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engineering
mechanical engineering
Vector Mechanics For Engineers Statics And Dynamics 8th Edition Ferdinand Beer, E. Russell Johnston, Jr., Elliot Eisenberg, William Clausen, David Mazurek, Phillip Cornwell - Solutions
Knowing that a 120-mm-diameter disk rolls at a constant velocity down a 2 percent incline, determine the coefficient of rolling resistance between the disk and the incline
Determine the horizontal force required to move a 1-Mg automobile with 460-mm-diameter tires along a horizontal road at a constant speed. Neglect all forms of friction except rolling resistance, and assume the coefficient of rolling resistance to be 1 mm.
Solve Prob. 8.88 including the effect of a coefficient of rolling resistance of 0.25 in. Problem 8.88: A 500-lb crate rests on a dolly as shown. The dolly has four 5-in.-diameter wheels with 0.5-in.-diameter axles. Knowing that the coefficients of friction are 0.12 and 0.08, μs= μk= determine
Solve Prob. 8.89 including the effect of a coefficient of rolling resistance of 1.75 mm. Problem 8.89: A scooter is designed to roll down a 3 percent slope at a constant speed. Assuming that the coefficient of kinetic friction between the 25-mm-diameter axles and the bearing is 0.12, determine the
A hawser is wrapped two full turns around a bollard. By exerting a 320-N force on the free end of the hawser, a dockworker can resist a force of 20kN on the other end of the hawser. Determine(a) The coefficient of static friction between the hawser and the bollard,(b) The number of times the hawser
Blocks A and B are connected by a cable that passes over support C. Friction between the blocks and the inclined surfaces may be neglected. Knowing that motion of block B up the incline is impending when 8 kg, mB = determine(a) The coefficient of static friction between the rope and the support,(b)
Blocks A and B are connected by a cable that passes over support C. Friction between the blocks and the inclined surfaces may be neglected. Knowing that the coefficient of static friction between the rope and the support is 0.50, determine the range of values of mB for which equilibrium is
A 120-kg block is supported by a rope which is wrapped 1 1/2 times around a horizontal rod. Knowing that the coefficient of static friction between the rope and the rod is 0.15, determine the range of values of P for which equilibrium is maintained.
Knowing that the coefficient of static friction is 0.25 between the rope and the horizontal pipe and 0.20 between the rope and the vertical pipe determine the range of values of P for which equilibrium is maintained.
Knowing that the coefficient of static friction is 0.30 between the rope and the horizontal pipe and that the smallest value of P for which equilibrium is maintained is 20 lb, determine(a) The largest value of P for which equilibrium is maintained,(b) The coefficient of static friction between the
In the pivoted motor mount shown, the weight W of the 175-lb motor is used to maintain tension in the drive belt. Knowing that the coefficient of static friction between the flat belt and drums A and B is 0.40, and neglecting the weight of platform CD, determine the largest couple which can be
Solve Prob. 8.107 assuming that the drive drum A is rotating counterclockwise. Problem 8.107: In the pivoted motor mount shown, the weight W of the 175-lb motor is used to maintain tension in the drive belt. Knowing that the coefficient of static friction between the flat belt and drums A and B is
A couple MB of magnitude 2.4 N m ‹… 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 48 N, and μk = 0.10 between the belt and the sanding platen D.
The setup shown is used to measure the output of a small turbine. When the flywheel is at rest, the reading of each spring scale is 70 N. If a 12.60 N m ⋅ couple must be applied to the flywheel to keep it rotating clockwise at a constant speed, determine(a) The reading of each scale at that
The setup shown is used to measure the output of a small turbine. The coefficient of kinetic friction is 0.20, and the reading of each spring scale is 80 N when the flywheel is at rest. Determine(a) The reading of each scale when the flywheel is rotating clockwise at a constant speed,(b) The couple
The band brake shown is used to control the speed of a rotating drum. Determine the magnitude of the couple being applied to the drum knowing that the coefficient of kinetic friction between the belt and the drum is 0.25 and that the drum is rotating clockwise at a constant speed.
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 125 lb ⋅ft is applied to the drum, determine the corresponding magnitude of
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.
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 4.5kN, determine(a) The magnitude of the largest counterclockwise couple that can be applied to the drum,(b) The smallest
Blocks A and C are connected by a rope that passes over drum B. Knowing that the drum rotates slowly clockwise and that the coefficients of friction at all surfaces are μs =0.30 and μk = 0.20, determine the smallest mass of block C for which block A(a) Will remain at rest,(b) Will be in
A cord is placed over two 100-mm diameter cylinders. Knowing that the coefficients of friction are μs = 0.30 and μk = 0.25, determine the largest mass m that can be raised when cylinder B is rotated slowly and cylinder A is kept fixed.
