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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
Determine by direct integration the centroid of the area shown.
Locate the centroid of the plane area shown.
Determine the centroid of the area shown in terms of a.
Determine the centroid of the area shown when a = 4 in.
Determine the volume and the surface area of the solid obtained by rotating the area of Prob. 5.1 about(a) The x axis,(b) The line x = 72 mm.
Determine the volume and the surface area of the solid obtained by rotating the area of Problem 5.2 about(a) The x-axis,(b) The y-axis.
Determine the volume and the surface area of the solid obtained by rotating the area of Problem 5.6 about(a) The line x = -60 mm,(b) The line y = 120 mm.
Determine the volume and the surface area of the chain link shown, which is made from a 6-mm-diameter bar, if R = 10 mm and L = 30 mm.
Determine the volume of the solid generated by rotating the parabolic area shown about(a) The x-axis,(b) The axis AA'.
Verify that the expressions for the volumes of the first four shapes in Fig. 5.21 are correct?
Knowing that two equal caps have been removed from a 10-in.-diameter wooden sphere, determine the total surface area of the remaining portion.
Three different drive belt profiles are to be studied. If at any given time each belt makes contact with one-half of the circumference of its pulley, determine the contact area between the belt and the pulley for each design.(a)(b)(c)
Locate the centroid of the plane area shown.
Determine the capacity, in liters, of the punch bowl shown if R = 250 mm.
Determine the volume and weight of the solid brass knob shown, knowing that the specific weight of brass is 0.306 lb/in3.
Determine the total surface area of the solid brass knob shown.
The shade for a wall-mounted light is formed from a thin sheet of translucent plastic. Determine the surface area of the outside of the shade, knowing that it has the parabolic cross section shown.
For the beam and loading shown, determine(a) The magnitude and location of the resultant of the distributed load,(b) The reactions at the beam supports.
For the beam and loading shown, determine(a) The magnitude and location of the resultant of the distributed load,(b) The reactions at the beam supports.
Determine the reactions at the beam supports for the given loading.
Determine the reactions at the beam supports for the given loading.
Locate the centroid of the plane area shown.
Determine the reactions at the beam supports for the given loading.
Determine the reactions at the beam supports for the given loading.
Determine the reactions at the beam supports for the given loading.
Determine(a) The distance a so that the vertical reactions at supports A and B are equal,(b) The corresponding reactions at the supports.
Determine(a) The distance a so that the reaction at support B is minimum,(b) The corresponding reactions at the supports.
Determine the reactions at the beam supports for the given loading when wO = 400 lb/ft.
Determine(a) The distributed load wO at the end A of the beam ABC for which the reaction at C is zero,(b) The corresponding reaction at B.
The beam AB supports two concentrated loads and rests on soil that exerts a linearly distributed upward load as shown. Determine the values of (A and (B corresponding to equilibrium.
For the beam and loading of Problem 5.78, determine(a) The distance a for which (A = 20 kN/m,(b) The corresponding value of (B.PROBLEM 5.78 The beam AB supports two concentrated loads and rests on soil that exerts a linearly distributed upward load as shown. Determine the values of (A and (B
Locate the centroid of the plane area shown.
The cross section of a concrete dam is as shown. For a 1-ft-wide dam section determine(a) The resultant of the reaction forces exerted by the ground on the base AB of the dam,(b) The point of application of the resultant of part a,(c) The resultant of the pressure forces exerted by the water on the
The cross section of a concrete dam is as shown. For a 1-m-wide dam section, determine(a) The resultant of the reaction forces exerted by the ground on the base AB of the dam,(b) The point of application of the resultant of part a,(c) The resultant of the pressure forces exerted by the water on the
The dam for a lake is designed to withstand the additional force caused by silt that has settled on the lake bottom. Assuming that silt is equivalent to a liquid of density ps = 1.76 Ã 103 kg/m3 and considering a 1-m-wide section of dam, determine the percentage increase in the force
The base of a dam for a lake is designed to resist up to 120 percent of the horizontal force of the water. After construction, it is found that silt (that is equivalent to a liquid of density Ps = 1.76 Ã 103 kg / m3) is settling on the lake bottom at the rate of 12 mm/year. Considering
An automatic valve consists of a 9 Ã 9-in. square plate that is pivoted about a horizontal axis through A located at a distance h = 3.6 in. above the lower edge. Determine the depth of water d for which the valve will open.
The 3 Ã 4-m side AB of a tank is hinged at its bottom A and is held in place by a thin rod BC. The maximum tensile force the rod can withstand without breaking is 200 kN, and the design specifications require the force in the rod not to exceed 20 percent of this value. If the tank is
The 3 × 4-m side of an open tank is hinged at its bottom A and is held in place by a thin rod BC. The tank is to be filled with glycerine, whose density is 1263 kg/m3. Determine the force T in the rod and the reactions at the hinge after the tank is filled to a depth of 2.9 m.
