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- Q8): To find how much heat is required to bring a kettle of water to its boiling point, you are asked to calculate the specific heat of water at 61°C. The specific heat of water is given as a function of time in Table below. Temperature, T Specific heat, C₂ (°C) J kg-°C 22 42 52 82 100 4181 4179 4186 4199 4217 Determine the value of the specific heat at 7=61°C using the direct T method of interpolation and a third order polynomial. Find the absolute relative approximate error for the third order polynomial approximation (Lagrange Method).Supercomp Ltd produces two computer models PC1086 and PC1186. The matrix A shows the cost per computer (in thousands of dollars) and B the production figures for the year 2010 (in multiples of 10,000 units.) Find a matrix C that shows the shareholders the cost per quarter (in millions of dollars) for raw material, labor, and miscellaneous. Quarter 1 2 3 4 PC1086 PC186 1.2 1.6 Raw Components 3 8 6 9 B PC1086 0.3 0.4 Labor 6 2 4 3 PC1186 0.5 0.6 MiscellaneousThe upward velocity of a rocket can be computed by the following formula: m. v = u ln mo gt qt where v =upward velocity,u = the velocity at which fuel is expelled relative to the rocket, m, = the initial mass of the rocket, q = the fuel consumption rate, and g = the downward acceleration of gravity (assumed constant =9.81 m/s2). %3D If u = 2200 m/s, m, = 160000 kg and q v = 1000 m/s using, = 2680 kg/s, compute the time at which 1. The graphical method, take t = 0 to 30 s with step (10 s). 2. The false-position method to within ɛ, = 0.12%. Use initial guesses of t = 20 s and 30 s. %3D
- is a mass hanging by a spring under the influence of gravity. The force due to gravity, Fg, is acting in the negative-y direction. The dynamic variable is y. On the left, the system is shown without spring deflection. On the right, at the beginning of an experiment, the mass is pushed upward (positive-y direction) by an amount y₁. The gravitational constant g, is 9.81 m/s². DO C.D Frontly у Your tasks: No Deflection m k Fg = mg Initial Condition y m k Write down an expression for the total energy If as the sum Write down an expression for the total energy H Fg = mg Figure 3: System schematic for Problem 4. Yi & X Write down, in terms of the variables given, the total potential energy stored in the system when it is held in the initial condition, relative to the system with no deflection. as the sum of potential and kinetic energy in terms of y, y, yi C After the system is released, it will start to move. Write down an expression for the kinetic energy of the system, T, in terms of…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? In the piping system above, what is the uncertainty in computed head loss contributed by the velocity of the pipe?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?
- 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? With all the above uncertainties, what is the total uncertainty in the head loss?Q1: The number of bacterial cells (P) in a given reactor is related to time in days (t) as described by the following mathematical model: dp dt 0.0000007 P², If at initial time (P = 106). Determine the number of cells when (t 2days) using the fourth order Runge-Kutta method and at time increment of (1 day). = = 0.3 P 1Consider the following data with reference to elementary deterministic economic order quantity model Annual demand of an item 100000 Unit price of the item (in Rs.) 10 Inventory carrying cost per unit per year (in Rs.) 1.5 Unit order cost (in Rs.) 30 The total number of economic orders per year to meet the annual demand is
- The population of a community is known to increase at a rate proportional to the number of people present at time t. If an initial population P, has doubled in 7 years, how long will it take to triple? (Round your answer to one decimal place.) yr How long will it take to quadruple? (Round your answer to one decimal place.) yr еВook100 80 60 40 20 0.002 0.004 0.006 0.008 0.01 0.012 Strain, in/in. FIGURE P1.17 1.18 Use Problem 1.17 to graphically determine the following: a. Modulus of resilience b. Toughness Hint: The toughness (u) can be determined by calculating the area under the stress-strain curve u = de where & is the strain at fracture. The preceding integral can be approxi- mated numerically by using a trapezoidal integration technique: u, = Eu, = o, + o e, - 6) %3D c. If the specimen is loaded to 40 ksi only and the lateral strain was found to be -0.00057 in./in., what is Poisson's ratio of this metal? d. If the specimen is loaded to 70 ksi only and then unloaded, what is the permanent strain? Stress, ksiis a mass hanging by a spring under the influence of gravity. The force due to gravity, Fg, is acting in the negative-y direction. The dynamic variable is y. On the left, the system is shown without spring deflection. On the right, at the beginning of an experiment, the mass is pushed upward (positive-y direction) by an amount y₁. The gravitational constant g, is 9.81 m/s². No Deflection m k Fg = mg Initial Condition m k Fg = mg Figure 3: System schematic for Problem 4. Yi 8 Your tasks: A Write down, in terms of the variables given, the total potential energy stored in the system when it is held in the initial condition, relative to the system with no deflection. B Write down an expression for the total energy H as the sum of potential and kinetic energy in terms of y, y, yi and element parameters. Will H change as the mass moves? C After the system is released, it will start to move. Write down an expression for the kinetic energy of the system, T, in terms of position, y, the initial…