A cable passes around three 2-in.-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 weight of block A for which
A cable passes around three 2-in.-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 cable passes around three 2-in.-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 weight of block A for which
A cable passes around three 2-in.-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 20-mm-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
Solve Prob. 8.122 assuming that the idler drum C is frozen and cannot rotate. Problem 8.122: A recording tape passes over the 20-mm-radius drive drum B and under the idler drum C. Knowing that the coefficients of friction between the tape and the drums μs = are 0.40 and μk = 0.30 and that
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 Prob. 8.124 assuming that a counterclockwise moment is applied to the drum. Problem 8.124: 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
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 = 200 mm, r = 30 mm, and θ
Solve Prob. 8.126 assuming that θ =75°. Problem 8.126: 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
Prove that Eqs. (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 Eq. (8.15), which relates the tension in both parts of a V belt.
Solve Prob. 8.107 assuming that the flat belt and drums are replaced by a V belt and V pulleys with α =36°. (The angle α is as shown in Fig. 8.15a.) Problem 8.107: In the pivoted motor mount shown, the weight W of the 175-lb motor is used to maintain tension in the drive belt,
The V pulleys A and B have diameters of 4 in. and 8 in., respectively, and are connected by a V belt for which α =36°. Pulley A is mounted on the shaft of an electric motor that develops a couple M=5lb⋅ft and the tension in the belt is controlled by a mechanism that applies a
Considering only values of θ less than 90° , determine the smallest value of θ for which motion of the block to the right is impending when(a) 30 m = kg,(b) m = 40 kg.
Considering only values of θ less than 90°, determine the smallest value of θ for which motion of the block to the right is impending when(a) 30 m = kg,(b) m = 40 kg.
The coefficients of friction are μs = 0.40 and μk = 0.30 between all surfaces of contact. Determine the force P for which motion of the 60-lb block is impending if cable AB(a) Is attached as shown,(b) Is removed.
A 19.5-ft ladder AB leans against a wall as shown. Assuming that the coefficient of static friction s μ is the same at A and B, determine the smallest value of s μ for which equilibrium is maintained.
A window sash having a mass of 4 kg is normally supported by two 2-kg sash weights, knowing that the window remains open after one sash cord has broken determine the smallest possible value of the coefficient of static friction. (Assume that the sash is slightly smaller than the frame and will bind
A collar B of weight W is attached to the spring AB and can move along the rod shown. The constant of the spring is 1.5kN/m and the spring is unstretched when θ = 0. Knowing that the coefficient of static friction between the collar and the rod is 0.40, determine the range of values of
Two slender rods of negligible weight are pin-connected at C and attached to blocks A and B each of weight W. Knowing that θ = 70o and that the coefficient of static friction between the blocks and the horizontal surface is 0.30, determine the largest value of P for which equilibrium
Block A supports a pipe column and rests as shown on wedge B. Knowing that the coefficient of static friction at all surfaces of contact is 0.25 and that θ =45°, determine the smallest force P required to raise block A.
The ends of two fixed rods A and B are single-threaded screws of mean radius 0.3 in. and pitch 0.1 in. Rod A has a right-handed thread, and rod B has a left-handed thread. The coefficient of static friction between the rods and the threaded sleeve is 0.12. Determine the magnitude of the couple that
A 120-mm-radius pulley of mass 5 kg is attached to a 30-mm-radius shaft which fits loosely in a fixed bearing. It is observed that motion of the pulley is impending if a 0.5-kg mass is added to block A. Determine the coefficient of static friction between the shaft and the bearing.
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
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
Determine by direct integration the moment of inertia of the shaded area with respect to the y axis.
Determine by direct integration the moment of inertia of the shaded area with respect to the y axis.
Determine by direct integration the moment of inertia of the shaded area with respect to the y axis.
Determine by direct integration the moment of inertia of the shaded area with respect to the y axis.
Determine by direct integration the moment of inertia of the shaded area with respect to the x axis.
Determine by direct integration the moment of inertia of the shaded area with respect to the x axis.
Determine by direct integration the moment of inertia of the shaded area with respect to the x axis.
Determine by direct integration the moment of inertia of the shaded area with respect to the x axis.
Determine by direct integration the moment of inertia of the shaded area with respect to the x axis.