A 0.5 × 0.8-m gate AB is located at the bottom of a tank filled with water. The gate is hinged along its top edge A and rests on a frictionless stop at B. Determine the reactions at A and B when cable BCD is slack.
A 0.5 × 0.8-m gate AB is located at the bottom of a tank filled with water. The gate is hinged along its top edge A and rests on a frictionless stop at B. Determine the minimum tension required in cable BCD to open the gate.
Locate the centroid of the plane area shown.
Solve Problem 5.90 if the gate weighs 1000 lb.PROBLEM 5.90 A 4 00d7x 2-ft gate is hinged at A and is held in position by rod CD. End D rests against a spring whose constant is 828 lb/ft. The spring is un deformed when the gate is vertical. Assuming that the force exerted by rod CD on the gate
A prismatically shaped gate placed at the end of a freshwater channel is supported by a pin and bracket at A and rests on a frictionless support at B. The pin is located at a distance h = 0.10 m below the center of gravity C of the gate. Determine the depth of water d for which the gate will open.
A prismatically shaped gate placed at the end of a freshwater channel is supported by a pin and bracket at A and rests on a frictionless support at B. Determine the distance h if the gate is to open when d = 0.75 m.
Determine the location of the centroid of the composite body shown when(a) h = 2b,(b) h = 2.5b.
Locate the centroid of the frustum of a right circular cone when r1 = 40 mm, r2 = 50 mm, and h = 60 mm.
Using the method of joints, determine the force in each member of the truss shown. State whether each member is in tension or compression.
Knowing that P = 60 lb and Q = 90 lb, determine the components of all forces acting on member BCDE of the assembly shown.
The axis of the three-hinge arch ABC is a parabola with the vertex at B. Knowing that P = 112 kN and Q = 140 kN, determine(a) The components of the reaction at A,(b) The components of the force exerted at B on segment AB.
The axis of the three-hinge arch ABC is a parabola with the vertex at B. Knowing that P = 140 kN and Q = 112 kN, determine(a) The components of the reaction at A,(b) The components of the force exerted at B on segment AB.
Neglecting the effect of friction at the horizontal and vertical surfaces, determine the forces exerted at B and C on member BCE.
Neglecting the effect of friction at the horizontal and vertical surfaces, determine the forces exerted at B and C on member BCE.
Four beams, each of length 3a, are held together by single nails at A, B, C, and D. Each beam is attached to a support located at a distance a from an end of the beam as shown. Assuming that only vertical forces are exerted at the connections, determine the vertical reactions at E, F, G, and H.
A 100-lb force directed vertically downward is applied to the toggle vise at C. Knowing that link BD is 6 in. long and that a = 4 in., determine the horizontal force exerted on block E.
A 100-lb force directed vertically downward is applied to the toggle vise at C. Knowing that link BD is 6 in. long and that a = 8 in., determine the horizontal force exerted on block E.
The control rod CE passes through a horizontal hole in the body of the toggle system shown. Knowing that link BD is 250 mm long, determine the force Q required to hold the system in equilibrium when β = 20 °.
Solve Problem 6.125 when (a) β = 0, (b) β = 6°.PROBLEM 6.125 The control rod CE passes through a horizontal hole in the body of the toggle system shown. Knowing that link BD is 250 mm long, determine the force Q required to hold the system in equilibrium when
The press shown is used to emboss a small seal at E. Knowing that the vertical component of the force exerted on the seal must be 900 N, determine (a) the required vertical force P, (b) the corresponding reaction at A.
The pin at B is attached to member ABC and can slide freely along the slot cut in the fixed plate. Neglecting the effect of friction, determine the couple M required to hold the system in equilibrium when θ = 30°.
The pin at B is attached to member ABC and can slide freely along the slot cut in the fixed plate. Neglecting the effect of friction, determine the couple M required to hold the system in equilibrium when θ = 60°.
Arm ABC is connected by pins to a collar at B and to crank CD at C. Neglecting the effect of friction, determine the couple M required to hold the system in equilibrium when θ = 0.
Arm ABC is connected by pins to a collar at B and to crank CD at C. Neglecting the effect of friction, determine the couple M required to hold the system in equilibrium when θ = 90°.
The Whitworth mechanism shown is used to produce a quick-return motion of Point D. The block at B is pinned to the crank AB and is free to slide in a slot cut in member CD. Determine the couple M that must be applied to the crank AB to hold the mechanism in equilibrium when(a) α = 0,(b) α =
Solve Problem 6.133 when (a) α = 60°, (b) α = 90°.PROBLEM 6.133 The Whitworth mechanism shown is used to produce a quick-return motion of Point D. The block at B is pinned to the crank AB and is free to slide in a slot cut in member CD. Determine the couple M
Two rods are connected by a frictionless collar B. Knowing that the magnitude of the couple MA is 500 lb · in., determine (a) the couple MC required for equilibrium, (b) the corresponding components of the reaction at C.
