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mechanical engineering

Vector Mechanics For Engineers Statics 7th Edition R.C.Hibbeler - Solutions

The centroidal polar moment of inertia a JC of the 15.5 ×103 mm2 shaded region is 250 ×106 mm4. Determine the polar moments of inertia JB and JD of the shaded region knowing that JD = 2JB and d = 100 mm.
A flat belt is used to transmit a torque from pulley A to pulley B. The radius of each pulley is 3 in., and a force of magnitude P = 225 lb is applied as shown to the axle of pulley A. Knowing that the coefficient of static friction is 0.35, determine(a) The largest torque which can be
Determine the centroidal polar moment of inertia a JC of the 10 ×103 mm2 shaded area knowing that the polar moments of inertia of the area with respect to points A, B, and D are JA = 45 × 106mm4, JB =130 × 106 mm4, and JD =252 × 106mm4, respectively.
Solve Problem 8.109 assuming that the belt is looped around the pulleys in a figure eight.
A couple MB of magnitude 2 lb ⋅ ft is applied to the drive drum B of a portable belt sander to maintain the sanding belt C at a constant speed. The total downward force exerted on the wooden work piece E is 12 lb, and μ k = 0.10 between the belt and the sanding platen D. Knowing that μs = 0.35
A band belt is used to control the speed of a flywheel as shown. Determine the magnitude of the couple being applied to the flywheel knowing that the coefficient of kinetic friction between the belt and the flywheel is 0.25 and that the flywheel is rotating clockwise at a constant speed. Show that
The drum brake shown permits clockwise rotation of the drum but prevents rotation in the counterclockwise direction. Knowing that the maximum allowed tension in the belt is 7.2kN, determine(a) The magnitude of the largest counterclockwise couple that can be applied to the drum,(b) The smallest
Determine the moments of inertia Ix and Iy of the area shown with respect to centroidal axes respectively parallel and perpendicular to side AB.
A differential band brake is used to control the speed of a drum which rotates at a constant speed. Knowing that the coefficient of kinetic friction between the belt and the drum is 0.30 and that a couple of magnitude is 150 N m ⋅ applied to the drum, determine the corresponding magnitude of the
Determine the moments of inertia Ix and Iy of the area shown with respect to centroidal axes respectively parallel and perpendicular to side AB.
A differential band brake is used to control the speed of a drum. Determine the minimum value of the coefficient of static friction for which the brake is self-locking when the drum rotates counterclockwise.
Determine the moments of inertia Ix and Iy of the area shown with respect to centroidal axes respectively parallel and perpendicular to side AB.
Bucket A and block C are connected by a cable that passes over drum B. Knowing that drum B rotates slowly counterclockwise and that the coefficients of friction at all surfaces are μs = 0.35 and μk = 0.25, determine the smallest combined weight W of the bucket and its contents for which block C
Solve Problem 8.116 assuming that drum B is frozen and cannot rotate.
Determine the moments of inertia Ix and Iy of the area shown with respect to centroidal axes respectively parallel and perpendicular to side AB.
Determine the polar moment of inertia of the area shown with respect to(a) Point O,(b) The centroid of the area.
A cable passes around three 30-mm-radius pulleys and supports two blocks as shown. Pulleys C and E are locked to prevent rotation, and the coefficients of friction between the cable and the pulleys are μs = 0.20 and μk = 0.15. Determine the range of values of the mass of block A for which
Determine the polar moment of inertia of the area shown with respect to(a) Point O,(b) The centroid of the area.
A cable passes around three 30-mm-radius pulleys and supports two blocks as shown. Two of the pulleys are locked to prevent rotation, while the third pulley is rotated slowly at a constant speed. Knowing that the coefficients of friction between the cable and the pulleys are μs = 0.20 and μk =
Determine the polar moment of inertia of the area shown with respect to(a) Point O,(b) The centroid of the area.
Determine the polar moment of inertia of the area shown with respect to(a) Point O,(b) The centroid of the area.
A cable passes around three 30-mm-radius pulleys and supports two blocks as shown. Pulleys C and E are locked to prevent rotation, and the coefficients of friction between the cable and the pulleys are μs = 0.20 and μk = 0.15 determine the largest mass mA which can be raised(a) If pulley C is
Two 1-in. steel plates are welded to a rolled S section as shown. Determine the moments of inertia and the radii of gyration of the section with respect to the centroidal x and y axes.
