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engineering
civil engineering

Engineering Mechanics Statics 11 Edition Russell C. Hibbeler - Solutions

Determine the principal moments of inertia for the angle's cross-sectional area with respect to a set of principal axes that have their origin located at the centroid C. Use the equation developed in Section 10.7. For the calculation, assume all corners to be square.Given:a = 100 mmb = 100 mmt = 20
The area of the cross section of an airplane wing has the listed properties about the x and y axes passing through the centroid C. Determine the orientation of the principal axes and the principal moments of inertia.Given: Ix = 450 in4 Iy = 1730 in4Ixy = 138 in4
Using Mohr’s circle, determine the principal moments of inertia for the triangular area and the orientation of the principal axes of inertia having an origin at point O.Given:a = 30 mmb = 40 mm
Determine the directions of the principal axes with origin located at point O, and the principal moments of inertia for the rectangular area about these axes.Solve using Mohr's circle.Given:a = 6 inb = 3 in
Determine the principal moments of inertia for the beam's cross-sectional area about the principal axes that have their origin located at the centroid C. For the calculation, assume all corners to be square. Solve using Mohr's circle.Given:a = 4 inb = 4 int = 3/8 in
Determine the principal moments of inertia for the angle's cross-sectional area with respect to a set of principal axes that have their origin located at the centroid C. For the calculation, assume all corners to be square. Solve using Mohr's circle.Given: a = 100 mm b = 100 mm t = 20 mm
Determine the directions of the principal axes with origin located at point O, and the principal moments of inertia for the area about these axes. Solve using Mohr's circleGiven:a = 4 inb = 2 inc = 2 ind = 2 inr = 1 in
The area of the cross section of an airplane wing has the listed properties about the x and y axes passing through the centroid C. Determine the orientation of the principal axes and the principal moments of inertia. Solve using Mohr's circle.Given: Ix = 450 in4Iy = 1730 in4Ixy = 138 in4
The right circular cone is formed by revolving the shaded area around the x axis. Determine the moment of inertia lx and express the result in terms of the total mass m of the cone. The cone has a constant density ρ.
Determine the moment of inertia of the thin ring about the z axis. The ring has a mass m.
The solid is formed by revolving the shaded area around the y axis. Determine the radius of gyration ky. The specific weight of the material is γ.Given:a = 3 inb = 3 inγ = 380lb/ft3
Determine the moment of inertia Ix for the sphere and express the result in terms of the total mass m of the sphere. The sphere has a constant density ρ.
Determine the radius of gyration kx of the paraboloid. The density of the material is ρ.Units Used: Mg = 1000 kgGiven: ρ = 5Mg/m3a = 200 mm b = 100 mm
Determine the moment of inertia of the semi-ellipsoid with respect to the x axis and express the result in terms of the mass m of the semi-ellipsoid. The material has a constant density ρ.
Determine the radius of gyration kx of the body. The specific weight of the material is γ.Given:γ = 380lb/ft3a = 8 inb = 2 in
Determine the moment of inertia for the ellipsoid with respect to the x axis and express the result in terms of the mass m of the ellipsoid. The material has a constant density ρ.
Determine the moment of inertia of the homogeneous pyramid of mass m with respect to the z axis. The density of the material is ρ. Suggestion: Use a rectangular plate element having a volume of dV = (2x) (2y) dz.
