Ch 9
112 Pages

Ch 9

Course Number: CE Statics, Fall 2010

College/University: SUBR

Word Count: 9441

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9 Solutions 44918 1/28/09 2:34 PM Page 815 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 91. Determine the mass and the location of the center of mass (x, y) of the uniform...

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Solutions 9 44918 1/28/09 2:34 PM Page 815 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 91. Determine the mass and the location of the center of mass (x, y) of the uniform parabolic-shaped rod. The mass per unit length of the rod is 2 kg> m. y y2 4x 4m x 4m 8 15 9 Solutions 44918 1/28/09 2:34 PM Page 816 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 92. The uniform rod is bent into the shape of a parabola and has a weight per unit length of 6 lb> ft. Determine the reactions at the fixed support A. y y2 3x 3 ft A x 3 ft 8 16 9 Solutions 44918 1/28/09 2:34 PM Page 817 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 93. Determine the distance x to the center of mass of the homogeneous rod bent into the shape shown. If the rod has a mass per unit length of 0.5 kg> m, determine the reactions at the fixed support O. y 1m 1m y2 O x x3 8 17 9 Solutions 44918 1/28/09 2:34 PM Page 818 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *94. Determine the mass and locate the center of mass (x, y) of the uniform rod. The mass per unit length of the rod is 3 kg> m. y y 4 x2 4m x 2m 8 18 9 Solutions 44918 1/28/09 2:34 PM Page 819 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 95. Determine the mass and the location of the center of mass x of the rod if its mass per unit length is m = m0(1 + x> L). y x L 8 19 9 Solutions 44918 1/28/09 2:34 PM Page 820 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 96. Determine the location (x, y) of the centroid of the wire. y 2 ft 4 ft y x2 x 97. Locate the centroid x of the circular rod. Express the answer in terms of the radius r and semiarc angle a. y r a C x a r x 8 20 9 Solutions 44918 1/28/09 2:34 PM Page 821 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *98. Determine the area and the centroid (x, y) of the area. y 4m y2 4x x 4m 8 21 9 Solutions 44918 1/28/09 2:34 PM Page 822 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 99. Determine the area and the centroid (x, y) of the area. y 1m y2 x3 x 1m 8 22 9 Solutions 44918 1/28/09 2:34 PM Page 823 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 910. Determine the area and the centroid (x, y) of the area. y 3 ft y 1 x3 9 x 3 ft 8 23 9 Solutions 44918 1/28/09 2:34 PM Page 824 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 911. Determine the area and the centroid (x, y) of the area. y y2 2 ab 4ax x b 8 24 9 Solutions 44918 1/28/09 2:34 PM Page 825 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *912. Locate the centroid x of the area. y y x1/ 2 2x5/ 3 x 2 ft 8 25 9 Solutions 44918 1/28/09 2:34 PM Page 826 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 913. Locate the centroid y of the area. y y x1/ 2 2x5/ 3 x 2 ft 8 26 9 Solutions 44918 1/28/09 2:34 PM Page 827 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 914. Determine the area and the centroid (x, y) of the area. y xy c2 x a b 8 27 9 Solutions 44918 1/28/09 2:34 PM Page 828 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 915. Determine the area and the centroid (x, y) of the area. y h y h x2 a2 x a 8 28 9 Solutions 44918 1/28/09 2:34 PM Page 829 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *916. Locate the centroid (x, y) of the area. y 1 1 x2 4 y 1m x 2m 8 29 9 Solutions 44918 1/28/09 2:34 PM Page 830 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 917. Determine the area and the centroid (x, y) of the area. y h y h x2 a2 x a 8 30 9 Solutions 44918 1/28/09 2:34 PM Page 831 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 918. The plate is made of steel having a density of 7850 kg> m3. If the thickness of the plate is 10 mm, determine the horizontal and vertical components of reaction at the pin A and the tension in cable BC. y C B y3 2m A x 2x 4m 8 31 9 Solutions 44918 1/28/09 2:34 PM Page 832 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 919. Determine the location x to the centroid C of the upper portion of the cardioid, r = a(1 - cos u). r a (1 cos u) y C r u _ x x 8 32 9 Solutions 44918 1/28/09 2:34 PM Page 833 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *920. The plate has a thickness of 0.5 in. and is made of steel having a specific weight of 490 lb> ft3. Determine the horizontal and vertical components of reaction at the pin A and the force in the cord at B. y B 3 ft x2 3 x 3 ft y A 8 33 9 Solutions 44918 1/28/09 2:34 PM Page 834 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 921. Locate the centroid x of the shaded area. y x2 ) 2a y 2k(x ka x a 922. Locate the centroid x of the area. y 0.5 in. 2 in. y 1 x 0.5 in. x 2 in. 8 34 9 Solutions 44918 1/28/09 2:34 PM Page 835 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 923. Locate the centroid y of the area. y 0.5 in. 2 in. y 1 x 0.5 in. x 2 in. *924. Locate the centroid (x, y) of the area. y y 9 ft 9 x2 x 3 ft 8 35 9 Solutions 44918 1/28/09 2:34 PM Page 836 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 925. Determine the area and the centroid (x, y) of the area. y y 3 ft x y x3 9 x 3 ft 8 36 9 Solutions 44918 1/28/09 2:34 PM Page 837 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 926. Locate the centroid x of the area. y y2 1m x x2 x y 1m 927. Locate the centroid y of the area. y y2 1m x x2 x y 1m 8 37 9 Solutions 44918 1/28/09 2:34 PM Page 838 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *928. Locate the centroid x of the area. y y h xn an h x a 929. Locate the centroid y of the area. y y h xn an h x a 8 38 9 Solutions 44918 1/28/09 2:34 PM Page 839 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 930. The steel plate is 0.3 m thick and has a density of 7850 