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 8.108P: If the intensity of the line loading is w=[(40xx2)/40]lb/in., where x is measured in inches, use...
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Can you show how to solve this problem in both vector and scalar method
Transcribed Image Text: 3.25 The resultant of the three forces is a force R that passes through point B."
Determine R and F.
VECTOR METHOD
30.5 lb
36 lb
Solution:
• Move all the forces to point B.
Write the forces in vector form.
3 ft
-1.5 ft
Add all the forces to obtain
30.5 lb
resultant force at B, which will
be equal to R.
We need one more equation as
we have three variables F, R,
and Ry-
F-
F
12
4 ft
36 lb
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Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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