The concrete shape is formed by rotating the shaded area about the y axis.Determine the moment of inertia Iy. The specific weight of concrete is γ.Given:γ = 150lb/ft3a = 6 inb = 4 inc = 8 in
Determine the moment of inertia of the thin plate about an axis perpendicular to the page and passing through the pin at O. The plate has a hole in its center.Its thickness is c, and the material has a density of ρGiven:a = 1.40 mc = 50 mmb = 150 mm ρ = 50kg/m3
Determine the moment of inertia Iz of the frustum of the cone which has a conical depression. The material has a density ρ.Given:ρ = 200kg/m3a = 0.4 mb = 0.2 mc = 0.6 md = 0.8 m
Determine the moment of inertia for the assembly about an axis which is perpendicular to the page and passes through the center of mass G. The material has a specific weight γ.Given:a = 0.5 ft d = 0.25 ftb = 2 ft e = 1 ftc = 1 ft γ = 90lb/ft3
Determine the moment of inertia for the assembly about an axis which is perpendicular to the page and passes through point O. The material has a specific weight γ.Given:a = 0.5 ft d = 0.25 ftb = 2 ft e = 1 ftc = 1 ft γ = 90lb/ft3
The wheel consists of a thin ring having a mass M1 and four spokes made from slender rods, each having a mass M2. Determine the wheel’s moment of inertia about an axis perpendicular to the page and passing through point A.Given:M1 = 10 kgM2 = 2 kga = 500 mm
The slender rods have a weight density γ. Determine the moment of inertia for the assembly about an axis perpendicular to the page and passing through point A.Given:γ = 3lb/fta = 1.5 ftb = 1 ftc = 2 ft
Each of the three rods has a mass m. Determine the moment of inertia for the assembly about an axis which is perpendicular to the page and passes through the center point O.
The slender rods have weight density γ. Determine the moment of inertia for the assembly about an axis perpendicular to the page and passing through point A Given:γ = 3lb/fta = 1.5 ftb = 2 ft
The pendulum consists of a plate having weight Wp and a slender rod having weight Wr. Determine the radius of gyration of the pendulum about an axis perpendicular to the page and passing through point O.Given:Wp = 12 lb a = 1 ftWr = 4 lb b = 1 ftc = 3 ftd = 2 ft
Determine the moment of inertia for the overhung crank about the x axis. The material is steel having density ρ.Units Used:Mg = 1000 kgGiven:ρ = 7.85Mg/m3a = 20 mmb = 20 mmc = 50 mmd = 90 mme = 30 mm
Determine the moment of inertia for the overhung crank about the x' axis. The material is steel having density ρ.Units used:Mg = 1000 kgGiven:ρ = 7.85Mg/m3a = 20 mmb = 20 mmc = 50 mmd = 90 mme = 30 mm
Determine the moment of inertia for the solid steel assembly about the x axis.Steel has a specific weight γst.Given:a = 2 ftb = 3 ftc = 0.5 ftd = 0.25 ftγst = 490lb/ft3
The pendulum consists of two slender rods AB and OC which have a mass density ρr. The thin plate has a mass density ρp. Determine the location yc of the center of mass G of the pendulum then calculate the moment of inertia of the pendulum about an axis perpendicular to the page and passing
Determine the moment of inertia for the shaded area about the x axis.Given:a = 2 inb = 8 in
Determine the moment of inertia for the shaded area about the y axis.Given:a = 2 inb = 8 in
Determine the mass moment of inertia Ix of the body and express the result in terms of the total mass m of the body. The density is constant.
Determine the product of inertia for the shaded area with respect to the x and y axes.Given:a = 1 mb = 1 m
Determine the area moments of inertia Iu and Iv and the product of inertia Iuv for the semicircular area.Given:r = 60 mmθ = 30 deg
Determine the moment of inertia for the shaded area about the x axis.Given:a = 3 inb = 9 in
Determine the moment of inertia for the shaded area about the y axis.Given:a = 3 inb = 9 in
Determine the area moment of inertia of the area about the x axis. Then, using the parallel-axis theorem, find the area moment of inertia about the x' axis that passes through the centroid C of the area.Given:a = 200 mmb = 200 mm
Determine the area moment of inertia for the triangular area about(a) The x axis, and(b) The centroidal x' axis.
Determine the product of inertia of the shaded area with respect to the x and y axes.Given:a = 2 inb = 1 in
The thin rod of weight W rests against the smooth wall and floor. Determine the magnitude of force P needed to hold it in equilibrium.
The disk has a weight W and is subjected to a vertical force P and a couple moment M. Determine the disk’s rotation θ if the end of the spring wraps around the periphery of the disk as the disk turns. The spring is originally unstretched.Given:W = 10 lbP = 8 lbM = 8 lb ⋅ fta = 1.5 ftk =
The platform supports a load W. Determine the horizontal force P that must be supplied by the screw in order to support the platform when the links are at the arbitrary angle θ.
