ADVANCED ENGINEERING MATH W/ACCESS
10th Edition
ISBN: 9781119096023
Author: Kreyszig
Publisher: WILEY
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Obtain the voltage across the capacitor for the following input: (a) 5Volts; (b) 3sin(t); (c) 2 cos(t). please show that you use Laplace transform and Cramer's rule.
5.12 A steel wire 300 feet long and 1½-½ inch in diameter
weighs 0.042 #/ft. If the wire is suspended vertically from
its upper end, calculate (a) the maximum tensile stress due
to its own weight and (b) the maximum weight W that can
be safely supported assuming a safety factor of three and
an ultimate tensile stress of 65 ksi.
a. The maximum tensile stress due to
its own weight
b. Maximum weight
5.6
The turnbuckles in the diagram shown are tightened
until the compression block DB exerts a force of 10,000# on
the beam at B. Member DB is a hollow shaft with an inner
diameter of 1.0 inch and outer diameter of 2 inches. Rods
AD and CD each have cross-sectional areas of 1.0 in.². Pin
C has a diameter of 0.75 inch. Determine:
a. The axial stress in BD-
b. The axial stress in CD-
c. The shearing stress in pin C.
B
UB
CD
PIN
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- 5.15 The ends of the laminated-wood roof arch shown are tied together with a horizontal steel rod 90 feet, "10 inches" long, which must withstand a total load of 60 k. Two turn- buckles are used. All threaded rod ends are upset. a. Determine the required diameter D of the rod if the maximum allowable stress is 20 ksi. b. If the unstressed length of the rod is 90 feet, "10 inches" and there are four threads per inch on the upset ends, how many turns of one turnbuckle will bring it back to its unstressed length after it has elongated under full allowable tensile stress? E = 29 × 103 ksi. a. Required diameter D b. Number of turns LAMINATED WOOD ROOF ARCH TIE ROD TURNBUCKLE DETAIL: UPSET ENDarrow_forward5.8 A reinforced concrete column is 12 feet long, and un- der load, it shortens 3 inches". Determine its average unit strain. Average Unit Strainarrow_forward5.10 A 500-foot-long steel cable is loaded in tension and registers an average unit strain of 0.005. Determine the total elongation due to this load. Total Elongationarrow_forward
- 5.14 A 100-foot-long surveyor's steel tape with a cross- sectional area of 0.006 square inch must be stretched with a pull of 16# when in use. If the modulus of elasticity of this steel is E = 30,000 ksi, (a) what is the total elongation 8 in the 100 foot tape and (b) what unit tensile stress is pro- duced by the pull? a. Elongation b. Tensile Stressarrow_forwardObtain the voltage across the capacitor for the following input: (a) 5Volts; (b) 3sin(t); (c) 2 cos(t). Use Laplace transform and Cramer's rule.arrow_forwardObtain the voltage across the capacitor for the following input: (a) 5Volts; (b) 3sin(t); (c) 2 cos(t). Use Laplace transform and Cramer's rule.arrow_forward
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- For communcation marks. In the questions answered above should have the criteria show proper mathematical form use proper symbols, notations, conventions, graph(s) where applicable solution is neat, clear and easy to follow If you write on the paper in online version you will be assigned 0 marks except graph.arrow_forwarda) If is a polynomial function, does always have to have a horizontal asymptote? If no, provide a counterexample. ax+b b) Write an equation for a rational function whose graph of the formex+d where f(x) has all the indicated features. X-intercept of 14 Y-intercept of -1/2 VA with equation -2/3 HA with equation 4/3arrow_forwardAn airplane has a speed of 400 km/h with no wind. The airplane flies 2140 km with the wind. The airplane can only fly 1860 km against the wind in the same time. If w represents the speed of the wind, create an equation could be used to solve for w? Find the speed f the wind. hint; Use Time = Distance / speedarrow_forward
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