kg> m3. Determine the location of its center of mass. Also determine the horizontal and vertical reactions at the pin and the reaction at the roller support. Hint: The normal force at B is perpendicular to the tangent at B, which is found from tan u = dy> dx. y y2 2x 2m A x 2m B 2m 8 39 9 Solutions 44918 1/28/09 2:34 PM Page 840 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 931. Locate the centroid of the area. Hint: Choose elements of thickness dy and length [(2 - y) - y2]. y y2 1m x y x 2 x 1m 1m 8 40 9 Solutions 44918 1/28/09 2:34 PM Page 841 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *932. Locate the centroid x of the area. y y2 4x 2 ft y 2x x 1 ft 933. Locate the centroid y of the area. y y2 4x 2 ft y 2x x 1 ft 8 41 9 Solutions 44918 1/28/09 2:34 PM Page 842 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 934. If the density at any point in the rectangular plate is defined by r = r0(1 + x> a), where r0 is a constant, determine the mass and locate the center of mass x of the plate. The plate has a thickness t. y b 2 x b 2 a 8 42 9 Solutions 44918 1/28/09 2:34 PM Page 843 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 935. Locate the centroid y of the homogeneous solid formed by revolving the shaded area about the y axis. z y2 (z a)2 a2 a y x 8 43 9 Solutions 44918 1/28/09 2:34 PM Page 844 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *936. Locate the centroid z of the solid. z a z 1 a (a y)2 y a x 8 44 9 Solutions 44918 1/28/09 2:34 PM Page 845 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 937. Locate the centroid y of the homogeneous solid formed by revolving the shaded area about the y axis. z z2 1 y3 16 2m y x 4m 8 45 9 Solutions 44918 1/28/09 2:34 PM Page 846 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 938. Locate the centroid z of the homogeneous solid frustum of the paraboloid formed by revolving the shaded area about the z axis. z h2 (a a2 y2) z h 2 h 2 y a x 8 46 9 Solutions 44918 1/28/09 2:34 PM Page 847 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 939. Locate the centroid y of the homogeneous solid formed by revolving the shaded area about the y axis. z 5 ft z2 y2 9 4 ft 3 ft y x 8 47 9 Solutions 44918 1/28/09 2:34 PM Page 848 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *940. Locate the center of mass y of the circular cone formed by revolving the shaded area about the y axis. The density at any point in the cone is defined by r = (r0 > h)y, where r0 is a constant. a z h z a y h a y x 8 48 9 Solutions 44918 1/28/09 2:34 PM Page 849 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 941. Determine the mass and locate the center of mass y of the hemisphere formed by revolving the shaded area about the y axis. The density at any point in the hemisphere can be defined by r = r0(1 + y> a), where r0 is a constant. z y2 z2 a2 r y x 8 49 9 Solutions 44918 1/28/09 2:34 PM Page 850 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 942. Determine the volume and locate the centroid (y, z) of the homogeneous conical wedge. z h a y h z x a y 8 50 9 Solutions 44918 1/28/09 2:34 PM Page 851 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 943. The hemisphere of radius r is made from a stack of very thin plates such that the density varies with height, r = kz, where k is a constant. Determine its mass and the distance z to the center of mass G. G z r x _ z y 8 51 9 Solutions 44918 1/28/09 2:34 PM Page 852 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *944. Locate the centroid (x, y) of the uniform wire bent in the shape shown. y 100 mm 20 mm 150 mm x 50 mm 8 52 9 Solutions 44918 1/28/09 2:34 PM Page 853 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 945. Locate the centroid (x, y, z) of the wire. z 400 mm 200 mm x y 8 53 9 Solutions 44918 1/28/09 2:34 PM Page 854 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 946. Locate the centroid (x, y, z) of the wire. z 6 in. 4 in. x y 8 54 9 Solutions 44918 1/28/09 2:34 PM Page 855 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 947. Locate the centroid (x, y, z) of the wire which is bent in the shape shown. 2 in. z 2 in. 4 in. x y 8 55 9 Solutions 44918 1/28/09 2:34 PM Page 856 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *948. The truss is made from seven members, each having a mass per unit length of 6 kg/m. Locate the position (x, y) of the center of mass. Neglect the mass of the gusset plates at the joints. y E D 3m A 3m B 3m C x 8 56 9 Solutions 44918 1/28/09 2:34 PM Page 857 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 949. Locate the centroid (x, y) of the wire. If the wire is suspended from A, determine the angle segment AB makes with the vertical when the wire is in equilibrium. y A 60 B 200 mm 200 mm C x 8 57 9 Solutions 44918 1/28/09 2:34 PM Page 858 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 950. Each of the three members of the frame has a mass per unit length of 6 kg/m. Locate the position (x, y) of the center of mass. Neglect the size of the pins at the joints and the thickness of the members. Also, calculate the reactions at the pin A and roller E. 6m y 4m 4m E C D B 7m A x 8 58 9 Solutions 44918 1/28/09 2:34 PM Page 859 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 951. Locate the centroid (x, y) of the cross-sectional area of the channel. y 1 in. 22 in. x 1 in. 9 in. 1 in. 8 59 9 Solutions 44918 1/28/09 2:34 PM Page 860 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *952. Locate the centroid y of the cross-sectional area of the concrete beam. 12 in. 3 in. y 12 in. 27 in. 6 in. x 3 in. 3 in. 8 60 9 Solutions 44918 1/28/09 2:34 PM Page 861 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 953. Locate the centroid y of the cross-sectional area of the built-up beam. y 6 in. 1 in. 1 in. 6 in. x 3 in. 1 in. 3 in. 1 in. 8 61 9 Solutions 44918 1/28/09 2:34 PM Page 862 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 954. Locate the centroid y of the channels crosssectional area. 