A cable passes around three 30-mm-radius pulleys and supports two blocks as shown. Two of the pulleys are locked to prevent rotation, while the third pulley is rotated slowly at a constant speed. Knowing that the coefficients of friction between the cable and the pulleys are μs = 0.20 and μk =
A recording tape passes over the 1-in.-radius drive drum B and under the idler drum C. Knowing that the coefficients of friction between the tape and the drums are μs = 0.40 and μk = 0.30 and that drum C is free to rotate, determine the smallest allowable value of P if slipping of the tape on
Solve Problem 8.122 assuming that the idler drum C is frozen and cannot rotate.
To form a reinforced box section, two rolled W sections and two plates are welded together. Determine the moments of inertia and the radii of gyration of the combined section with respect to the centroidal axes shown.
Two C250 × 30 channels are welded to a 250 × 52 rolled S section as shown. Determine the moments of inertia and the radii of gyration of the combined section with respect to its centroidal x and y axes.
For the band brake shown, the maximum allowed tension in either belt is 5.6kN. Knowing that the coefficient of static friction between the belt and the 160-mm-radius drum is 0.25, determine(a) The largest clockwise moment M0 that can be applied to the drum if slipping is not to occur,(b) The
Solve Problem 8.124 assuming that a counterclockwise moment is applied to the drum.
Two channels are welded to a d × 300-mm steel plate as shown. Determine the width d for which the ratio Ix / Iy of the centroidal moments of inertia of the section is 16.
Two L3 × 3 × ¼-in. angles are welded to a C10 × 20 channel. Determine the moments of inertia of the combined section with respect to centroidal axes respectively parallel and perpendicular to the web of the channel.
To form an unsymmetrical girder, two L3 × 3 × ¼ -in. angles and two L6 × 4 × ½ -in. angles are welded to a 0.8-in. steel plate as shown. Determine the moments of inertia of the combined section with respect to its centroidal x and y axes.
The strap wrench shown is used to grip the pipe firmly without marring the surface of the pipe. Knowing that the coefficient of static friction is the same for all surfaces of contact, determine the smallest value of μs for which the wrench will be self-locking when a = 10 in., r = 1.5 in., and θ
Solve Problem 8.126 assuming that θ = 75o.
Two L127 × 76 × 12.7-mm angles are welded to a 10-mm steel plate. Determine the distance b and the centroidal moments of inertia a Ix and Iy of the combined section knowing that Iy = 3Ix.
A channel and an angle are welded to an a × 20-mm steel plate. Knowing that the centroidal y axis is located as shown, determine(a) The width a,(b) The moments of inertia with respect to the centroidal x and y axes.
Prove that Equations (8.13) and (8.14) are valid for any shape of surface provided that the coefficient of friction is the same at all points of contact.
Complete the derivation of Equation (8.15), which relates the tension in both parts of a V belt.
Solve Problem 8.107 assuming that the flat belt and drums are replaced by a V belt and V pulleys with α = 36o. (The angle α is as shown in Figure 8.15a.)
The panel-shown forms the end of a trough which is filled with water to the line AA′. Referring to Sec. 9.2, determine the depth of the point of application of the resultant of the hydrostatic forces acting on the panel (the center of pressure).
Solve Problem 8.109 assuming that the flat belt and drums are replaced by a V belt and V pulleys with α = 36o. (The angle α is as shown in Figure 8.15a.)
Considering only values of θ less than 90°, determine the smallest value of θ required to start the block moving to the right when(a) W = 75lb,(b) W = 100lb.
The machine base shown has a mass of 75 kg and is fitted with skids at A and B. The coefficient of static friction between the skids and the floor is 0.30. If a force P of magnitude 500 N is applied at corner C, determine the range of values of θ for which the base will not move.
Knowing that a couple of magnitude 30 N m ⋅ is required to start the vertical shaft rotating, determine the coefficient of static friction between the annular surfaces of contact.
The panel shown forms the end of a trough which is filled with water to the line AA′ . Referring to Sec. 9.2, determine the depth of the point of application of the resultant of the hydrostatic forces acting on the panel (the center of pressure).
The 20-lb block A and the 30-lb block B are supported by an incline which is held in the position shown. Knowing that the coefficient of static friction is 0.15 between the two blocks and zero between block B and the incline, determine the value of θ for which motion is impending.
