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engineering
engineering mechanics statics 15th

Engineering Mechanics Statics 15th Edition Russell C. Hibbeler - Solutions

Locate the centroid ȳ of the beam's cross-sectional area. 50 mm 150 mm 150 mm 300 mm 25 mm 25 mm Prob. F9-8 -X
Locate the centroid ȳ of the area. 4 m y - 4 m ·x
Locate the centroid x̄ of the area. h y =1/3x² -b. h X
Determine the surface area and volume of the solid formed by revolving the shaded area 360° about the z-axis. 2 m 2m 1.5 m Prob. F9-13
Locate the centroid ȳ of the area. y 4 m - ↓ y = 4- 1 16 -8 m- [2] R -X
Locate the centroid x̄ of the area. Solve the problem by evaluating the integrals using Simpson’s rule. y y = 0.5ex² 1 m -X
Locate the centroid ȳ of the area. Solve the problem by evaluating the integrals using Simpson’s rule. y y = 0.5ex² 1 m -X
Locate the centroid x̄ of the shaded area. Solve the problem by evaluating the integrals using Simpson’s rule. a y -L- - y = a sin JUX L X
Locate the centroid of the area. a y -L- - y = a sin ЛХ L -X
Determine the magnitude of the hydrostatic force acting per meter width of the wall. Water has a density of p = 1 Mg/m³. Prob. F9-17 6 m
Locate the centroid ȳ of the area. Solve the problem by evaluating the integrals using Simpson’s rule. 1 m y = 0.5ex² X
Locate the centroid ȳ of the area. 16 ft y _y= (4 − x ²¹) ² - -4 ft- IT 4 ft ↓ ·x
Determine the magnitude of the hydrostatic force acting on gate AB, which has a width of 1.5 m. Water has a density of p = 1 Mg/m³. B -1.5 m Prob. F9-19 2 m
Determine the magnitude of the hydrostatic force acting on gate AB, which has a width of 2 m. Water has a density of p = 1 Mg/m³. 3 m 2 m A B Prob. F9-20
Locate the centroid ȳ of the area. a h h X
Locate the centroid x̄ of the area. 16 ft y -y = (4-x²) ² 4 ft- T 4 ft X
Locate the centroid x̄ of the area. 100 mm -100 mm- y=x y=100x² X
Locate the centroid x̄ of the area. h y a y=hx b = (h)(x-b) X
Locate the centroid x̄ of the area. y y h a²x+h h X
Locate the centroid x̄ of the area. a aπT y = a sin X
Locate the centroid ȳ of the area. h b y: (h)(x-b) X
Locate the centroid of the volume formed by rotating the shaded area about the aa axis. 2²=2y- N -3 m -1 m. a a ∙y
Locate the centroid ȳ of the area. a aπ- y = a sin X
The king’s chamber of the Great Pyramid of Giza is located at its centroid. Assuming the pyramid to be a solid, prove that this point is at z̄ = 1/4 h, Suggestion: Use a rectangular differential plate element having a thickness dz and area (2x)(2y). N X
Locate the centroid ȳ of the paraboloid. N 2²= 4y -4m 4 m y
Locate the centroid of the solid. X - y² = a (a-²)
Locate the centroid (x̄, ȳ) of the metal cross section. Neglect the thickness of the material and slight bends at the corners. 50 mm. 50' mm 100 mm 100 mm 50 mm 150 mm X
Determine the distance ȳ to the centroid of the bell-shaped volume. N -1 ft. z = y² 1 ft y
Determine the location ȳ of the centroid C of the “rollformed” member. Neglect the thickness of the material and any slight bends at the corners. 40 mm y C 20 mm y 40 mm 150 mm
Determine the location (x̄, ȳ) of the centroid of the sheet metal cross section. Neglect the thickness of the material and slight bends at the corners. y 2 in. 8 in. -3 in.3 in. X
The steel and aluminum plate assembly is bolted together and fastened to the wall. Each plate has a constant width in the z direction of 200 mm and thickness of 20 mm. If the density of A and B is ρs = 7.85 Mg/m3, and for C, ρal = 20.71 Mg/m3, determine the location of the center of mass.