2 in. 4 in. 2 in. 12 in. 2 in. y C 955. Locate the distance y to the centroid of the members cross-sectional area. y 0.5 in. 0.5 in. 6 in. 1.5 in. 1 in. 3 in. 3 in. x 8 62 9 Solutions 44918 1/28/09 2:34 PM Page 863 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *956. Locate the centroid y of the cross-sectional area of the built-up beam. y 1.5 in. 1.5 in. 4in. 4 in. 1.5 in. 3.5 in. 11.5 in. 1.5 in. x 8 63 9 Solutions 44918 1/28/09 2:34 PM Page 864 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 957. The gravity wall is made of concrete. Determine the location (x, y) of the center of mass G for the wall. y 1.2 m _ x G _ y 0.4 m x 3m 2.4 m 0.6 m 0.6 m 8 64 9 Solutions 44918 1/28/09 2:34 PM Page 865 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 958. Locate the centroid x of the composite area. y r0 x ri 8 65 9 Solutions 44918 1/28/09 2:34 PM Page 866 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 959. Locate the centroid (x, y) of the composite area. y 3 in. 4 in. 3 in. 3 in. x 8 66 9 Solutions 44918 1/28/09 2:34 PM Page 867 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *960. Locate the centroid (x, y) of the composite area. y 3 ft 1.5 ft 3 ft 1 ft x 8 67 9 Solutions 44918 1/28/09 2:34 PM Page 868 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 961. Divide the plate into parts, and using the grid for measurement, determine approximately the location (x, y) of the centroid of the plate. y 200 mm 200 mm x 8 68 9 Solutions 44918 1/28/09 2:34 PM Page 869 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 962. To determine the location of the center of gravity of the automobile it is first placed in a level position, with the two wheels on one side resting on the scale platform P. In this position the scale records a reading of W1. Then, one side is elevated to a convenient height c as shown. The new reading on the scale is W2. If the automobile has a total weight of W, determine the location of its center of gravity G(x, y). y G c x b W2 P 8 69 9 Solutions 44918 1/28/09 2:34 PM Page 870 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 963. Locate the centroid y of the cross-sectional area of the built-up beam. 150 mm y 150 mm 20 mm 200 mm 450 mm x 20 mm 8 70 9 Solutions 44918 1/28/09 2:34 PM Page 871 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *964. Locate the centroid y of the cross-sectional area of the built-up beam. 200 mm y 200 mm 20 mm 50 mm 150 mm 10 mm 300 mm 20 mm 10 mm 20 mm x 8 71 9 Solutions 44918 1/28/09 2:34 PM Page 872 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 965. The composite plate is made from both steel (A) and brass (B) segments. Determine the mass and location 1x, y, z2 of its mass center G. Take rst = 7.85 Mg> m3 and rbr = 8.74 Mg> m3. A G z 225 mm 150 mm B 150 mm 30 mm x y 8 72 9 Solutions 44918 1/28/09 2:34 PM Page 873 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 966. The car rests on four scales and in this position the scale readings of both the front and rear tires are shown by FA and FB. When the rear wheels are elevated to a height of 3 ft above the front scales, the new readings of the front wheels are also recorded. Use this data to compute the location x and y to the center of gravity G of the car. The tires each have a diameter of 1.98 ft. G B _ x _ y A 9.40 ft FB 975 lb 984 lb FA 1959 lb 1129 lb 1168 lb 2297 lb 3.0 ft B G A FA 1269 lb 1307 lb 2576 lb 8 73 9 Solutions 44918 1/28/09 2:34 PM Page 874 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 967. Uniform blocks having a length L and mass m are stacked one on top of the other, with each block overhanging the other by a distance d, as shown. If the blocks are glued together, so that they will not topple over, determine the location x of the center of mass of a pile of n blocks. y 2d d x L 8 74 9 Solutions 44918 1/28/09 2:34 PM Page 875 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws they as currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *968. Uniform blocks having a length L and mass m are stacked one on top of the other, with each block overhanging the other by a distance d, as shown. Show that the maximum number of blocks which can be stacked in this manner is n 6 L> d. y 2d d x L 8 75 9 Solutions 44918 1/28/09 2:34 PM Page 876 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 969. Locate the center of gravity (x, z) of the sheetmetal bracket if the material is homogeneous and has a constant thickness. If the bracket is resting on the horizontal xy plane shown, determine the maximum angle of tilt u which it can have before it falls over, i.e., begins to rotate about the y axis. z 60 mm 60 mm 20 mm y 20 mm 20 mm 10 mm dia. holes 80 mm 20 mm 60 mm u x 8 76 9 Solutions 44918 1/28/09 2:34 PM Page 877 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 970. Locate the center of mass for the compressor assembly. The locations of the centers of mass of the various components and their masses are indicated and tabulated in the figure. What are the vertical reactions at blocks A and B needed to support the platform? y 2 4 4.83 m 5 3 1 3.68 m 3.15 m 1.20 m A 1.80 m 2.30 m B 3.26 m x 2.42 m 1.19 m 2.87 m 1.64 m 1 Instrument panel 2 Filter system 3 Piping assembly 4 Liquid storage 5 Structural framework 230 kg 183 kg 120 kg 85 kg 468 kg 8 77 9 Solutions 44918 1/28/09 2:34 PM Page 878 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 971. Major floor loadings in a shop are caused by the weights of the objects shown. Each force acts through its respective center of gravity G. Locate the center of gravity (x, y) of all these components. z y 450 lb 1500 lb G1 9 ft 6 ft 12 ft 8 ft 4 ft 5 ft 3 ft x 7 ft 600 lb G3 G2 280 lb G4 8 78 9 Solutions 44918 1/28/09 2:34 PM Page 879 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *972. Locate the center of mass (x, y, z) of the homogeneous block assembly. z 250 mm 200 mm x 100 mm 150 mm 150 mm 150 mm y 8 79 9 Solutions 44918 1/28/09 2:34 PM Page 880 