The panel-shown forms the end of a trough which is filled with water to the line AA′. Referring to Sec. 9.2, determine the depth of the point of application of the resultant of the hydrostatic forces acting on the panel (the center of pressure).
The 20-lb block A and the 30-lb block B are supported by an incline which is held in the position shown. Knowing that the coefficient of static friction is 0.15 between all surfaces of contact, determine the value of θ for which motion is impending.
Two cylinders are connected by a rope that passes over two fixed rods as shown. Knowing that the coefficient of static friction between the rope and the rods is 0.40, determine the range of values of the mass m of cylinder D for which equilibrium is maintained.
The panel-shown forms the end of a trough which is filled with water to the line AA′. Referring to Sec. 9.2, determine the depth of the point of application of the resultant of the hydrostatic forces acting on the panel (the center of pressure).
Two cylinders are connected by a rope that passes over two fixed rods as shown. Knowing that for cylinder D upward motion impends when 20 m = kg, determine(a) The coefficient of static friction between the rope and the rods,(b) The corresponding tension in portion BC of the rope.
The cover for a 10 × 22-in. access hole in an oil storage tank is attached to the outside of the tank with four bolts as shown. Knowing that the specific weight of the oil is 57.4 lb/ft3 and that the center of the cover is located 10 ft below the surface of the oil determine the additional force
A vertical trapezoidal gate that is used as an automatic valve is held shut by two springs attached to hinges located along edge AB. Knowing that each spring exerts a couple of magnitude 8.50kN ⋅ m, determine the depth d of water for which the gate will open.
A 10° wedge is used to split a section of a log. The coefficient of static friction between the wedge and the log is 0.35. Knowing that a force P of magnitude 600 lb was required to insert the wedge, determine the magnitude of the forces exerted on the wood by the wedge after insertion.
Determine the x coordinate of the centroid of the volume shown.
A flat belt is used to transmit a torque from drum B to drum A. Knowing that the coefficient of static friction is 0.40 and that the allowable belt tension is 450 N, determine the largest torque that can be exerted on drum A.
Determine the x coordinate of the centroid of the volume shown; this volume was obtained by intersecting an elliptic cylinder with an oblique plane.
Two 10-lb blocks A and B are connected by a slender rod of negligible weight. The coefficient of static friction is 0.30 between all surfaces of contact, and the rod forms an angle θ = 30° with the vertical.(a) Show that the system is in equilibrium when P = 0.(b) Determine the largest value of P
Show that the system of hydrostatic forces acting on a submerged plane area A can be reduced to a force P at the centroid C of the area and two couples. The force P is perpendicular to the area and is of magnitude P = γ Ay sin θ, where γ is the specific weight of the liquid, and the couples are
Determine the range of values of P for which equilibrium of the block shown is maintained.
Show that the resultant of the hydrostatic forces acting on a submerged plane area A is a force P perpendicular to the area and of magnitude P = γ Ay sin θ = pA , where γ is the specific weight of the liquid and p is the pressure at the centroid C of the area. Show that P is applied at a point
Two identical uniform boards, each of weight 40 lb, are temporarily leaned against each other as shown. Knowing that the coefficient of static friction between all surfaces is 0.40, determine(a) The largest magnitude of the force P for which equilibrium will be maintained,(b) The surface at which
Determine by direct integration the product of inertia of the given area with respect to the x and y axes.
Determine by direct integration the product of inertia of the given area with respect to the x and y axes.
Determine by direct integration the product of inertia of the given area with respect to the x and y axes.
Determine by direct integration the product of inertia of the given area with respect to the x and y axes.
Using the parallel-axis theorem, determine the product of inertia of the area shown with respect to the centroidal x and y axes.
Using the parallel-axis theorem, determine the product of inertia of the area shown with respect to the centroidal x and y axes.
Using the parallel-axis theorem, determine the product of inertia of the area shown with respect to the centroidal x and y axes.
Using the parallel-axis theorem, determine the product of inertia of the area shown with respect to the centroidal x and y axes.
Using the parallel-axis theorem, determine the product of inertia of the area shown with respect to the centroidal x and y axes.
Using the parallel-axis theorem, determine the product of inertia of the area shown with respect to the centroidal x and y axes.
Using the parallel-axis theorem, determine the product of inertia of the area shown with respect to the centroidal x and y axes.
Using the parallel-axis theorem, determine the product of inertia of the area shown with respect to the centroidal x and y axes.
