Question A single phase AC generator feeds a load. The generator may be modeled as an ideal sinusoidal voltage source (Ex volts) in series with an ideal inductance (X, ohms) and a small winding resistance. The resistance is about 10% of the ohmic value of the inductive reactance. The load draws a current of I, amps with a power factor of 80% lagging at a voltage being VL volts. The voltages and current just mentioned are all in their rms values. Draw and label the circuit, write down the governing equation(s) and draw an appropriate phasor diagram for this operation.

3/129 An 80-kg pole vaulter carrying a uniform 4.9-m, 4.5-kg pole approaches the jump with a velocity v and man- ages to barely clear the bar set at a height of 5.5 m. As he clears the bar, his velocity and that of the pole are essen- tially zero. Calculate the minimum possible value of v re- quired for him to make the jump. Both the horizontal pole and the center of gravity of the vaulter are 1.1 m above the ground during the approach. 099 5.5 m TESTS 1/ 4.9 m 1.1 m

Use Algorithm 3.2 to construct the interpolating polynomial of degree three for the unequally spaced points given in the following table: x f(x) -0.1 5.30000 0.0 2.00000 0.2 3.19000 0.3 1.00000

Underground water as shown Figure 2 is to be pumped by a 78%-efficient 5 kW submerged pump to a pool whose free surface is 30 m above the underground water level. The diameter of the pipe is 7 cm on the intake side and 5 cm on the discharge side. Determine i. The maximum flow rate of water. ii. The velocity of the water through the pipe at the discharge side. Assume the elevation difference between the pump inlet and the outlet and the effect of the kinetic energy correction factors to be negligible. Pool 30 m Figure 2

The Anderson County board of supervisors has agreed to fund an ambitious project that will spend money now to save much more money in the future. A total of $16.2 million will be awarded to the York Corporation for energy improvements in 40 buildings, 27 parks, and 37 traffic intersections. These improvements include lighting upgrades, solar hot water collectors, more efficient heating/cooling systems, and light-emitting diodes for traffic signals. Bonds paying 7% per year over the next 15 years will be used to pay for these improvements. If the annual savings fail to average $2 million, York Corporation will reimburse the county the difference. Will York need to pay any money to the county? If so, how much?

Problem 5. [15 pts) Work out the curl of integrand F in the following line integrals to determine whether it is path independent. If yes, find out the corresponding potential function f and calculate the integration from (0, 0, 0) to (a, b, c). (a) [5 pts) Sexydx + x2ydy + 6zędz (b) [10 pts] Sc sin(x2 + 2y2 + z2) (2xdx + 4ydy + 2zdz)

 The area bounded by the curve y^2 = 12x and the line x = 3 is revolved about the line x =3. What is the volume generated? Show full solution