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physics
mechanics
Vector Mechanics for Engineers Statics and Dynamics 11th edition Ferdinand Beer, E. Russell Johnston Jr., David Mazurek, Phillip Cornwell, Brian Self - Solutions
A 15° wedge is forced under a 50-kg pipe as shown. The coefficient of static friction at all surfaces is 0.20.(a) Show that slipping will occur between the pipe and the vertical wall.(b) Determine the force P required to move the wedge.
A 15° wedge is forced under a 50-kg pipe as shown. Knowing that the coefficient of static friction at both surfaces of the wedge is 0.20, determine the largest coefficient of static friction between the pipe and the vertical wall for which slipping will occur at A.
A 200-N block rests as shown on a wedge of negligible weight. The coefficient of static friction μs is the same at both surfaces of the wedge, and friction between the block and the vertical wall may be neglected. For P = 100 N, determine the value of μs for which motion is impending.
Solve Problem 8.66 assuming that the rollers are removed and that μs is the coefficient of friction at all surfaces of contact.PROBLEM 8.66*A 200-N block rests as shown on a wedge of negligible weight. The coefficient of static friction μs is the same at both surfaces of the wedge, and
The square-threaded worm gear shown has a mean radius of 2 in. and a lead of 0.5 in. The large gear is subjected to a constant clockwise couple of 9.6 kip · in. Knowing that the coefficient of static friction between the two gears is 0.12, determine the couple that must be applied to shaft
The 10-kg block is attached to link AB and rests on a moving belt. Knowing that μs = 0.30 and μk = 0.25 and neglecting the weight of the link, determine the magnitude of the horizontal force P that should be applied to the belt to maintain its motion(a) To the left as shown,(b) To the right.
In Problem 8.69, determine the couple that must be applied to shaft AB in order to rotate the large gear clockwise.PROBLEM 8.69The square-threaded worm gear shown has a mean radius of 2 in. and a lead of 0.5 in. The large gear is subjected to a constant clockwise couple of 9.6 kip ∙ in.
The vise shown consists of two members connected by two double-threaded screws with a mean radius of 0.25 in. and pitch of 0.08 in. The lower member is threaded at A and B (μs = 0.35), but the upper member is not threaded. It is desired to apply two equal and opposite forces of 120 lb on the
The ends of two fixed rods A and B are each made in the form of a single-threaded screw of mean radius 6 mm and pitch 2 mm. 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
Assuming that in Problem 8.75 a right-handed thread is used on both rods A and B, determine the magnitude of the couple that must be applied to the sleeve in order to rotate it.PROBLEM 8.75The ends of two fixed rods A and B are each made in the form of a single-threaded screw of mean radius 6 mm
A lever of negligible weight is loosely fitted onto a 75-mmdiameter fixed shaft. It is observed that the lever will just start rotating if a 3-kg mass is added at C. Determine the coefficient of static friction between the shaft and the lever.
A hot-metal ladle and its contents weigh 130 kips. Knowing that the coefficient of static friction between the hooks and the pinion is 0.30, determine the tension in cable AB required to start tipping the ladle.
The double pulley shown is attached to a 10-mm-radius shaft that fits loosely in a fixed bearing. Knowing that the coefficient of static friction between the shaft and the poorly lubricated bearing is 0.40, determine the magnitude of the force P required to start raising the load.
The double pulley shown is attached to a 10-mm-radius shaft that fits loosely in a fixed bearing. Knowing that the coefficient of static friction between the shaft and the poorly lubricated bearing is 0.40, determine the magnitude of the force P required to start raising the load.
The double pulley shown is attached to a 10-mm-radius shaft that fits loosely in a fixed bearing. Knowing that the coefficient of static friction between the shaft and the poorly lubricated bearing is 0.40, determine the magnitude of the smallest force P required to maintain equilibrium.
The double pulley shown is attached to a 10-mm-radius shaft that fits loosely in a fixed bearing. Knowing that the coefficient of static friction between the shaft and the poorly lubricated bearing is 0.40, determine the magnitude of the smallest force P required to maintain equilibrium.
The block and tackle shown are used to raise a 150-lb load. Each of the 3-in.- diameter pulleys rotates on a 0.5-in.-diameter axle. Knowing that the coefficient of static friction is 0.20, determine the tension in each portion of the rope as the load is slowly raised.