Determine by direct integration the moment of inertia of the shaded area with respect to the x axis.
Determine by direct integration the moment of inertia of the shaded area with respect to the x axis.
Determine by direct integration the moment of inertia of the shaded area with respect to the y axis.
Determine by direct integration the moment of inertia of the shaded area with respect to the y axis.
Determine by direct integration the moment of inertia of the shaded area with respect to the y axis.
Determine by direct integration the moment of inertia of the shaded area with respect to the x axis.
Determine by direct integration the moment of inertia of the shaded area with respect to the x axis.
Determine by direct integration the moment of inertia of the shaded area with respect to the y axis.
Determine by direct integration the moment of inertia of the shaded area with respect to the y axis.
Determine by direct integration the moment of inertia of the shaded area with respect to the x axis.
Determine by direct integration the moment of inertia of the shaded area with respect to the y axis.
Determine the polar moment of inertia and the polar radius of gyration of the rectangle shown with respect to the midpoint of one of its(a) Longer sides,(b) Shorter sides.
Determine the polar moment of inertia and the polar radius of gyration of the shaded area shown with respect to point P.
Determine the polar moment of inertia and the polar radius of gyration of the shaded area shown with respect to point P.
Determine the polar moment of inertia and the polar radius of gyration of the shaded area shown with respect to point P.
(a) Determine by direct integration the polar moment of inertia of the area shown with respect to point O.(b) Using the result of part a, determine the moments of inertia of the given area with respect to the x and y axes.
(a) Show that the polar radius of gyration kO of the area shown is approximately equal to the mean radius Rm = (R1 + R2)/2 for small values of the thickness t = R2 ˆ’ R1.(b) Determine the percentage error introduced by using Rm in place of kO for the following values of t/Rm: 1, 1/4, 1/16.
Determine the polar moment of inertia and the polar radius of gyration of the shaded area shown with respect to point O.
Determine the polar moment of inertia and the radius of gyration of the isosceles triangle shown with respect to point O.
Using the polar moment of inertia of the isosceles triangle of Prob. 9.28, show that the centroidal polar moment of inertia of a circular area of radius r is π r4/2.
Prove that the centroidal polar moment of inertia of a given area A cannot be smaller than A2/2π.
Determine the moment of inertia and the radius of gyration of the shaded area with respect to the x axis.
Determine the moment of inertia and the radius of gyration of the shaded area with respect to the x axis.
Determine the moment of inertia and the radius of gyration of the shaded area with respect to the y axis.
Determine the moment of inertia and the radius of gyration of the shaded area with respect to the y axis.
Determine the moment of inertia and the radius of gyration of the shaded area with respect to the y axis.
Determine the moment of inertia and the radius of gyration of the shaded area with respect to the y axis.
Determine the shaded area and its moment of inertia with respect to a centroidal axis parallel l to AA€², knowing that its moments of inertia with respect to AA€² and BB€² are 2.2 × 106 mm4 and 4×106 mm4, respectively, and that d1 = 25 mm and
Knowing that the shaded area is equal to 6000 mm2 and that its moment of inertia with respect to AA€² is 18 × 106 mm4, determine its moment of inertia with respect to BB€² for d1 = 50 mm and d2 = 10 mm.
If d1 = 2a, determine the distance a and the centroidal polar moment of inertia of the 24- in2 shaded area shown knowing that d2 = 2in. and that the polar moments of inertia of the area with respect to points A and B are 256 in4 and 190 in4, respectively.
The centroidal polar moment of inertia JC of the 30- in2 shaded area shown is 52.5 in4. Knowing that d1 = d2 = 2.5 in., determine(a) The distance a so that JB =3JA,(b) The polar moment of inertia JB.
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 moments of inertia Ix and Iy of the area shown with respect to centroidal axes respectively parallel and perpendicular to side AB.
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 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.
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.
Determine the polar moment of inertia of the area shown with respect to(a) Point O,(b) The centroid of the area.
Two 6 × 4 × ½-in. angles are welded together to form the section shown. Determine the moments of inertia and the radii of gyration of the section with respect to the centroidal axes shown.
Two channels and two plates are used to form the column section shown. Determine the moments of inertia and the radii of gyration of the combined section with respect to the centroidal axes shown.
Two C10 × 20 channels are welded to a 10 × 35 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.
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 L76 × 76 × 6.4-mm angles are welded to a C250 × 30 channel. Determine the moments of inertia of the combined section with respect to centroidal axes respectively perpendicular and parallel to the web of the channel.
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