Determine the location y of the centroid for the beam’s cross-sectional area. 15 mm 400 mm 15 mm -300 mm- - 15 mm -200 mm-
The rectangular horn antenna is used for receiving microwaves. Determine the location x̄ of its center of gravity G. The horn is made of plates having a constant thickness and density and is open at each end. 0.1 ft 0.3 ft -0.4 ft 30° 30° G -0.6 ft- 0.3 ft
Locate the centroid ȳ for the beam’s cross-sectional area. 120 mm 240 mm -120 mm X
Locate the centroid ȳ of the cross-sectional area of the beam. 1 6 in. 10 in. 8 in.- -8 in.- -1 in. 4+ 1 in. IA 1 in. -X
Locate the centroid (x̄, ȳ) of the cross-sectional area of the beam. 6 in. 3 in. 6 in. - 3 in. 2 in. 1
Locate the centroid ȳ of the cross-sectional area of the beam constructed from a channel and a plate. Assume all corners are square and neglect the size of the weld at A. 350 mm 325 mm A -20 mm y 10 mm 325 mm 70 mm
Determine the location y of the centroid of the area. a y 가을을 어 a D D ·X
Determine the distance ȳ to the centroid of the area. 150 mm 150 mm 100 mm 300 mm C y 600 mm X
The rectangular horn antenna is used for receiving microwaves. Determine the location x̄ of its center of gravity G. The horn is made of plates having a constant thickness and density and is open at each end. 0.1 ft 0.3 ft -x- -0.4 ft- 30° 30° G 0.6 ft 0.3 ft
Determine the location of the centroid of the solid made from a hemisphere, cylinder, and cone. y 80 mm- -— -60 mm T 30 mm -30 mm- -X
Determine the distance ȳ to the centroid of the beam’s cross-sectional area. 25 mm 50 mm 100 mm -75 mm-75 mm- 25 mm C 50 mm 25 mm
Determine the location (x̄, ȳ) of the centroid of the area. C | b + X
The sheet metal part has the dimensions shown. Determine the location (x̄, ȳ, z̄) of its centroid. N B 6 in. 3 in. 4 in. с y
Determine the distance x̄ to the center of gravity of the generator assembly. The weight and the center of gravity of each of the various components are indicated. What are the vertical reactions at blocks A and B needed to support the assembly? G₁(200 lb) A Oo 1 ft -3 ft- -X- G₂(1000 lb) -4
The assembly is made from a steel hemisphere ρst = 7.80 Mg/m3, and an aluminum cylinder ρst = 7.80 Mg/m3 . Determine the height h of the cylinder so that the mass center of the assembly is located at z̄ = 160 mm. x IN 80 mm Z G h 160 mm -y
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
The buoy is made from two homogeneous cones each having a radius of 1.5 ft. If h = 1.2 find the distance to the buoy’s center of gravity G. h 4 ft 1.5 ft G
The assembly is made from a steel hemisphere, ρst = 7.80 Mg/m3, and an aluminum cylinder, ρal = 2.70 Mg/m3 . Determine the mass center of the assembly if the height of the cylinder is h = 200 mm. X 80 mm G h 160 mm ↓
The solid is formed by boring a conical hole into the cylinder. Determine the distance to the center of gravity. h I G Z a Z
Determine the distance z̄ to the center of mass of the casting that is formed from a hollow cylinder having a density of 8 Mg/m3 and a hemisphere having a density of 3 Mg/m3. 20 mm - 40 mm 120 mm 40 mm y
Determine the dimension h of the block so that the centroid C of the assembly lies at the base of the cylinder as shown. 6 in. 6 in. 5 in. 2 in X
Locate the center of mass z̄ of the assembly. The material has a density of ρ = 7.80 Mg/m3 There is a 30-mm diameter hole bored through the center. 30 mm 100 mm X Z 40 mm 20 mm
The composite plate is made from both steel (A) and brass (B) segments. Determine the mass and location (x̄, ȳ, z̄)of its mass center G. Take ρst = 7.85 Mg/m3 and ρst = 8.74 Mg/m3. 30 mm, X B 150 mm A Z 225 mm 150 mm - y
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 (x̄, ȳ) of all these objects. Z 450 lb G₁ 12 ft 7 ft 9 ft 8 ft. 1500 lb G₂ 600 lb G3 4 ft 280 lb GA 5 ft 3 ft x
Determine the outside surface area of the storage tank. 4 ft 30 ft -15 ft-
Determine the volume of the storage tank. 4 ft 30 ft -15 ft-
The starter for an electric motor is a full cylinder and has the cross-sectional areas shown. If copper wiring has a density of ρcu = 8.90 Mg/m3 and the steel frame has a density of ρst = 7.80 Mg/m3, estimate the total mass of the starter. Neglect the size of the copper wire.