The block and tackle shown are used to lower a 150-lb load. Each of the 3-in.- diameter pulleys rotates on a 0.5-in.-diameter axle. Knowing that the coefficient of static friction is 0.20, determine the tension in each portion of the rope as the load is slowly lowered.
A lever AB of negligible weight is loosely fitted onto a 2.5-in.-diameter fixed shaft. Knowing that the coefficient of static friction between the fixed shaft and the lever is 0.15, determine the force P required to start the lever rotating counterclockwise.
A lever AB of negligible weight is loosely fitted onto a 2.5-in.-diameter fixed shaft. Knowing that the coefficient of static friction between the fixed shaft and the lever is 0.15, determine the force P required to start the lever rotating counterclockwise.
A lever AB of negligible weight is loosely fitted onto a 2.5-in.-diameter fixed shaft. Knowing that the coefficient of static friction between the fixed shaft and the lever is 0.15, determine the force P required to start the lever rotating clockwise.
Knowing that θ = 40°, determine the smallest force P for which equilibrium of the 7.5-kg block is maintained.
A lever AB of negligible weight is loosely fitted onto a 2.5-in.-diameter fixed shaft. Knowing that the coefficient of static friction between the fixed shaft and the lever is 0.15, determine the force P required to start the lever rotating clockwise.
A loaded railroad car has a mass of 30 Mg and is supported by eight 800-mm-diameter wheels with 125-mm-diameter axles. Knowing that the coefficients of friction are μs = 0.020 and μk = 0.015, determine the horizontal force required (a) To start the car moving, (b) To keep the car moving at a
A 50-lb electric floor polisher is operated on a surface for which the coefficient of kinetic friction is 0.25. Assuming that the normal force per unit area between the disk and the floor is uniformly distributed, determine the magnitude Q of the horizontal forces required to prevent motion of the
Determine the horizontal force required to move a 2500-lb automobile with 23-in.-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 0.05 in.
Knowing that a 6-in.-diameter disk rolls at a constant velocity down a 2 percent incline, determine the coefficient of rolling resistance between the disk and the incline.
Knowing that the coefficient of friction between the 25-kg block and the incline is μs = 0.25, draw the free-body diagram needed to determine both the smallest value of P required to start the block moving up the incline and the corresponding value of β.
Two blocks A and B are connected by a cable as shown. Knowing that the coefficient of static friction at all surfaces of contact is 0.30 and neglecting the friction of the pulleys, draw the free-body diagrams needed to determine the smallest force P required to move the blocks.
A cord is attached to and partially wound around a cylinder with a weight of W and radius r that rests on an incline as shown. Knowing that θ = 30°, draw the free-body diagram needed to determine both the tension in the cord and the smallest allowable value of the coefficient of
It is known that for a given area I̅y = 48 × 106 mm4 and I̅xy = - 20× 106 mm4, where the x and y axes are rectangular centroidal axes. If the axis corresponding to the maximum product of inertia is obtained by rotating the x axis 67.5° counterclockwise about C, use Mohr's circle to
Determine the mass moment of inertia of a ring of mass m, cut from a thin uniform plate, with respect to (a) the axis AAʹ, (b) the centroidal axis CCʹ that is perpendicular to the plane of the ring.
The parabolic spandrel shown was cut from a thin, uniform plate. Denoting the mass of the spandrel by m, determine its mass moment of inertia with respect to (a) the axis BBʹ, (b) the axis DDʹ that is perpendicular to the spandrel.
A thin rectangular plate of mass m is welded to a vertical shaft AB as shown. Knowing that the plate forms an angle θ with the y axis, determine by direct integration the mass moment of inertia of the plate with respect to (a) the y axis, (b) the z axis.
The machine part shown is formed by machining a conical surface into a circular cylinder. For b = 1/2h, determine the mass moment of inertia and the radius of gyration of the machine part with respect to the y axis.
A square hole is centered in and extends through the aluminum machine component shown. Determine (a) the value of a for which the mass moment of inertia of the component with respect to the axis AAʹ, which bisects the top surface of the hole, is maximum, (b) the corresponding values of the mass
After a period of use, one of the blades of a shredder has been worn to the shape shown and is of mass 0.18 kg. Knowing that the mass moments of inertia of the blade with respect to the AAʹ and BBʹ axes are 0.320 g ∙ m2 and 0.680 g ∙ m2, respectively, determine(a) the location of
A 2-mm thick piece of sheet steel is cut and bent into the machine component shown. Knowing that the density of steel is 7850 kg/m3, determine the mass moment of inertia of the component with respect to each of the coordinate axes.
