Numerical Methods for Engineers
7th Edition
ISBN: 9780073397924
Author: Steven C. Chapra Dr., Raymond P. Canale
Publisher: McGraw-Hill Education
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Chapter 18, Problem 13P
Develop quadratic splines for the first five data points in Prob. 18.5 and predict
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Given that an L-shaped member (OAB) can rotate about OA, determine the moment vector created by the force about the line OA at the instant shown in the figure below. OA lies in the xy-plane, and the AB part is vertical. Express your answer as a Cartesian vector.
Determine the magnitude of the moment created by the force about the point A.
Chapter 18 Solutions
Numerical Methods for Engineers
Ch. 18 - 18.1 Estimate the common logarithm of 10 using...Ch. 18 - 18.2 Fit a second-order Newton’s interpolating...Ch. 18 - 18.3 Fit a third-order Newton’s interpolating...Ch. 18 - Repeat Probs. 18.1 through 18.3 using the Lagrange...Ch. 18 - 18.5 Given these...Ch. 18 - 18.6 Given these data
x 1 2 3 5 7 8
...Ch. 18 - Repeat Prob. 18.6 using Lagrange polynomials of...Ch. 18 - 18.8 The following data come from a table that was...Ch. 18 - 18.9 Use Newton’s interpolating polynomial to...Ch. 18 - Use Newtons interpolating polynomial to determine...
Ch. 18 - 18.11 Employ inverse interpolation using a cubic...Ch. 18 - 18.12 Employ inverse interpolation to determine...Ch. 18 - 18.13 Develop quadratic splines for the first five...Ch. 18 - 18.14 Develop cubic splines for the data in Prob....Ch. 18 - Determine the coefficients of the parabola that...Ch. 18 - Determine the coefficients of the cubic equation...Ch. 18 - 18.17 Develop, debug, and test a program in either...Ch. 18 - 18.18 Test the program you developed in Prob....Ch. 18 - 18.19 Use the program you developed in Prob. 18.17...Ch. 18 - Use the program you developed in Prob. 18.17 to...Ch. 18 - Develop, debug, and test a program in either a...Ch. 18 - 18.22 A useful application of Lagrange...Ch. 18 - Develop, debug, and test a program in either a...Ch. 18 - Use the software developed in Prob. 18.23 to fit...Ch. 18 - Use the portion of the given steam table for...Ch. 18 - The following is the built-in humps function that...Ch. 18 - 18.28 The following data define the sea-level...Ch. 18 - 18.29 Generate eight equally-spaced points from...Ch. 18 - 18.30 Temperatures are measured at various points...
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- = MMB 241- Tutorial 1.pdf 2/3 80% + + 10. Determine a ats = 1 m v (m/s) 4 s (m) 2 11. Draw the v-t and s-t graphs if v = 0, s=0 when t=0. a (m/s²) 2 t(s) 12. Draw the v-t graph if v = 0 when t=0. Find the equation v = f(t) for each a (m/s²) 2 segment. 2 -2 13. Determine s and a when t = 3 s if s=0 when t = 0. v (m/s) 2 t(s) t(s) 2arrow_forwardQ.5) A cylinder is supported by spring AD and cables AB and AC as shown. The spring has an at rest length (unstretched length) of 4 meters. If the maximum allowable tension in cables AB and AC is 200 N, determine (a) the largest mass (kg) of cylinder E the system can support, (b) the necessary spring constant (stiffness) to maintain equilibrium, and (b) the tension (magnitude) in each cable when supporting the maximum load found in part (a). B 4 m 3 m A E 1 m 3 m D 5 marrow_forwardDetermine the moment created by the force about the point O. Express your answer as a Cartesian vector.arrow_forward
- 4. An impeller rotating at 1150 rpm has the following data: b, = 1 ¼ in., b2 = ¾ in., d, = 7 in., d2 = 15 in., B1 = 18", B2 = 20°, cross-sectional area A = Db if vane thickness is neglected. Assuming radial inlet flow, determine the theoretical capacity in gpm head in ft horsepower 5. If the impeller in Problem (4) develops an actual head of 82 ft and delivers 850 gpm at the point of maximum efficiency and requires 22 BHP. Determine overall pump efficiency virtual velocities V2 and W2arrow_forward(30 pts) Problem 1 A thin uniform rod of mass m and length 2r rests in a smooth hemispherical bowl of radius r. A moment M mgr 4 is applied to the rod. Assume that the bowl is fixed and its rim is in the horizontal plane. HINT: It will help you to find the length l of that portion of the rod that remains outside the bowl. M 2r a) How many degrees of freedom does this system have? b) Write an equation for the virtual work in terms of the angle 0 and the motion of the center of mass (TF) c) Derive an equation for the variation in the position of the center of mass (i.e., Sŕƒ) a. HINT: Use the center of the bowl as the coordinate system origin for the problem. d) In the case of no applied moment (i.e., M 0), derive an equation that can be used to solve for the equilibrium angle of the rod. DO NOT solve the equation e) In the case of an applied moment (i.e., M = mgr = -) derive an equation that can be used to 4 solve for the equilibrium angle of the rod. DO NOT solve the equation. f) Can…arrow_forwardPlease show all work step by steparrow_forward
- Copyright 2013 Pearson Education, publishing as Prentice Hall 2. Determine the force that the jaws J of the metal cutters exert on the smooth cable C if 100-N forces are applied to the handles. The jaws are pinned at E and A, and D and B. There is also a pin at F. E 400 mm 15° D B 30 mm² 80 mm/ 20 mm 15° $15° 20 mm 400 mm 15° 100 N 100 N 15°arrow_forwardDraw for it make a match which directionarrow_forwardQ.1) Block A is connected to block B by a pulley system as shown. The weights of blocks A and B are 100 lbs and 70 lbs, respectively. Assume negligible friction between the rope and all pulleys as well as between block B and the incline and neglect the mass of all pulleys and cables. Determine the angle 0 required to keep the system in equilibrium. (At least two FBDs must be drawn for full credit) B Ꮎ 000arrow_forward
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