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 973. Locate the center of mass z of the assembly. The hemisphere and the cone are made from materials having densities of 8 Mg> m3 and 4 Mg> m3, respectively. z 100 mm 300 mm x y 8 80 9 Solutions 44918 1/28/09 2:34 PM Page 881 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 974. Locate the center of mass z of the assembly. The cylinder and the cone are made from materials having densities of 5 Mg> m3 and 9 Mg> m3, respectively. z 0.4 m 0.6 m 0.2 m 0.8 m x y 8 81 9 Solutions 44918 1/28/09 2:34 PM Page 882 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 975. Locate the center of gravity (x, y, z) of the homogeneous block assembly having a hemispherical hole. z 3 in. 1 in. 2.5 in. 2.5 in. x 1 in. 2.25 in. 3 in. 2.25 in. y 8 82 9 Solutions 44918 1/28/09 2:34 PM Page 883 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *976. Locate the center of gravity (x, y, z) of the assembly. The triangular and the rectangular blocks are made from materials having specific weights of 0.25 lb> in3 and 0.1 lb> in3, respectively. z 3 in. 1 in. 2.5 in. 2.5 in. x 1 in. 2.25 in. 3 in. 2.25 in. y 8 83 9 Solutions 44918 1/28/09 2:34 PM Page 884 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 977. Determine the distance x to the centroid of the solid which consists of a cylinder with a hole of length h = 50 mm bored into its base. 40 mm y 120 mm x 20 mm h 8 84 9 Solutions 44918 1/28/09 2:34 PM Page 885 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 978. Determine the distance h to which a hole must be bored into the cylinder so that the center of mass of the assembly is located at x = 64 mm. The material has a density of 8 Mg> m3. 40 mm y 120 mm x 20 mm h 8 85 9 Solutions 44918 1/28/09 2:34 PM Page 886 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 979. The assembly is made from a steel hemisphere, and an aluminum cylinder, rst = 7.80 Mg> m3, ral = 2.70 Mg> m3. Determine the mass center of the assembly if the height of the cylinder is h = 200 mm. z 80 mm G _ z h 160 mm y x 8 86 9 Solutions 44918 1/28/09 2:35 PM Page 887 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *980. The assembly is made from a steel hemisphere, rst = 7.80 Mg> m3, and an aluminum cylinder, ral = 2.70 Mg> m3. Determine the height h of the cylinder so that the mass center of the assembly is located at z = 160 mm. z 80 mm G _ z h 160 mm y x 8 87 9 Solutions 44918 1/28/09 2:35 PM Page 888 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 981. The elevated water storage tank has a conical top and hemispherical bottom and is fabricated using thin steel plate. Determine how many square feet of plate is needed to fabricate the tank. 8 ft 6 ft 10 ft 8 ft 8 88 9 Solutions 44918 1/28/09 2:35 PM Page 889 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 982. The elevated water storage tank has a conical top and hemispherical bottom and is fabricated using thin steel plate. Determine the volume within the tank. 8 ft 6 ft 10 ft 8 ft 8 89 9 Solutions 44918 1/28/09 2:35 PM Page 890 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 983. Determine the volume of the solid formed by revolving the shaded area about the x axis using the second theorem of PappusGuldinus.The area and centroid y of the shaded area should first be obtained by using integration. y 4 ft y2 4x 4 ft x 8 90 9 Solutions 44918 1/28/09 2:35 PM Page 891 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *984. Determine the surface area from A to B of the tank. B z 3m 1.5 m A 1m 985. Determine the volume within the thin-walled tank from A to B. B z 3m 1.5 m A 1m 8 91 9 Solutions 44918 1/28/09 2:35 PM Page 892 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 986. Determine the surface area of the roof of the structure if it is formed by rotating the parabola about the y axis. y y 16 (x2/16) 16 m x 16 m 8 92 9 Solutions 44918 1/28/09 2:35 PM Page 893 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 987. Determine the surface area of the solid formed by revolving the shaded area 360 about the z axis. z 0.75 in. 0.5 in. 0.75 in. 2 in. 1 in. 3 in. 8 93 9 Solutions 44918 1/28/09 2:35 PM Page 894 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *988. Determine the volume of the solid formed by revolving the shaded area 360 about the z axis. z 0.75 in. 0.5 in. 0.75 in. 2 in. 1 in. 3 in. 989. Determine the volume of the solid formed by revolving the shaded area 360 about the z axis. z 75 mm 75 mm 75 mm 250 mm 75 mm 300 mm 8 94 9 Solutions 44918 1/28/09 2:35 PM Page 895 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 990. Determine the surface area and volume of the solid formed by revolving the shaded area 360 about the z axis. z 1 in. 2 in. 1 in. 8 95 9 Solutions 44918 1/28/09 2:35 PM Page 896 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 991. Determine the surface area and volume of the solid formed by revolving the shaded area 360 about the z axis. z 75 mm 50 mm 300 mm 400 mm 75 mm 50 mm *992. The process tank is used to store liquids during manufacturing. Estimate both the volume of the tank and its surface area. The tank has a flat top and a thin wall. 3m 3m 6m 4m 8 96 9 Solutions 44918 1/28/09 2:35 PM Page 897 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 993. The hopper is filled to its top with coal. Estimate the volume of coal if the voids (air space) are 35 percent of the volume of the hopper. z 1.5 m 4m 1.2 m 0.2 m 994. The thin-wall tank is fabricated from a hemisphere and cylindrical shell. Determine the vertical reactions that each of the four symmetrically placed legs exerts on the floor if the tank contains water which is 12 ft deep in the tank. The specific gravity of water is 62.4 lb> ft3. Neglect the weight of the tank. 8 ft water surface 6 ft 4 ft 8 ft 8 97 9 Solutions 44918 1/28/09 2:35 PM Page 898 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 995. Determine the approximate amount of paint needed to cover the outside surface of the open tank. Assume that