Each member of the pin-connected mechanism has mass m1. If the spring is unstretched when θ = 0ο, determine the angle θ for equilibrium.Given:M1 = 8 kgK =2500 N/ML = 300 mmM = 50 Nmg = 9.81m/s2
Each member of the pin-connected mechanism has mass m1. If the spring is unstretched when θ = 0ο, determine the required stiffness k so that the mechanism is in equilibrium when θ = θ0.Units Used:kN = 103 NGiven:m1 = 8 kgθ = 30 degL = 300 mmM = 0 N⋅ mg 9.81ms2
The crankshaft is subjected to torque M. Determine the horizontal compressive force F applied to the piston for equilibrium when θ = θ0Given:M = 50 Nmθ0 = 60 dega = 100 mmb = 400 mm
The crankshaft is subjected to torque M. Determine the horizontal compressive force F and plot the result of F (ordinate) versus θ (abscissa) for 0ο Units Used:kN = 103 NGiven:M = 0.05 kN ⋅ ma = 0.1mb = 0.4m
If a force P is applied perpendicular to the handle of the toggle press, determine the compressive force developed at C.Given:P = 30lbθ = 30 dega = 12 inb = 2 in
A force P is applied to the end of the lever. Determine the horizontal force F on the piston for equilibrium.
The mechanism consists of the four pin-connected bars and three springs, each having a stiffness k and an unstretched length l0 Determine the horizontal forces P that must be applied to the pins in order to hold the mechanism in the horizontal position for equilibrium.
When θ = θ0, the uniform block of weight Wb compresses the two vertical springs a distance δ. If the uniform links AB and CD each weigh WL, determine the magnitude of the applied couple moments M needed to maintain equilibrium.Given:θ0 = 20 deg a = 1 ftWb = 50 lb b = 4 ftδ = 4 in c = 1 ftWL =
The spring is unstretched when θ = 0. Determine the angle θ for equilibrium. Due to the roller guide, the spring always remains vertical. Neglect the weight of the links.Given:P = 8 lbK= 50lb/fta = 2 ftb = 2 ft
Determine the force P required to lift the block of mass M using the differential hoist. The lever arm is fixed to the upper pulley and turns with it.Given:a = 800 mmM = 15 kgb = 150 mmc = 300 mmg= 9.81 m/s2
Determine the magnitude of the applied couple moments M needed to maintain equilibrium at θ. The plate E has a weight W. Neglect the weight of the links AB and CD.Given:a = 0.5 ftd = 2 ftb = 1 ftc = 2 ftW = 50 lbθ = 20 deg
The members of the mechanism are pin connected. If a horizontal force P acts at A, determine the angle θ for equilibrium. The spring is unstretched when θ = 90°.Units Used:kN = 103 NGiven:a = 0.5 mk = 20 kN/mP = 400 N
Determine the force F needed to lift the block having weight W. Hint: Note that the coordinates SA and SB can be related to the constant vertical length l of the cord.Given:W = 100 lb
Each member of the pin-connected mechanism has a mass m1. If the spring is unstretched when θ = 0° determine the angle θ for equilibrium.Given:a = 300 mmk = 2500 N/mm1 = 8 kgM = 50 N ⋅ m
The bar is supported by the spring and smooth collar that allows the spring to be always perpendicular to the bar for any angle θ. If the unstretched length of the spring is l0, determine the force P needed to hold the bar in the equilibrium position θ. Neglect the weight of the bar.
The scissors jack supports a load P. Determine the axial force in the screw necessary for equilibrium when the jack is in the position θ. Each of the four links has a length L and is pin-connected at its center. Points B and D can move horizontally.