A 2-mm thick piece of sheet steel is cut and bent into the machine component shown. Knowing that the density of steel is 7850 kg/m3, determine the mass moment of inertia of the component with respect to each of the coordinate axes.
A subassembly for a model airplane is fabricated from three pieces of 1.5- mm plywood. Neglecting the mass of the adhesive used to assemble the three pieces, determine the mass moment of inertia of the subassembly with respect to each of the coordinate axes. (The density of the plywood is 780
A section of sheet steel 0.03 in. thick is cut and bent into the sheet metal machine component shown. Determine the mass moment of inertia of the component with respect to each of the coordinate axes. (The specific weight of steel is 490 lb/ft3.)
A framing anchor is formed of 0.05-in.-thick galvanized steel. Determine the mass moment of inertia of the anchor with respect to each of the coordinate axes. (The specific weight of galvanized steel is 470 lb/ft3.)
A farmer constructs a trough by welding a rectangular piece of 2-mm-thick sheet steel to half of a steel drum. Knowing that the density of steel is 7850 kg/m3 and that the thickness of the walls of the drum is 1.8 mm, determine the mass moment of inertia of the trough with respect to each of the
Determine the mass moment of inertia of the steel machine element shown with respect to the x axis. (The density of steel is 490 lb/ft3.)
Determine the mass moment of inertia of the steel machine element shown with respect to the y axis. (The density of steel is 490 lb/ft3.)
Aluminum wire with a weight per unit length of 0.033 lb/ft is used to form the circle and the straight members of the figure shown. Determine the mass moment of inertia of the assembly with respect to each of the coordinate axes.
The figure shown is formed of 1/8-in.-diameter steel wire. Knowing that the specific weight of the steel is 490 lb/ft3, determine the mass moment of inertia of the wire with respect to each of the coordinate axes.
A homogeneous wire with a mass per unit length of 0.056 kg/m is used to form the figure shown. Determine the mass moment of inertia of the wire with respect to each of the coordinate axes.
The figure shown is formed of 1.5-mm-diameter aluminum wire. Knowing that the density of aluminum is 2800 kg/m3, determine the mass products of inertia Ixy, Iyz, and Izx of the wire figure.
A piece of sheet steel of thickness t and specific weight γ is cut and bent into the machine component shown. Determine the mass moment of inertia of the component with respect to the joining the origin O and Point A.
Determine the moment of inertia and the radius of gyration of the shaded area shown with respect to the x axis.
Two L4 × 4 × 1/2 -in. angles are welded to a steel plate as shown. Determine the moments of inertia of the combined section with respect to centroidal axes respectively parallel and perpendicular to the plate.
Using the parallel-axis theorem, determine the product of inertia of the L5 × 3 × 1/2 -in. angle cross section shown with respect to the centroidal x and y axes.
A thin plate of mass m was cut in the shape of a parallelogram as shown. Determine the mass moment of inertia of the plate with respect to(a) the y axis,(b) the axis AAʹ, which is perpendicular to the plate.
A 2-mm thick piece of sheet steel is cut and bent into the machine component shown. Knowing that the density of steel is 7850 kg/m3, determine the mass moment of inertia of the component with respect to each of the coordinate axes.
Determine the mass moment of inertia of the steel machine element shown with respect to the z axis. (The specific weight of steel is 490 lb/ft3.)
The centroidal polar moment of inertia JÌ…C of the 24-in2 shaded area is 600 in4. Determine the polar moments of inertia JB and JD of the shaded area knowing that JD = 2JB and d = 5 in.
A channel and a plate are welded together as shown to form a section that is symmetrical with respect to the y axis. Determine the moments of inertia of the combined section with respect to its centroidal x and y axes.
The strength of the rolled W section shown is increased by welding a channel to its upper flange. Determine the moments of inertia of the combined section with respect to its centroidal x and y axes.
Two L76 × 76 × 6.4-mm angles are welded to a C250 × 22.8 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.
Two steel plates are welded to a rolled W section as indicated. Knowing that the centroidal moments of inertia IÌ…x and IÌ…y of the combined section are equal, determine (a) the distance a, (b) the moments of inertia with respect to the centroidal x and y axes.