Determine for the quarter ellipse of Problem 9.67 the moments of inertia and the product of inertia with respect to new axes obtained by rotating the x and y axes about O(a) Through 45o counterclockwise,(b) Through 30o clockwise.
Determine the moments of inertia and the product of inertia of the area of Problem 9.72 with respect to new centroidal axes obtained by rotating the x and y axes 45° clockwise.
Determine the moments of inertia and the product of inertia of the area of Problem 9.73 with respect to new centroidal axes obtained by rotating the x and y axes through 30o clockwise.
Determine the moments of inertia and the product of inertia of the area of Problem 9.75 with respect to new centroidal axes obtained by rotating the x and y axes through 60o counterclockwise.
Determine the moments of inertia and the product of inertia of the L76 × 51 × 6.4-mm angle cross section of Problem 9.74 with respect to new centroidal axes obtained by rotating the x and y axes through 45o clockwise.
Determine the moments of inertia and the product of inertia of the L5 × 3 × ½ -in. angle cross section of Problem 9.78 with respect to new centroidal axes obtained by rotating the x and y axes through 30o counterclockwise.
For the quarter ellipse of Problem 9.67, determine the orientation of the principal axes at the origin and the corresponding values of the moments of inertia.
For the area indicated, determine the orientation of the principal axes at the origin and the corresponding values of the moments of inertia. Area of Problem 9.72
For the area indicated, determine the orientation of the principal axes at the origin and the corresponding values of the moments of inertia. Area of Problem 9.73
For the area indicated, determine the orientation of the principal axes at the origin and the corresponding values of the moments of inertia. Area of Problem 9.75
For the angle cross section indicated, determine the orientation of the principal axes at the origin and the corresponding values of the moments of inertia. The L76 × 51 × 6.4-mm angle cross section of Problem 9.74
For the angle cross section indicated, determine the orientation of the principal axes at the origin and the corresponding values of the moments of inertia. The L5 × 3 × 1/2 -in. angle cross section of Problem 9.78
Using Mohr’s circle, determine for the quarter ellipse of Problem 9.67 the moments of inertia and the product of inertia with respect to new axes obtained by rotating the x and y axes about O (a) Through 45o counterclockwise, (b) Through 30o clockwise.
Using Mohr’s circle, determine the moments of inertia and the product of inertia of the area of Problem 9.72 with respect to new centroidal axes obtained by rotating the x and y axes 45° clockwise.
Using Mohr’s circle, determine the moments of inertia and the product of inertia of the area of Problem 9.73 with respect to new centroidal axes obtained by rotating the x and y axes through 30o clockwise.
Using Mohr’s circle, determine the moments of inertia and the product of inertia of the area of Problem 9.75 with respect to new centroidal axes obtained by rotating the x and y axes through ugh 60o counterclockwise.
Using Mohr’s circle, determine the moments of inertia and the product of inertia of the L76 × 51 × 6.4-mm angle cross section of Problem 9.74 with respect to new centroidal axes obtained by rotating the x and y axes through 45o clockwise.
Using Mohr’s circle, determine the moments of inertia and the product of inertia of the L5 × 3 × ½ -in. angle cross section of Problem 9.78 with respect to new centroidal axes obtained by rotating the x and y axes through h 30o counterclockwise.
For the quarter ellipse of Problem 9.67, use Mohr’s circle to determine the orientation of the principal axes at the origin and the corresponding values of the moments of inertia.
Using Mohr’s circle, determine for the area indicated the orientation of the principal centroidal axes and the corresponding values of the moments of inertia. Area of Problem 9.72
Using Mohr’s circle, determine for the area indicated the orientation of the principal centroidal axes and the corresponding values of the moments of inertia. Area of Problem 9.76
Using Mohr’s circle, determine for the area indicated the orientation of the principal centroidal axes and the corresponding values of the moments of inertia. Area of Problem 9.73
Using Mohr’s circle, determine for the area indicated the orientation of the principal centroidal axes and the corresponding values of the moments of inertia. Area of Problem 9.74
Using Mohr’s circle, determine for the area indicated the orientation of the principal centroidal axes and the corresponding values of the moments of inertia. Area of Problem 9.75
Using Mohr’s circle, determine for the area indicated the orientation of the principal centroidal axes and the corresponding values of the moments of inertia. Area of Problem 9.71

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