1. Obtain the equivalent viscous-friction coefficient beg of the system shown below: X b₁ H b₂ H b3
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- Find the constant of proportionality. z is directly proportional to the sum of x and y. If x=2 and y=5, then z=28.Find the constant of proportionality. y is directly proportional to x. If x=30, then y=15.A mass weighing 16 pounds is attached to a spring, stretching it 2 feet. A damping mechanism provides a resistance numerically equal to b times the instantaneous velocity. The mass is pulled down 1 foot below equilibrium and released from rest. a. Find the equations of motion for b = 3, b = 4, b = 5. b. Determine if each system is underdamped, critically damped, or overdamped.
- The internal energy U of a gas can be expressed in the form U=f(p,V,T) with variables defined by: p is the pressure, V is the volume, and T is the temperature. For an ideal gas, PV = nRT where the number of moles n and R (gas-specific) are constants.Suppose the potential energy of some system is given by the equation U(x,y, z) = -4x³z² + y %3D A. 8x³z В. 12х2 С. 1 E. 12x²z? F. 24x²z G. -8x³z Н. —12x2 I. –1 J. –12x?z? К. —24x2z i) Which of the above expressions correctly gives the force in the x – direction? Answer: ii) Which of the above expressions correctly gives the force in the y – direction? Answer: iii) Which of the above expressions correctly gives the force in the z – direction? Answer:Q.4 Baiji north Refinery use kirkuk crude oil(API=36) with total flowrate 150000 BBL/ Day(the price of one BBI of crude oil=87000 Iraqi Dinar).It has the following products: Gasoline 20%(one litre price=450 Iraqi Dinar),Kerosine 15% (one litre price=150 Iraqi Dinar),Gas oil 20%(one litre price-400 Iraqi Dinar).and 45% remaining is Black oil(one litre price-50 Iraqi Dinar). Is this Refinery Win or Lose?
- 5. Okay, time for some mathematics. We're going to focus on the interactions between the hares and their main predators, the lynx. The tool we need is differential equations (last seen when we talked about the S-I-R disease model). We will let H(t) be the density of hares at time t, and L(t) the density of lynx at time t. Our first assumption is that, if there are no lynx around, the hares grow exponentially. Hares lead to more hares and faster growth. This gives us the differential equation (trust me): HP = aH dt where a is a positive constant. Second we assume that, if there are no hares around, the lynx starve and thus their numbers decay exponentially. This gives us: TP = -bL dt9) The potential energy of a compressed spring is: 1 -kx U where k is the spring constant and x is the length of spring deflection. The spring constant is known to be 201 + 7 Newtons per meter. The spring deflection has been measured to be 0.11 + 0.004 meters. Determine the uncertainty in the potential energy of the deflected spring.Q5. Write the governing equation of 1-D heat transfer with convective heat loss and indicate all the parameters involved in it.
- Assume that traffic flows freely through the intersections A, B, C, and D. The values x, X, X, andx, and the other numbers in the figure represent flow rates in vehicles per hour. 328 431 194 281 274 329 308 379For the calibration data in the Table below, determine the static sensitivity of the system at (a) X = 5, (b) X = 10, and (c) X = 20. For which input values is the system more sensitive? Explain what this might mean in terms of a measurement and in terms of measurement errors. Calibration Data: X(cm) 0.5 1.0 2.0 5.0 Y(V) 0.4 1.0 2.3 6.9 10.0 20.0 50.0 15.8 36.4 110.1 100.0 253.2The density of air changes with height. Under some conditions density p, depends on height z, and temperature T according to the following equation where Po and A are both constants. A meteorological balloon ascends (i.e., starts at z = 1 and gains height) over the course of several hours. Complete parts (a) and (b) below. Az P(z,T) = Po e ..... dz v) and that the temperature changes over time (i.e., that T is given by a function T(t)), derive, using the chain rule, an expression for the rate of change of air density, (a) Assuming that the balloon ascends at a speed v (i.e., dt as measured by the weather balloon. Choose the correct answer below. dp Az dT O A. dt T2 dt dp %3D dt Az dT dp С. dt %3D + T dt dp Az) dT O D. dt T2) dt (b) Assume that v = 1, Po = 1, and A = 1 and that when t= 0, T= 1. Are there any conditions under which the density, as measured by the balloon will not change in time? That is, find a differential equation that T must satisfy, if dp = 0, and solve this…