a gallon of paint covers 400 ft2. water surface 8 ft 6 ft 4 ft 8 ft *996. Determine the surface area of the tank, which consists of a cylinder and hemispherical cap. 4m 8m 8 98 9 Solutions 44918 1/28/09 2:35 PM Page 899 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 997. Determine the volume of the thin-wall tank, which consists of a cylinder and hemispherical cap. 4m 8m 8 99 9 Solutions 44918 1/28/09 2:35 PM Page 900 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 998. The water tank AB has a hemispherical top and is fabricated from thin steel plate. Determine the volume within the tank. B 1.6 m 1.5 m 1.6 m A 0.2 m 9 00 9 Solutions 44918 1/28/09 2:35 PM Page 901 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 999. The water tank AB has a hemispherical roof and is fabricated from thin steel plate. If a liter of paint can cover 3 m2 of the tanks surface, determine how many liters are required to coat the surface of the tank from A to B. B 1.6 m 1.5 m 1.6 m A 0.2 m 9 01 9 Solutions 44918 1/28/09 2:35 PM Page 902 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *9100. Determine the surface area and volume of the wheel formed by revolving the cross-sectional area 360 about the z axis. z 1 in. 1 in. 1.5 in. 2 in. 4 in. 9 02 9 Solutions 44918 1/28/09 2:35 PM Page 903 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 9101. Determine the outside surface area of the storage tank. 4 ft 15 ft 30 ft 9102. Determine the volume of the thin-wall storage tank. 4 ft 15 ft 30 ft 9 03 9 Solutions 44918 1/28/09 2:35 PM Page 904 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 9103. Determine the height h to which liquid should be poured into the conical paper cup so that it contacts half the surface area on the inside of the cup. 100 mm 150 mm h *9104. The tank is used to store a liquid having a specific weight of 80 lb> ft3. If it is filled to the top, determine the magnitude of the force the liquid exerts on each of its two sides ABDC and BDFE. C A 4 ft D B F 6 ft 6 ft E 12 ft 8 ft 9 04 9 Solutions 44918 1/28/09 2:35 PM Page 905 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 9105. The concrete gravity dam is held in place by its own weight. If the density of concrete is rc = 2.5 Mg> m3, and water has a density of rw = 1.0 Mg> m3, determine the smallest dimension d that will prevent the dam from overturning about its end A. 6m A d 9 05 9 Solutions 44918 1/28/09 2:35 PM Page 906 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 9106. The symmetric concrete gravity dam is held in place by its own weight. If the density of concrete is rc = 2.5 Mg> m3, and water has a density of rw = 1.0 Mg> m3, determine the smallest distance d at its base that will prevent the dam from overturning about its end A. The dam has a width of 8 m. 1.5 m 9m A d 9 06 9 Solutions 44918 1/28/09 2:35 PM Page 907 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 9107. The tank is used to store a liquid having a specific weight of 60 lb> ft3. If the tank is full, determine the magnitude of the hydrostatic force on plates CDEF and ABDC. z E D F C 1.5 ft 1.5 ft x A 1.5 ft 1.5 ft y 2 ft 2 ft 5 ft B 9 07 9 Solutions 44918 1/28/09 2:35 PM Page 908 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *9108. The circular steel plate A is used to seal the opening on the water storage tank. Determine the magnitude of the resultant hydrostatic force that acts on it. The density of water is rw = 1 Mg> m3. 2m 45 1m A 1m B 0.5 m 0.5 m 1m 9 08 9 Solutions 44918 1/28/09 2:35 PM Page 909 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 9109. The elliptical steel plate B is used to seal the opening on the water storage tank. Determine the magnitude of the resultant hydrostatic force that acts on it. The density of water is rw = 1 Mg> m3. 2m 45 1m A 1m B 0.5 m 0.5 m 1m 9 09 9 Solutions 44918 1/28/09 2:35 PM Page 910 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 9110. Determine the magnitude of the hydrostatic force acting on the glass window if it is circular, A. The specific weight of seawater is gw = 63.6 lb> ft3. 4 ft 0.5 ft 1 ft A 0.5 ft B 1 ft 1 ft 9 10 9 Solutions 44918 1/28/09 2:35 PM Page 911 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 9111. Determine the magnitude and location of the resultant hydrostatic force acting on the glass window if it is elliptical, B. The specific weight of seawater is gw = 63.6 lb> ft3. 4 ft 0.5 ft 1 ft A 0.5 ft B 1 ft 1 ft 9 11 9 Solutions 44918 1/28/09 2:35 PM Page 912 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *9112. Determine the magnitude of the hydrostatic force acting per foot of length on the seawall. gw = 62.4 lb> ft3. y 2 x2 y x 8 ft 2 ft 9 12 9 Solutions 44918 1/28/09 2:35 PM Page 913 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 9113. If segment AB of gate ABC is long enough, the gate will be on the verge of opening. Determine the length L of this segment in order for this to occur. The gate is hinged at B and has a width of 1 m. The density of water is rw = 1 Mg> m3. A 4m L B 2m C 9 13 9 Solutions 44918 1/28/09 2:35 PM Page 914 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 9114. If L = 2 m, determine the force the gate ABC exerts on the smooth stopper at C. The gate is hinged at B, free at A, and is 1 m wide. The density of water is rw = 1 Mg> m3. 4m L B A 2m C 9 14 9 Solutions 44918 1/28/09 2:35 PM Page 915 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 9115. Determine the mass of the counterweight A if the 1-m-wide gate is on the verge of opening when the water is at the level shown. The gate is hinged at B and held by the smooth stop at C. The density of water is rw = 1 Mg> m3. 2m 1m B 45 2m A C 9 15 9 Solutions 44918 1/28/09 2:35 PM Page 916 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *9116. If the mass of the counterweight at A is 6500 kg, determine the force the gate exerts on the smooth stop at C. The gate is hinged at B and is 1-m wide. The density of water is rw = 1 Mg> m3. 