1 Introduction To Statics 2 Basic Operations With Force Systems 3 Resultants Of Force Systems 4 Coplanar Equilibrium Analysis 5 Three-dimensional Equilibrium 6 Beams And Cables 7 Dry Friction 8 Centroids And Distributed Loads 9 Moments And Products Of Inertia Of Areas 10 Virtual Work And Potential Energy Chapter8: Centroids And Distributed Loads
Chapter Questions Section: Chapter Questions
Problem 8.1P: Use integration to determine the coordinates of the centroid of the plane region shown. Problem 8.2P: Use integration to determine the coordinates of the centroid of the plane region shown. Problem 8.3P: Use integration to determine the coordinates of the centroid of the plane region shown. Problem 8.4P: Use integration to determine the coordinates of the centroid of the plane region shown. Problem 8.5P: Use integration to determine the coordinates of the centroid of the plane region shown. Problem 8.6P: Use integration to determine the coordinates of the centroid of the plane region shown. Problem 8.7P: Using integration, locate the centroid of the area under the n-th order parabola in terms of b, h,... Problem 8.8P: Determine the y-coordinate of the centroid of the half-elliptical area. Use integration. Problem 8.9P: Determine the y-coordinate 0f the centroid of the semicircular segment, given that a = 18 in. and... Problem 8.10P: Use integration to locate the centroid of the shaded region in terms of R and t. (b) Show that when... Problem 8.11P: Locate the centroid of the parabola by integration. Problem 8.12P: Use integration to locate the centroid of the quarter circular are shown in Table 8.2. Problem 8.13P: The parametric equations of the plane curve known as a cycloid are x=a(sin) and y=a(1cos). Use... Problem 8.14P: Use the method of composite areas to calculate the centroidal coordinates of the plane regions... Problem 8.15P: Use the method of composite areas to calculate the centroidal coordinates of the plane regions... Problem 8.16P: Use the method of composite areas to calculate the centroidal coordinates of the plane regions... Problem 8.17P: Use the method of composite areas to calculate the centroidal coordinates of the plane regions... Problem 8.18P: Use the method of composite areas to calculate the centroidal coordinates of the plane regions... Problem 8.19P: Use the method of composite areas to calculate the centroidal coordinates of the plane regions... Problem 8.20P: Use the method of composite areas to calculate the centroidal coordinates of the plane regions... Problem 8.21P: Use the method of composite areas to calculate the centroidal coordinates of the plane regions... Problem 8.22P: The plane region is bounded by a semicircle of radius R and a parabola of height h. Determine the... Problem 8.23P: The centroid of the plane region shown is at C. Use the method of composite areas to determine the... Problem 8.24P: Compute the centroidal coordinates of the L-shaped region in terms of b and t using the method of... Problem 8.25P: Find the centroidal coordinates of the plane region shown. Use the method of composite areas. Problem 8.26P: Using the method of composite areas, find the dimension h that maximizes the centroid coordinate y... Problem 8.27P: Given that the centroid of the plane region is at C, find the radius R. Use the method of composite... Problem 8.28P: Using the method of composite curves, locate the centroids of the plane curves shown. Problem 8.29P: Using the method of composite curves, locate the centroids of the plane curves shown. Problem 8.30P: Using the method of composite curves, locate the centroids of the plane curves shown. Problem 8.31P: Using the method of composite curves, locate the centroids of the plane curves shown. Problem 8.32P: Using the method of composite curves, locate the centroids of the plane curves shown. Problem 8.33P: Using the method of composite curves, locate the centroids of the plane curves shown. Problem 8.34P: Determine the ratio a/b for which the centroid of the composite curve will be located at point O. Problem 8.35P: Use numerical integration to locate the centroid of the symmetric plane Problem 8.36P: Determine the centroidal coordinates of the plane region by numerical integration. Problem 8.37P: Compute the centroidal y-coordinate of the plane curve y=ex2 between x=0 and x=1, where x and y are... Problem 8.38P: The equation of the catenary shown is y = 100 cosh (x/100) where x and y are measured in feet (the... Problem 8.39P: Use integration to locate the centroid of the volume of the hemisphere. Compare your results with... Problem 8.40P: By integration, find the centroid of the surface of the hemisphere. Compare your result With