The Gates Manufacturing Co. produces pulley wheels such as the one shown. Determine the weight of the wheel if it is made from steel having a specific weight of 490 lb/ft3. 1 in. 11 0.5/in. 1/in. 5 in. 1 in. -0.25 in.
Aring is generated by rotating the quarter circular area about the x-axis. Determine its volume. X 2a a
The Gates Manufacturing Co. produces pulley wheels such as the one shown. Determine the total surface area of the wheel in order to estimate the amount of paint needed to protect its surface from rust. 1 in. + 1/in. N 0.5 in. 5 in. 1 in. -0.25 in.
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. 3002000 REGE 8 ft I 6 ft 10 ft + 8 ft
Determine the surface area of the silo which consists of a cylinder and hemispherical cap. Neglect the thickness of the plates. 10 ft, 10 ft, TO 10 ft 80 ft
Using integration, determine the area and the centroidal distance y of the shaded area. Then, using the second theorem of Pappus-Guldinus, determine the volume of a paraboloid formed by revolving the area about the x axis. y |y2 = x- C -1 ft- 1 ft X
Using integration, determine the area and the centroidal distance ȳ of the shaded area. Then, using the second theorem of Pappus–Guldinus, determine the volume of a solid formed by revolving the area about the x axis. y - xy = 1 0.5 ft 2 ft X
Determine the surface area and volume of the wheel formed by revolving the cross-sectional area 360° about the z axis. N 1 in. 2 in. 1 1 in. -4 in.- 1.5 in.
Determine the weight of the wedge which is formed by rotating a right triangle of base 6 in. and height 3 in. through an angle of 30°. The specific weight of the material is γ = 0.22 lb/in3. 6 in. 30° 3 in.
Determine the moment of inertia of the area about the y axis. y y³ = x 1 in. 1 in. X
Determine the centroid (x̄, ȳ) of the area. 1m -y=x²³ -1m- Prob. F9-1 X
Using integration, determine the area and the centroidal distance of the shaded area. Then, using the second theorem of Pappus–Guldinus, determine the volume of a paraboloid formed by revolving the area about the x axis. y²=x+4 с П - 4 ft - 2 ft X
The pressure loading on the plate is described by the function p = [-240/(x + 1) + 340] Pa. Determine the magnitude of the resultant force and the coordinates (x̄, ȳ) of the point where the line of action of the source intersects the plate. 100 Pa P 5 m X 300 Pa 6 m
Locate the center of mass of the straight rod if its = x̄ 0.5 (1+x²) kg.mass per unit length is given by m = 0.5(1 + x2) kg. -1m- Prob. F9-4 X
Determine the moment of inertia of the area about the the x axis. 80 mm y E 20 mm = (400-x²) X
Determine the centroid ȳ of the area. 2 m -1 m- -1 m- -y = 2x² X
Determine the moment of inertia of the triangular area about the y axis. h y b - y = h (b − x) X
Locate the centroid (x̄, ȳ, z̄) of the wire bent in theshape shown. 300 mm 600 mm 400 mm Prob. F9-7
Determine the moment of inertia of the area about the x axis. Solve the problem in two ways, using rectangular differential elements: (a) having a thickness dx and (b) having a thickness of dy. 2.5 ft -y=2.5-0.1x² -5 ft- X
Determine the moment of inertia of the area about the y axis. 80 mm y 20 mm -y =(400-x²) X
Determine the moment of inertia for the area about the x axis y y² = 4x- - 4 in. 4 in. --x
Determine the moment of inertia of the area about the x axis. y = 2 cos -4 in.- y 4 in.- T 2 in.