2m 1m B 45 2m A C 9 16 9 Solutions 44918 1/28/09 2:35 PM Page 917 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 9117. The concrete gravity dam is designed so that it is held in position by its own weight. Determine the factor of safety against overturning about point A if x = 2 m. The factor of safety is defined as the ratio of the stabilizing moment divided by the overturning moment. The densities of concrete and water are rconc = 2.40 Mg> m3 and rw = 1 Mg> m3, respectively. Assume that the dam does not slide. y x 3 x2 2 6m y A 2m x 9 17 9 Solutions 44918 1/28/09 2:35 PM Page 918 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 9 18 9 Solutions 44918 1/28/09 2:35 PM Page 919 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 9118. The concrete gravity dam is designed so that it is held in position by its own weight. Determine the minimum dimension x so that the factor of safety against overturning about point A of the dam is 2. The factor of safety is defined as the ratio of the stabilizing moment divided by the overturning moment. The densities of concrete and water are rconc = 2.40 Mg> m3 and rw = 1 Mg> m3, respectively. Assume that the dam does not slide. y x 3 x2 2 6m y A 2m x 9 19 9 Solutions 44918 1/28/09 2:35 PM Page 920 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 9 20 9 Solutions 44918 1/28/09 2:35 PM Page 921 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 9119. The underwater tunnel in the aquatic center is fabricated from a transparent polycarbonate material formed in the shape of a parabola. Determine the magnitude of the hydrostatic force that acts per meter length along the surface AB of the tunnel. The density of the water is rw = 1000 kg/m3. y 2m y 4 x 2 A 4m 2m 2m B x 9 21 9 Solutions 44918 1/28/09 2:35 PM Page 922 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *9120. Locate the centroid x of the shaded area. y y x2 4 in. 1 in. x 1 in. 1 in. 9121. Locate the centroid y of the shaded area. y y x2 4 in. 1 in. x 1 in. 1 in. 9 22 9 Solutions 44918 1/28/09 2:35 PM Page 923 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 9122. area. Locate the centroid y of the beams cross-sectional 50 mm 75 mm 25 mm y 50 mm 75 mm 100 mm C y x 25 mm 25 mm 9123. Locate the centroid z of the solid. z y2 z a a 2 2a a y x 9 23 9 Solutions 44918 1/28/09 2:35 PM Page 924 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *9124. The steel plate is 0.3 m thick and has a density of 7850 kg> m3. Determine the location of its center of mass. Also compute the reactions at the pin and roller support. y y2 2x 2m x A 2m y x B 2m 9125. Locate the centroid (x, y) of the area. y 3 in. 1 in. 6 in. 3 in. x 9 24 9 Solutions 44918 1/28/09 2:35 PM Page 925 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 9126. Determine the location (x, y) of the centroid for the structural shape. Neglect the thickness of the member. y 3 in. x 1.5 in. 1.5 in. 1 in. 1 in. 1.5 in. 1.5 in. 9127. Locate the centroid y of the shaded area. y a a x a a 2 a 2 9 25 9 Solutions 44918 1/28/09 2:35 PM Page 926 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *9128. The load over the plate varies linearly along the sides of the plate such that p = 2 [x(4 - y)] kPa. Determine 3 the resultant force and its position (x, y) on the plate. p 8 kPa 3m y 4m x 9129. The pressure loading on the plate is described by the function p = 5 - 240> (x + 1) + 3406 Pa. Determine the magnitude of the resultant force and coordinates of the point where the line of action of the force intersects the plate. 100 Pa y p 300 Pa 6m 5m x 9 26

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AN AFROCENTRIC ANALYSIS OF HIP-HOP MUSICAL ART COMPOSITION AND PRODUCTION: ROLES, THEMES, TECHNIQUES, AND CONTEXTS_A Dissertation Submitted to the Temple University Graduate Board_in Partial Fulfillment of Requirements for the Degree DOCTOR OF PHILOSO
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Chapter10Photosynthesis LectureOutline Overview:TheProcessThatFeedstheBiosphere Life on Earth is solar powered. The chloroplasts of plants use a process called photosynthesis to capture light energy from the sun and convert it to chemicalenergy stored
Stanford - EE - EE359
EE 359 - Wireless Communications - Fall 2009Homework 4 Solutions1. (4-8) (10pts) (a) (4pts) If neither transmitter nor receiver knows when the interferer is on, they must transmit assuming worst case, i.e. as if the interferer was on all the time, ( ) S
Excelsior - ACC - ACC 212
UN IT TWO, 1L eads t o neglect of L . Amer icaLatin American Independence -Collision of People Columbian Moment discovery of New World by Columbus, exchange of all things (f rom the Old World to the New World)Native Americans Europeans Africans (sla
Strayer - ACCT - ACC557
P1-1A. Answerhttp:/edugen.wiley.com/edugen/shared/assignment/test/qanswer.uni?itemid=c01q_3_1Answer P1-1A Barone's Repair Inc. was started on May 1. A summary of May transactions is presented below. 1. Stockholder's invested $10,000 cash to start the re
Jackson State - SOC - 526
JermainePatrickArticle6 Theexplanationofgroupleveldisparitiesinthesevenmajorfactorsofqualityoflife cannotexplainedinasimpledefinitionorterms.Itvariesbygroupandtrendsforexample populationanddemographicchangesinacity.Thewhiteflighttothesuburbsthroughoutthe
Jackson State - SOC - 526
Profanity in Prime Time 1Jackson State University Jackson, MississippiProfanity in Prime Time Television: A Content Analysis of 60 YearsA Research Proposal Submitted to the Department of Mass Communication In Partial Fulfillment of the Requirements for
Jackson State - SOC - 526
Jermaine Patrick September 8, 2009 Sociology 526 Article ReadingsChapter 1 Harris used an argument of skin color and latitude for his reasoning behind white was beautiful because white is healthy and black is beautiful because black is healthy. The corre
Jackson State - SOC - 526
JermainePatrickArticle9Theideaofonedropofblackbloodmakesyoublackisantiquatedinasocietythatis becomingmoremultiethnicandmultiracialastimegoeson.Butatthesametimetheone droprulewaseventuallyembracedbytheblackcommunity.Becauseifpeopletookacloser lookintothe