The cover for a 0.5-m-diameter access hole in a water storage tank is attached to the tank with four equally spaced bolts as shown. Determine the additional force on each bolt due to the water pressure when the center of the cover is located 1.4 m below the water surface.
Determine the vertical force P that must be applied at C to maintain the equilibrium of the linkage.
Solve Problem 10.99 knowing that k = 20 lb/in., r = 3 in., l = 6 in., and (a) W = 15 lb, (b) W = 60 lb.PROBLEM 10.99*Two rods of negligible weight are attached to drums of radius r that are connected by a belt and spring of constant k. Knowing that the spring is undeformed when the rods are
Determine the vertical force P that must be applied at G to maintain the equilibrium of the linkage.
Determine the couple M that must be applied to member DEFG to maintain the equilibrium of the linkage.
Determine the force P required to maintain the equilibrium of the linkage shown. All members are of the same length and the wheels at A and B roll freely on the horizontal rod.
A force P of magnitude 240 N is applied to end E of cable CDE, which passes under pulley D and is attached to the mechanism at C. Neglecting the weight of the mechanism and the radius of the pulley, determine the value of θ corresponding to equilibrium. The constant of the spring is k = 4 kN/m,
Two identical rods ABC and DBE are connected by a pin at B and by a spring CE. Knowing that the spring is 4 in. long when unstretched and that the constant of the spring is 8 lb/in., determine the distance x corresponding to equilibrium when a 24-lb load is applied at E as shown.
Solve Problem 10.108 assuming that the 24-lb load is applied at C instead of E.PROBLEM 10.108Two identical rods ABC and DBE are connected by a pin at B and by a spring CE. Knowing that the spring is 4 in. long when unstretched and that the constant of the spring is 8 lb/in., determine the distance
A homogeneous hemisphere of radius r is placed on an incline as shown. Assuming that friction is sufficient to prevent slipping between the hemisphere and the incline, determine the angle θ corresponding to equilibrium when β = 10°.
A homogeneous hemisphere of radius r is placed on an incline as shown. Assuming that friction is sufficient to prevent slipping between the hemisphere and the incline, determine (a) the largest angle β for which a position of equilibrium exists, (b) the angle θ corresponding to equilibrium
A uniform rod AB of length l and weight W is suspended from two cords AC and BC of equal length. Derive an expression for the magnitude of the couple M required to maintain equilibrium of the rod in the position shown.
For the linkage shown, determine the force Q required for equilibrium when l =18 in., M = 600 lb ∙ in., and θ = 70°.
A 4-kN force P is applied as shown to the piston of the engine system. Knowing that AB = 50 mm and BC = 200 mm, determine the couple M required to maintain the equilibrium of the system when (a) θ = 30°, (b) θ =150°.
A couple M of magnitude 100 N ∙ m is applied as shown to the crank of the engine system. Knowing that AB = 50 mm and BC = 200 mm, determine the force P required to maintain the equilibrium of the system when (a) θ = 60°, (b) θ =120°.
Rod AB is attached to a block at A that can slide freely in the vertical slot shown. Neglecting the effect of friction and the weights of the rods, determine the value of ï± corresponding to equilibrium.
Solve Problem 10.23 assuming that the 800-N force is replaced by a 24-N∙m clockwise couple applied at D.PROBLEM 10.23Rod AB is attached to a block at A that can slide freely in the vertical slot shown. Neglecting the effect of friction and the weights of the rods, determine the value of θ
Determine the couple M that must be applied to member ABC to maintain the equilibrium of the linkage.
Two 5-kg bars AB and BC are connected by a pin at B and by a spring DE. Knowing that the spring is 150 mm long when unstretched and that the constant of the spring is 1 kN/m, determine the value of x corresponding to equilibrium.
A vertical force P of magnitude 150 N is applied to end E of cable CDE, which passes over a small pulley D and is attached to the mechanism at C. The constant of the spring is k = 4 kN/m, and the spring is unstretched when θ = 0. Neglecting the weight of the mechanism and the radius of the
A load W of magnitude 72 lb is applied to the mechanism at C. Neglecting the weight of the mechanism, determine the value of θ corresponding to equilibrium. The constant of the spring is k = 20 lb/in., and the spring is unstretched when θ = 0.