Determine the masses mA and mB of A and B required to hold the desk lamp of mass M in balance for any angles θ and ϕ. Neglect the weight of the mechanism and the size of the lamp.Given:M = 400 gma = 75 mmb = 75 mmc = 75 mmd = 300 mme = 300 mmg = 9.81m/s2
The Roberval balance is in equilibrium when no weights are placed on the pans A and B. If two masses mA and mB are placed at any location a and b on the pans, show that equilibrium is maintained if mA dA = mB dB.
The chain puller is used to draw two ends of a chain together in order to attach the “master link.” The device is operated by turning the screw S, which pushes the bar AB downward, thereby drawing the tips C and D towards one another. If the sliding contacts at A and B are smooth, determine the
The service window at a fast-food restaurant consists of glass doors that open and close automatically using a motor which supplies a torque M to each door. The far ends, A and B, move along the horizontal guides. If a food tray becomes stuck between the doors as shown, determine the horizontal
Rods AB and BC have centers of mass located at their midpoints. If all contacting surfaces are smooth and BC has mass mBC determine the appropriate mass mAB of AB required for equilibrium.Given:mBC = 100 kga = 0.75 mb = 1 mc = 2 md = 1.5 m
If the potential energy for a conservative two-degree-of-freedom system is expressed by the relation V = ay2 + bx2, where y and x, determine the equilibrium positions and investigate the stability at each position.Given:A = 3 N/MB = 2 N/M
If the potential energy for a conservative one-degree-of-freedom system is expressed by the relation V = (ax3 + bx2 + cx + d), determine the equilibrium positions and investigate the stability at each.PositionGiven:
If the potential energy for a conservative one-degree-of-freedom system is expressed by the relation V = a sin(θ) + b cos(2θ), 0 deg ≤ θ ≤ 180 deg , determine the equilibrium positions and investigate the stability at each position.Given:a = 24 ft⋅ lb b = 10 ft⋅ lb
If the potential energy for a conservative two-degree-of-freedom system is expressed by the Relation V = ay2 + bx2, where y and x, determine the equilibrium positions and investigate testability at each position.Given:
The spring of the scale has an unstretched length a. Determine the angle θ for equilibrium when a weight W is supported on the platform. Neglect the weight of the members. What value W would be required to keep the scale in neutral equilibrium when θ = 0°?
The two bars each have weight W. Determine the required stiffness k of the spring so that the two bars are in equilibrium at θ = θ0. The spring has an unstretched length δ.Given: W = 8 lb θ 0 = 30 deg δ = 1 ft a = 2 ft
Each of the two springs has an unstretched length δ. Determine the mass M of the cylinder when it is held in the equilibrium position shown, i.e., y = a.Given:a = 1 mb = 500 mmδ = 500 mmk = 200N/m
The uniform beam has mass M. If the contacting surfaces are smooth, determine the angle θ for equilibrium and investigate the stability of the beam when it is in this position. The spring has an unstretched length of δ.Units Used:KN = 103 NGiven:M = 200 kg k = 1.2kN/mδ = 0.5 m l = 2 m
The bar supports a weight W at its end. If the springs are originally unstretched when the bar is vertical, determine the required stiffness k1 = k2 =k of the springs so that the bar is in neutral equilibrium when it is vertical.Given:W = 500 lba = 3 ftb = 3 ftc = 3 ft
The uniform rod AB has a mass M. If spring DC is unstretched at θ = 90 deg, determine the angle θ for equilibrium and investigate the stability at the equilibrium position. The spring always acts in the horizontal position due to the roller guide at D.Units Used:kN = 103 NGiven:M = 80 kg a = 1 mk
Determine the angle θ for equilibrium and investigate the stability at this position. The bars each have mass mb and the suspended block D has mass mD Cord DC has a total length of L.Given:mb = 3 kgmD = 7 kga = 500 mmL = 1 mg 9.81m/s2
The bar supports a weight of W at its end. If the springs are originally unstretched when the bar is vertical, investigate the stability of the bar when it is in the vertical position.Given:k1 = 3001b/ftk2 = 5001b/ftW = 500 lbA = 3 ft
If each of the three links of the mechanism has a weight W, determine the angle θ for equilibrium. He spring, which always remains vertical, is unstretched when θ = 0°.