Jackson State - SOC - 526
Write a 750 or more word essay describing the consequences for women who did not live up to seventeenth-century society's gender expectations. In your essay, select three groups of women from the chapter, explain what constituted a violation of social nor
Jackson State - MC - 546
The movie "Une femme est Une femme" was a breakthrough work of cinema done by Jean Luc Godard. The movie focused on a few days in a turbulent relationship between Angela and Emile. This movie was not a box office success, but over time has become a cinema
Jackson State - MC - 500
British cultural studiesandtelevision didmention elementsofMarxistassumptions, suchashavingconcernwiththegenerationandcirculationofmeaninginindustrialsocieties. Italsohadtheassumptionthatcapitalistsocietiesaredividedsocieties.Thesocialpoweris thepowertoge
Jackson State - MC - 581
The field of education has been challenged to define teaching and teacher education. The idea of defining teaching is not a simple task. One might think of the task , instead of a static action that can be universally defined,as the current paradigm that
Jackson State - COUN - 526
JermainePatrick Counseling526 July22,20081.BothGestalttherapyandpersoncenteredtherapysharesomefeatureswiththeexistentialapproach,yettheyemployverydifferentmethodsinagroup.Althoughtheyhave somecommonphilosophicalviewsofhumannature.Gestalttherapyrelieson
Jackson State - HIST - 525
Amovementknownas"thecultoftruewomanhood"ortheideologyofseparate spheresorsimplydomesticity.Thissystemofideastookholdinthe19thcenturyastheUnited Stateswascomingintoitsownasanindependentnation,menandwomenweretreatedas completeoppositeswithalmostnocommonhuma
Jackson State - MC - 500
ThenextgroupofchaptersinEmerysHistoryofthePressinAmerica toucheduponawidevarietyofsubjectsbetweenthe1820sandtheevolutionof jazzmusicinthe1920s.thissummarywillfocusonthedevelopmentofthe blackpress.Theevolutionoftheunitedstatesbetween1865and1900,in industy,
Jackson State - MC - 500
-1ThehistoryofthepressinAmericachaptersthirteenthrusixteencovered theriseoftelevision,theadvancesofWilliamRandolphHearst.Thepresidency ofFDRandhisrelationshipwiththepress.ThelandmarkcaseofNearv. Minnesota.ThestepstowardtheevolutionofFMradio. Hearstbuiltt
Jackson State - MKT - 530
2.The products life cycle - period usually consists of five major steps or phases:Product development,Product introduction, Product growth, Product maturity and finally Product decline. These phases exist and are applicable to all products or services f
Jackson State - MKT - 530
JermainePatrickMyrollnumberissixteenandmyemailjmoo2k6@gmail.com.Myaddressis1704 JonesAvenueApt.DandIcanbereachedat6019441585.I'menrolledintheMaster'sof MassCommunicationprogramatJacksonStateUniversity.
Jackson State - MKT - 530
JermainePatrick1.Thefiveforcesmodelisananalysistoolusedtoidentifyopportunitiesandriskswhenenteringanuntappedterritoryinanymarketorindustry.TheFiveforcesanalysismodelas definedbyPrior:Theforcesindustryanalysishelpstoassessandmanagethelongterm attractive
Jackson State - MC - 430
Jermaine Patrick MC 430Software can produce Ads A Paris advertising agency has created CAI software that can produce basic advertisements. The software has to be programmed by humans and the demographic information has to come from somewhere. This techno
Jackson State - MC - 500
-1JermainePatrickMC500 WeeklySummaryThissectionofreadingsthethingsthatstoodoutwerethefeatureson advertising.Thefederalcommunicationcommissionrequiresbroadcasterstoset asidetimeforpublicserviceannouncements.Theobligationisavagueone,the FederalCommunicati
Jackson State - SOC - 526
26.Howdoyouexplaindifferencesinsentencingbyrace?Whatwouldhappeniftherewereawarondrugsandthesuburbs,ratherthanthecity,werethetarget?Whatwould whiteAmerica'sresponsebeifmillionsofyoung,white,middleclasssuburbaniteswere arrested,sentenced,andputinjailforan
Jackson State - SOC - 526
JermainePatrick Part4Questions SectionsA,B,C40.SteinbergsuggestsAmerica'smeltingpothasbeeninclusiveofeverybodybutblacks.IshisstatementaboutblackexclusionfromthemeltingpotjustifiedwhenweconsiderAfrican Americancontributionstopopularculture? Steinberg's
Jackson State - SOC - 526
16.Howdoesasenseofgrouppositionshapehowweseeotherracialandethnicgroups? Haveyoueverdefinedyourracialgroupmembershipinsuchawayastoheightenyourgroups statusattheexpenseofanother?Whatwasthecontext? Oneracewouldhavefeelingsofsuperiorityandthatthesubordinater
Jackson State - HIST - 525
TheProgressiveErafeaturedmanywomen'sgroupsthatfocusedonwomen'srights fromavarietyofdirections.Theunionsoftheerafocusedontherightsandworking conditionsofimmigrantwomen,butignoredtheplightofAfricanAmericans.TheNational Women'sPartywastheradicaloffshootofthe
Jackson State - MC - 546
Romeo and Juliet is an example of how cinematic interpretations of William Shakespeare have become more liberal over time. The play has universal themes of youthful passion, destructive feuds , and doomed romance, and it remains uniquely adaptable for any
Jackson State - SOC - 526
16.Oneracewouldhavefeelingsofsuperiorityandthatthesubordinateraceisforeignto them,andaclaimtocertainareasofprivilegeandadvantage,withafearandsuspiciousthat thesubordinateraceharbordesignsontheprerogativeofthedominantrace.Yes,eventhough itmayhavebeenmorecu
Jackson State - SOC - 526
Jermaine Patrick Final Examination What I Learned This semester in Sociology 526, we spent a lot of reading the Gallagher text The Color Line readings on various aspects of race. The main things that stuck out to me were the Tim Wise videos, the readings
Skyline College - ENGLISH - 2
War: Explosion of sand tiny granules block the sun all seem blind to peaceTrees over the place with frost White sparkly snow everywhereWe talk for hours That sweet smile upon your face Warmth under my skinWinter Cold Dark Chilling Snowing Darkening Ice
University of Texas - AST - 303