Table... Problem 8.41P: Locate the centroid of the volume obtained by revolving the triangle about the x-axis. Use... Problem 8.42P: Solve Prob. 8.41 assuming that the triangle is revolved about the y-axis. Problem 8.43P: Use integration to find the centroidal coordinates for the volume obtained by revolving the area... Problem 8.44P: Solve Prob. 8.43 assuming that the area is revolved about the y-axis. Problem 8.45P: Verify the centroidal z-coordinate of the pyramid shown in Table 8.3 by integration. Problem 8.46P: Use integration to compute the z-coordinate of the centroid of the half cone. Problem 8.47P: Determine the centroidal z-coordinate of the curved surface of the half cone by integration. Problem 8.48P Problem 8.49P: Locate the centroid of the volume between the curved surface and the xy-plane using integration. Problem 8.50P Problem 8.51P Problem 8.52P: By the method of composite volumes, determine the centroidal coordinates of the volume. Problem 8.53P: By the method of composite volumes, determine the centroidal coordinates of the volume. Problem 8.54P: By the method of composite volumes, determine the centroidal coordinates of the volume. Problem 8.55P: By the method of composite volumes, determine the centroidal coordinates of the volume. Problem 8.56P: By the method of composite volumes, determine the centroidal coordinates of the volume. Problem 8.57P: By the method of composite volumes, determine the centroidal coordinates of the volume. Problem 8.58P: Use the method of composite volumes to determine the centroidal coordinates of the volume. Problem 8.59P: The cylindrical container will have maximum stability against tipping when its centroid is located... Problem 8.60P: Using the method of composite surfaces, locate the centroid of the surface. Problem 8.61P: Using the method of composite surfaces, locate the centroid of the surface. Problem 8.62P: Using the method of composite surfaces, locate the centroid of the surface. Problem 8.63P: Using the method of composite surfaces, locate the centroid of the surface. Problem 8.64P: Using the method of composite surfaces, locate the centroid of the surface. Problem 8.65P: Using the method of composite surfaces, locate the centroid of the surface. Problem 8.66P: The picture board and its triangular supporting bracket form a composite surface. Calculate the... Problem 8.67P: By the method of composite curves, locate the centroid of the wire figure. Problem 8.68P: By the method of composite curves, locate the centroid of the wire figure. Problem 8.69P: By the method of composite curves, locate the centroid of the wire figure. Problem 8.70P: Use numerical integration to find the centroid of the volume generated by revolving the area shown... Problem 8.71P Problem 8.72P: Locate the centroid of the volume generated by revolving the area shown about the line AB. Use... Problem 8.73P Problem 8.74P Problem 8.75P Problem 8.76P: A 6-in. diameter hole is drilled in the conical frustum. Calculate the volume and the surface area... Problem 8.77P: A torus is formed by rotating the circle about the axis AB. Compute the volume and the surface area... Problem 8.78P: A solid of revolution is formed by rotating the plane area shown about the y-axis. Determine the... Problem 8.79P: Compute the volume of the spherical cap that is formed when the circular segment is revolved about... Problem 8.80P: Calculate the surface area of the truncated sphere that is formed by rotating the circular arc AB... Problem 8.81P: The rim of a steel V-belt pulley is formed by rotating the plane area shown about the axis AB. Find... Problem 8.82P: Determine the volume of the machine part shown. Problem 8.83P: A solid is generated by rotating the plane area about the axis AB. Compute the volume of the solid. Problem 8.84P Problem 8.85P: Find the surface area of the 90 duct elbow. Problem 8.86P: Determine the volume of the concrete arch dam. Problem 8.87P: (a) Find the volume of liquid contained in the flask when it is filled to the full mark. (b)... Problem 8.88P: Compute the surface area of the axi-symmetric domed structure. Problem 8.89P: The steel cylinder with a cylindrical hole is connected to the copper cone. Find the center of... Problem 8.90P: The hemispherical glass bowl is filled with water. Find the location y of the center of gravity of... Problem 8.91P: What is the ratio L/R for which the uniform wire figure can be balanced in the position shown? Problem 8.92P: Small screws are used to fasten a piece of hardwood to the bracket that is formed from... Problem 8.93P Problem 8.94P: 3.94 The aluminum cylinder is attached to the steel hemisphere. Find the height h of the cylinder... Problem 8.95P