Determine the couple M that must be applied to member ABC to maintain the equilibrium of the linkage.
A spring of constant 15 kN/m connects Points C and F of the linkage shown. Neglecting the weight of the spring and linkage, determine the force in the spring and the vertical motion of Point G when a vertical downward 120-N force is applied (a) at Point C, (b) at Points C and H.
A spring of constant 15 kN/m connects Points C and F of the linkage shown. Neglecting the weight of the spring and linkage, determine the force in the spring and the vertical motion of Point G when a vertical downward 120-N force is applied (a) at Point E, (b) at Points E and F.
Two uniform rods AB and CD, of the same length l, are attached to gears as shown. Knowing that rod AB weighs 3 lb and that rod CD weighs 2 lb, determine the positions of equilibrium of the system and state in each case whether the equilibrium is stable, unstable, or neutral.
Two uniform rods, each of mass m and length l, are attached to drums that are connected by a belt as shown. Assuming that no slipping occurs between the belt and the drums, determine the positions of equilibrium of the system and state in each case whether the equilibrium is stable, unstable, or
A load W of magnitude 100 lb is applied to the mechanism at C. Knowing that the spring is unstretched when θ = 15°, determine that value of θ corresponding to equilibrium and check that the equilibrium is stable.
A load W of magnitude 100 lb is applied to the mechanism at C. Knowing that the spring is unstretched when θ = 30°, determine that value of θ corresponding to equilibrium and check that the equilibrium is stable.
A slender rod AB, of weight W, is attached to two blocks A and B that can move freely in the guides shown. Knowing that the spring is unstretched when y = 0, determine the value of y corresponding to equilibrium when W = 80 N, l = 500 mm, and k = 600 N/m.
A slender rod AB, of weight W, is attached to two blocks A and B that can move freely in the guides shown. Knowing that both springs are unstretched when y = 0, determine the value of y corresponding to equilibrium when W = 80 N, l = 550 mm, and k = 600 N/m.
A slender rod AB, of weight W, is attached to two blocks A and B that can move freely in the guides shown. The constant of the spring is k, and the spring is unstretched when AB is horizontal. Neglecting the weight of the blocks, derive an equation in θ, W, l, and k that must be satisfied when
Knowing that the maximum friction force exerted by the bottle on the cork is 60 lb, determine (a) the force P that must be applied to the corkscrew to open the bottle, (b) the maximum force exerted by the base of the corkscrew on the top of the bottle.
A slender rod AB, of weight W, is attached to two blocks A and B that can move freely in the guides shown. Knowing that the spring is unstretched when AB is horizontal, determine three values of θ corresponding to equilibrium when W = 300 lb, l = 16 in., and k = 75 lb/in. State in each case
A spring AB of constant k is attached to two identical gears as shown. Knowing that the spring is undeformed when θ = 0, determine two values of the angle θ corresponding to equilibrium when P = 30 lb, a = 4 in., b = 3 in., r = 6 in., and k = 5 lb/in. State in each case whether the
A spring AB of constant k is attached to two identical gears as shown. Knowing that the spring is undeformed when θ = 0, and given that a = 60 mm, b = 45 mm, r = 90 mm, and k = 6 kN/m, determine (a) the range of values of P for which a position of equilibrium exists, (b) two values of θ
Cart B, which weighs 75 kN, rolls along a sloping track that forms an angle β with the horizontal. The spring constant is 5 kN/m, and the spring is unstretched when x = 0. Determine the distance x corresponding to equilibrium for the angle β indicated.Angle β = 30°.
Cart B, which weighs 75 kN, rolls along a sloping track that forms an angle β with the horizontal. The spring constant is 5 kN/m, and the spring is unstretched when x = 0. Determine the distance x corresponding to equilibrium for the angle β indicated.Angle β = 60°.
Collar A can slide freely on the semicircular rod shown. Knowing that the constant of the spring is k and that the unstretched length of the spring is equal to the radius r, determine the value of θ corresponding to equilibrium when W = 50 lb, r = 9 in., and k =15 lb/in.
Collar A can slide freely on the semicircular rod shown. Knowing that the constant of the spring is k and that the unstretched length of the spring is equal to the radius r, determine the value of θ corresponding to equilibrium when W = 50 lb, r = 9 in., and k = 15 lb/in.
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