AST 301 Review questions for Exam #3 Exam date: Friday Dec. 5 1. Describe how a star (or protostar) changes if it generates more (or less) energy by nuclear fusion than it radiates from its surface. 2. Describe the changes that occur near the center of a
College of the Desert - ECE - 3010
RiskandRatesofReturnLearningObjectivesChapter8Afterreadingthischapter,studentsshouldbeableto: Defineriskandcalculatetheexpectedrateofreturn,standarddeviation,andcoefficientofvariationfor aprobabilitydistribution. Specifyhowriskaversioninfluencesrequ
HKU - FINA - 030
FINA0301, DERIVATIVE SECURITIES HOMEWORK NUMBER 5First Semester, 2010 - 2011, Dr A. Carverhill 5.1 Please do McDonald, Questions 8.1, 8.2, page 245. 5.2 What are the oil swap prices in Question 5.1 above, if the interest rates are 3.0%. 3.5%, 4.0% for ma
University of Texas - ACC 310F - 310f
$0$0StuffCash Beginning Balance 0=Claims-to-StuffMy Claim Beginning Balance Current Balance 0 0Current Balance0These are the accounts currently in your system: CashSister's Claim Beginning Balance Current Balance 0 0My Claim Sister's ClaimRepo
University of Texas - ACC 310F - 310f
January 2009Date General Journal Account Debit Credit$0 Assets + Dr Cash 0 Cr=$0 Liabilities Dr Note Payable + Cr 0 0+$0 Owners' Equity Dr Common + Stock Cr 0 0Beg BalanceBeg Balance Current BalanceBeg Balance Current BalanceCurrent Balance0+
University of Texas - ACC 310F - 310f
January, 2009DateDepreciation ExampleCredit$67,000 Assets Dr Cash 8,500 Cr=$0 Liabilities Dr Wages Payable Cr 0 0 Unearned Revenue Cr 0 0+Dr$67,000 Owners' Equity Common Stock Cr 50,000 50,000General Journal Account DebitBeg BalanceBeg Balance
University of Phoenix - PSY - Psy 230
Motivation Theories CheckPointMy biggest theory agreement would have to be with the Diversity view. I agree that human beings are motivated by different things. One individuals goals and purposes will always be different from others. Therefore, each indi
Rider - ENGLISH - 2
Brian Taimanglo English II Professor Matthew Screnci Tuesdays and Thursdays 4:00-5:15Gender is the role that society assigns, to men and women based on their gender identity. Gender also involves hierarchy, placing men and women in different positions in
University of Toronto - MAT - mat137
University of Toronto - MAT - mat137
Department of Mathematics University of Toronto MAT137Y, 2010-2011 Winter SessionQuiz #1 Review Guide Not to be handed in Posted/Revised: October 12, 2010This document is intended to help you in studying for the rst quiz, which will be written in tutori
CSU Northridge - MANAGEMENT - 12121
1 Marks: 1 How could a firm best satisfy an employee's safety needs? Choose one answer. a. Enroll the employee in a Microsoft Office training course. b. Provide an employee appreciation luncheon. c. Develop a weekly employee bowling league. d. Create a jo
San Diego State - FIN - 323
Chapter5 Culture, Management Style, and Business SystemsMcGrawHill/Irwin InternationalMarketing,13/e2007TheMcGrawHillCompanies,Inc.,AllRightsReserved.Chapter Learning Objectives The necessity for adapting to cultural differences How and why managemen
University of Sydney - ECOS - 3003
NAME: _SID:_The University of SydneyHierarchies, incentives and firm structure ECOS 3003 Mid-semester examInstructions Answer the multiple choice questions on the answer sheet provided with a pencil. Time: 60 minutes Permitted materials: Non-programm
University of Sydney - ECOS - 3003
Divisional performance evaluation Most organisation have some subunits grants some decision rights and evaluated on performance (note organisational architecture performance evaluation and reward systems are consistent with decision rights granted to unit
University of Sydney - ECOS - 3003
Costs and benefits of choosing between alternative firm sizes What should a firm make and what should a firm buy? - integrate backwards or upstream: a firm that begins to make its own inputs - forwards or downstream integration: additional finishing or ma
University of Sydney - ECOS - 3003
bri75829_web_appendix.qxd8/20/0812:06 PMPage A-1Confirming PagesChapter 18 Corporate Governance A-1AppendixChoosing among the Legal Forms of OrganizationWhile large publicly traded corporations are prominent in todays business environment, other l
University of Sydney - ECOS - 3003
Hierarchies, incentives and firm structure ECOS3003Tutorial 61. In the following principal-agent problem suppose the agent can put in one or no units of effort, ie e = 1 or e = 0. Her utility is given by U(w,e) = (w)0.5 e, where w is the wage received a
University of Sydney - ECOS - 3003
Hierarchies, incentives and firm structure ECOS3003Tutorial 7 1. Performance measurement and incentive schemes are jointly determined. Comment. Performance measurement increases the accuracy of measuring effort; the more accurate, the less risk faced by
University of Sydney - ECOS - 3003
Hierarchies, incentives and firm structure ECOS3003Tutorial 8 1. Which of the following is not required in cost centre performance-evaluation systems?(a) The output must be measurable (b) The quality must be easily observable (c) The optimal input combi
University of Sydney - ECOS - 3003
Hierarchies, incentives and firm structure ECOS3003 Tutorial 9 1. Question 19-2 on page 634.once it makes its investment GN is stuck with BD coal need contract to be designed so as to limit hold-up (renegotiation) - important that the price of coal fixed
University of Sydney - ECOS - 3002
DEVELOPMENT ECONOMICS ECOS 3002 Second Semester, 2009 Week 1: IntroductionEconomies as Social Systems: The need to go beyond Simple Economics Social Systems Interdependent relationships between economic and noneconomic factorsImportance of institutiona
University of Sydney - ECOS - 3002
DEVELOPMENT ECONOMICS ECOS 3002 Second Semester, 2009 Week 2: Theories and Models of DevelopmentDevelopment vs. Growth Linear-Stages Theories of economic growth Rostows stages of growth The Harrod-Domar growth model Obstacles and constraintsCriticis