Problem 8.96P Problem 8.97P Problem 8.98P: Locate the center of gravity of the hammer if the mass of the steel head is 0.919 kg, and the mass... Problem 8.99P Problem 8.100P: The cylindrical water tank with R = 10 ft and H = 1.6 ft has thin steel walls of uniform thickness... Problem 8.101P Problem 8.102P: Five 34-in. diameter holes are to be drilled in a uniform plate. Determine the angle for the... Problem 8.103P: Wind pressure acting on a cylinder can be approximated by p=p0cos, where p0 is a constant (note that... Problem 8.104P Problem 8.105P: The pressure acting on the square plate varies as p=p0(xb +xyb2) where p0 is a constant. Use... Problem 8.106P Problem 8.107P Problem 8.108P: If the intensity of the line loading is w=[(40xx2)/40]lb/in., where x is measured in inches, use... Problem 8.109P Problem 8.110P: The intensity of the line loading acting on a quarter circle is w=w0(2/). Use intergration to... Problem 8.111P: Determine the resultant force or resultant couple for each of the line loads shown. In each case the... Problem 8.112P: The inside surface of each thin shell carries a uniform normal pressure of intensity p0. Compute R,... Problem 8.113P: Calculate the resultant force caused by the water acting on the parabolic arch dam. The water levels... Problem 8.114P: Determine the resultant force acting on the elbow of the thin-walled pipe when the pipe carries a... Problem 8.115P: Determine the smallest distance I) that would prevent the concrete dam from tipping about corner A.... Problem 8.116P: Each of the three gates has a constant width 1: (perpendicular to the paper). Calculate the force P... Problem 8.117P: The concrete dam shown in cross section holds back fresh water (=1000kg/m3). Determine the resultant... Problem 8.118P: A concrete seawater dam is shown in cross section. Is the dam safe against tipping about edge A? The... Problem 8.119P: Determine the force F required to pull up the 3.54m stopper from the drain of a sink if the depth of... Problem 8.120P: The normal pressure acting on the triangular plate is p=p0(y/h). Use intergration to determine the... Problem 8.121P: One side of the container has a 03-m square door that is hinged at its top edge. If the container is... Problem 8.122P: The 12-ft wide quarter-circular gate AB is hinged at A. Determine the contact force between the gate... Problem 8.123RP: The center of gravity of the plane wire figure is located at G. Determine the lengths a and b. Problem 8.124RP: The 10-m wide gate restrains water at a depth of 6 m. Calculate the magnitude of the hinge reaction... Problem 8.125RP: Find the resultant of the line load shown. Problem 8.126RP Problem 8.127RP: Determine the centroidal coordinates of the volume shown. Problem 8.128RP Problem 8.129RP Problem 8.130RP Problem 8.131RP: Using the method of composite areas, find the centroid of the truncated parabolic complement. Problem 8.132RP: Find the centroid of the truncated parabolic complement by integration. Problem 8.133RP Problem 8.134RP: A solid of revolution is formed by rotating the plane area about the axis AB. Compute the volume and... Problem 8.135RP: Two hemispherical shells of inner diameter 1 m are joined together with 12 equally spaced bolts. If... Problem 8.136RP: Calculate the area of the surface generated when the plane z-curve is rotated about (a) the x-axis;... Problem 8.137RP: Determine the resultant of the line loading, given that w0=36lb/ft. Problem 8.138RP: Determine the centroidal coordinates of the plane region. Problem 8.139RP: The sheet metal trough has a uniform wall thickness. Determine the coordinates of its center of... Problem 8.140RP: The trough is filled with water (=62.4lb/ft3). Determine the resultant force of the water pressure... Problem 8.141RP: The thin-walled cylindrical can with a spherical dimple weighs 0.2 lb. Determine the force P... Problem 8.142RP: Find the location of the centroid of the shaded plane region. Problem 8.121P: One side of the container has a 03-m square door that is hinged at its top edge. If the container is...
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Transcribed Image Text: The 4-m diameter circular gate shown in the figure is located in the inclined wall of a large reservoir containing water (y = 9800 N/m3). The
gate is mounted on a shaft along its horizontal diameter. For a water depth of 10 m above the shaft determine the external moment that
would have to be applied about the shaft to just open the gate. The weight of the gate can be neglected.
60°
10 m
Stop
Shaft
Am
Branch of science that deals with the stationary and moving bodies under the influence of forces.
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