of force versus time with direction. F (N) (s) appropriate values for both variables (Figure 7-26). Several answers are correct, just be sure that your answer is internally consistent. Figure 7-26 Problem 62arrow_forwardYou are the mechanical engineer supervising the layout of a piping system. In a certain portion of the pipe, the specifications are as follows: length of pipe is 10m, inside diameter of 30cm, outside diameter of 30.5cm, maximum allowable speed of 15m/s and a coefficient of 0.003456. If the uncertainties are 0.02mm for length, 0.8mm for the diameters and 0.1mm/s for the velocity, what loss of head will be imminent in this pipe? In the piping system above, what is the uncertainty in computed head loss contributed by the velocity of the pipe?arrow_forward
- You are the mechanical engineer supervising the layout of a piping system. In a certain portion of the pipe, the specifications are as follows: length of pipe is 10m, inside diameter of 30cm, outside diameter of 30.5cm, maximum allowable speed of 15m/s and a coefficient of 0.003456. If the uncertainties are 0.02mm for length, 0.8mm for the diameters and 0.1mm/s for the velocity, what loss of head will be imminent in this pipe?arrow_forwardYou are the mechanical engineer supervising the layout of a piping system. In a certain portion of the pipe, the specifications are as follows: length of pipe is 10m, inside diameter of 30cm, outside diameter of 30.5cm, maximum allowable speed of 15m/s and a coefficient of 0.003456. If the uncertainties are 0.02mm for length, 0.8mm for the diameters and 0.1mm/s for the velocity, what loss of head will be imminent in this pipe? With all the above uncertainties, what is the total uncertainty in the head loss?arrow_forward3G 4G 9:1V docs.google.com/forms :D Mechanics / صباحي *مطلوب Untitled Section F1 F2 a F3 B. d b C F4 D Consider the following values: - F5 a = 13 m; b = 8 m; c = 10 m; d = 5 m; F1 = 3 kN; F2 = 11 kN; F3 = 2 kN; F4 = 20 kN; F5 = 2 kN; a = 30° , 0 = 60° B = 30° 1] What is the resultant moment of the five forces acting on the rod about point A? a) 19.2 kN.m b) 32.7 kN.m c) 44.6 kN.m d) 29.8 kN.m e) 14.1 kN.m f) 21.3 kN.m 2] What is the resultant moment of the five forces acting on the rod about point B? a) 98.8 kN.m b) 23.7 kN.m c) 81.6 kN.m d) 65.6 kN.m e) 91.1 kN.m f) 74.2 kN.m 3] What is the resultant moment of the five forces acting on the rod about point C? a) 125.7 kN.m b) 111.1 kN.m c) 74.6 kN.m d) 109.4 kN.m e) 24.1 kN.m f) 65.3 kN.m 4] What is the resultant moment of the five forces acting on the rod about point D? a) 17.8 kN.m b) 88.7 kN.m c) 10.6 kN.m d) 59.5 kN.m e) 29.1 kN.m f) 70.1 kN.m 5] What is the moment of the force F2 about point E? Activate V ) 21.3 kN.m Go to Setting…arrow_forward
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