Determine the moment of inertia of the quarter circular area about the x axis. x² + y² =p² X
Determine the moment of inertia of the area about the y axis. y = 2 cos(x) -4 in.- y -4 in.- 2 in. X
Determine the magnitude of force P required tohold the 50-kg smooth rod in equilibrium at θ = 60°. B 5 m 0 Prob. F11-2 A P
Determine the required magnitude of force P to maintain equilibrium of the linkage at θ = 60°. Each link has a mass of 20 kg. A 1.5 m B Prob. F11-1 C 1.5 m
The spring has an unstretched length of 0.3 m. Determine the angle θ for equilibrium if P = 50 N. Neglect the weight of the links. 0.5 m 0.5 m/ B 0 k=200 N/m E P
The toggle joint is subjected to load P. Determine the compressive force F it creates on the cylinder at A as a function of θ. P L A Prob. R11-1 F
The linkage is subjected to a force of P = 6 kN.Determine the angle θ for equilibrium. The spring is unstretched at θ = 60°. Neglect the mass of the links. A 0.9 m B 10 k = 20 kN/m wwwwwwwwww P = 6 kN 0.9 m Prob. F11-4
The uniform bar AB weighs 10 lb. If the attached spring is unstretched when θ = 90°, use the method of virtual work and determine the angle for equilibrium. Note that the spring always remains in the vertical position due to the roller guide. + k = 51b/ft 4ft 4ft Prob. R11-4 B
The uniform links AB and BC each weigh 2 lb and the cylinder weighs 20 lb. Determine the horizontal force P required to hold the mechanism at θ = 45°. Thespring has an unstretched length of 6 in. 10 in. B 0=45° k=2 lb/in. Prob. R11-2 10 in. C A
The linkage is subjected to a force of P = 2 kN. Determine the angle for equilibrium. The spring is unstretched when θ = 0°. Neglect the mass of the links. k = 15 kN/m A B -0.6 m- -0.6 m- D Prob. F11-3 P = 2 kN 0.6 m
The spring has an unstretched length of 0.3 m. Use the method of virtual work and determine the angle for equilibrium if the uniform links each have a mass of 5 kg. 0.6 m/ B 0.1'm VA 0 C k = 400 N/m Prob. R11-5 D E
If a torque of M = 50 N · m is applied to the flywheel, determine the force F applied to the ram to hold it in the position θ = 60°. 0.1 m M B 0.4 m Prob. R11-3 A -R F
The block A has a mass of 40 kg. Determine the angle for equilibrium and investigate the stability of the mechanism in this position. The spring has a stiffness of k = 1.5 kN/m and is unstretched when = 90°. Neglect the mass of the links. B F bany 600 mm A E Prob. R11-6 fo D 450 mm
Determine the angle where the 50-kg bar is in equilibrium. The spring is unstretched at θ = 60°. A 5m 10 k = 600 N/m Prob. F11-5 B
The scissors linkage is subjected to a force of P = 150 N. Determine the angle θ for equilibrium. The spring is unstretched at θ = 0°. Neglect the mass of the links. A k = 15 kN/m B Om 0.3 m Prob. F11-6 0.3 m P = 150 N
When θ = 20° the 50-lb uniform block compresses the two vertical springs 4 in. If the uniform links AB and CD each weigh 10 lb, determine the magnitude of the applied couple moments M needed to maintain equilibrium when θ = 20°. k = 2 lb/in. M 1 ft A B C D 1 ft 2 ft M k = 2 lb/in. 1 ft 4 ft
Determine the force P that must be applied perpendicular to the handle in order to hold the mechanism in equilibrium for any angle θ of rod CD. There is a couple moment M applied to the link BA. A smooth collar attached at A slips along rod CD. C 2 P 1/2 M 1/2- B D
The spring is unstretched when θ = 0°. If P = 8 lb, determine the angle θ for equilibrium. Due to the roller guide, the spring always remains vertical. Neglect the weight of the links. 2 ft 4 ft. k = 50 lb/ft 2 ft. 4 ft P
Determine the moment M that must be applied to the slider mechanism in order to maintain the equilibrium position θ = 60° when the horizontal force F = 100 N is applied at D. D 0.5 m A 0 F 0.5 m BX M 0.5 m
If the disk is subjected to a couple moment M, determine the disk’s rotation θ required for equilibrium. The end of the spring wraps around the periphery of the disk as the disk turns. The spring is originally unstretched. k = 4 kN/m 0.5 m M = 300 N·m

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