The small postal scale consists of a counterweight W1 connected to the members having negligible eight. Determine the weight W2 that is on the pan in terms of the angles θ and ϕ and the dimension sown. All members are pin connected.
The uniform right circular cone having a mass m is suspended cord as shown. Determine the angle at which it hangs from the wall for equilibrium. Is the one in stable equilibrium?
The homogeneous cylinder has a conical cavity cut into its base as shown. Determine the depth d of the cavity so that the cylinder balances on the pivot and remains in neutral equilibrium.Given:a = 50 mmb = 150 mm
The conical manhole cap is made of concrete and has the dimensions shown. Determine the critical location h = hcr of the pick-up connectors at A and B so that when hoisted with constant velocity the cap is in neutral equilibrium.Explain what would happen if the connectors were placed at a point h >
Each bar has a mass per length of m0. Determine the angles θ and ϕ at which they are suspended in equilibrium. The contact at A is smooth, and both are pin connected at B.
The triangular block of weight W rests on the smooth corners which are a distance an apart. If the block has three equal sides of length d, determine the angle θ for equilibrium.
A homogeneous cone rests on top of the cylindrical surface. Derive a relationship between the radius r of the cylinder and the height h of the cone for neutral equilibrium. Hint: Establish the potential function for a small angle θ of tilt of the cone, i.e., approximate sin θ ≈ 0 and cos θ ≈
The door has a uniform weight W1. It is hinged at A and is held open by the weight W2 and the pulley.Determine the angle θ for equilibrium.Given:W1 = 50 lbW2 = 30 lba = 6 ftb = 6 ft
The hemisphere of weight W supports a cylinder having a specific weight γ. If the radii of the cylinder and hemisphere are both a., determine the height h of the cylinder which ill produce neutral equilibrium in the position shown.Given:W = 60 lba = 5 inγ = 3111b/ft3
Compute the force developed in the spring required to keep the rod of mass M rod in equilibrium at θ. The spring remains horizontal due to the roller guide.Given:k = 200N/MM = 40 N ⋅ ma = 0.5 mθ = 30 degM rod = 6 kg
Determine the force P acting on the cord which is required to maintain equilibrium of the horizontal bar CB of mass M. Hint: First show that the coordinates sA and sB are related to the constant vertical length l of the cord by the equation 5sB − sA = L.Given:M = 20 kg
The uniform bar AB has weight W. If the attached spring is unstretched when θ = 90 deg, use the method of virtual work and determine the angle θ for equilibrium.Note that the spring always remains in the vertical position due to the roller guide.Given:W = 10 lbk = 5 1b/fta = 4 ft
The uniform bar AB has weight W. If the attached spring is unstretched when θ = 90 deg, use the principle of potential energy and determine the angle θ for equilibrium. Investigate the stability of the equilibrium positions. Note that the spring always remains in the vertical position due to the
The punch press consists of the ram R, connecting rod AB, and a flywheel. If a torque M is applied to the flywheel, determine the force F applied at the ram to hold the rod in the position θ = θ 0.Given:M = 50 N⋅ mθ0 = 60 degr = 0.1 ma = 0.4 m
A horizontal force acts on the end of the link as shown. Determine the angles θ1 and θ2 for equilibrium of the two links. Each link is uniform and has a mass m.
Determine the following magnitude of the resultant force FR = F1 + F3 and its direction, measured counterclockwise from the positive xaxis.
Determine the magnitude of the resultant force if: (a) FR = F1 + F2; (b) FR = F1 ? F2.
Determine the magnitude of the resultant force FR = F1 + F2 and its direction, measured counterclockwise from the positive xaxis.
Determine the magnitude of the resultant force FR = F1 + F2 and its direction, measured clockwise from the positive uaxis.
Resolve the force F1, into components acting along the u and v axes and determine the magnitudes of thecomponents.
Resolve the force F2 into components acting along the u and v axes and determine the magnitudes of the components.
The plate is subjected to the two forces at A and B as shown. If ? = 60?, determine the magnitude of the resultant if these two forces and its direction measured from the horizontal.

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