Two rods are connected by a frictionless collar B. Knowing that the magnitude of the couple MA is 500 lb · in., determine (a) the couple MC required for equilibrium, (b) the corresponding components of the reaction at C.
Rod CD is attached to the collar D and passes through a collar welded to end B of lever AB. Neglecting the effect of friction, determine the couple M required to hold the system in equilibrium when θ = 30°.
Rod CD is attached to the collar D and passes through a collar welded to end B of lever AB. Neglecting the effect of friction, determine the couple M required to hold the system in equilibrium when θ = 30°.
Two hydraulic cylinders control the position of the robotic arm ABC. Knowing that in the position shown the cylinders are parallel, determine the force exerted by each cylinder when P = 160 N and Q = 80 N.
Two hydraulic cylinders control the position of the robotic arm ABC. In the position shown, the cylinders are parallel and both are in tension. Knowing the FAE = 600 N and FDG = 50 N, determine the forces P and Q applied at C to arm ABC.
A 39-ft length of railroad rail of weight 44 lb/ft is lifted by the tongs shown. Determine the forces exerted at D and F on tong BDF.
The pliers shown are used to grip a 0.3-in.-diameter rod. Knowing that two 60-lb forces are applied to the handles, determine(a) The magnitude of the forces exerted on the rod,(b) The force exerted by the pin at A on portion AB of the pliers.
Determine the magnitude of the gripping forces exerted along line AA on the nut when two 50-lb forces are applied to the handles as shown. Assume that pins A and D slide freely in slots cut in the jaws.
In using the bolt cutter shown, a worker applies two 300-N forces to the handles. Determine the magnitude of the forces exerted by the cutter on the bolt.
Determine the magnitude of the gripping forces produced when two 300-N forces are applied as shown.
Determine the force P that must be applied to the toggle CDE to maintain bracket ABC in the position shown.
Determine the force P that must be applied to the toggle CDE to maintain bracket ABC in the position shown.
Since the brace shown must remain in position even when the magnitude of P is very small, a single safety spring is attached at D and E. The spring DE has a constant of 50 lb/in. and an unstretched length of 7 in. Knowing that l = 10 in. and that the magnitude of P is 800 lb, determine the force Q
The specialized plumbing wrench shown is used in confined areas (e.g., under a basin or sink). It consists essentially of a jaw BC pinned at B to a long rod. Knowing that the forces exerted on the nut are equivalent to a clockwise (when viewed from above) couple of magnitude 135 lb · in.,
The motion of the backhoe bucket shown is controlled by the hydraulic cylinders AD, CG, and EF. As a result of an attempt to dislodge a portion of a slab, a 2-kip force P is exerted on the bucket teeth at J. Knowing that θ = 45°, determine the force exerted by each cylinder.
Solve Problem 6.157 assuming that the 2-kip force P acts horizontally to the right (θ = 0).PROBLEM 6.157 The motion of the backhoe bucket shown is controlled by the hydraulic cylinders AD, CG, and EF. As a result of an attempt to dislodge a portion of a slab, a 2-kip force P is exerted
The gears D and G are rigidly attached to shafts that are held by frictionless bearings. If rD = 90 mm and rG = 30 mm, determine(a) The couple M0 that must be applied for equilibrium,(b) The reactions at A and B.
In the planetary gear system shown, the radius of the central gear A is a = 18 mm, the radius of each planetary gear is b, and the radius of the outer gear E is (a + 2b). A clockwise couple of magnitude MA = 10 N · m is applied to the central gear A and a counterclockwise couple of magnitude MS
Two shafts AC and CF, which lie in the vertical xy plane, are connected by a universal joint at C. The bearings at B and D do not exert any axial force. A couple of magnitude 500 lb · in. (clockwise when viewed from the positive x-axis) is applied to shaft CF at F. At a time when the arm of the
Solve Problem 6.161 assuming that the arm of the crosspiece attached to shaft CF is vertical.PROBLEM 6.161 Two shafts AC and CF, which lie in the vertical xy plane, are connected by a universal joint at C. The bearings at B and D do not exert any axial force. A couple of magnitude 500 lb · in.
The large mechanical tongs shown are used to grab and lift a thick 7500-kg steel slab HJ. Knowing that slipping does not occur between the tong grips and the slab at H and J, determine the components of all forces acting on member EFH.
Determine the components of all forces acting on member ABD of the frame shown.
Determine the force in each member of the Pratt roof truss shown. State whether each member is in tension or compression.
Knowing that the pulley has a radius of 50 mm, determine the components of the reactions at B and E.
For the frame and loading shown, determine the components of the forces acting on member CFE at C and F.
Water pressure in the supply system exerts a downward force of 135 N on the vertical plug at A. Determine the tension in the fusible link DE and the force exerted on member BCE at B.
A couple M of magnitude 1.5 kN · m is applied to the crank of the engine system shown. For each of the two positions shown, determine the force P required to hold the system in equilibrium.(a)(b)
The compound-lever pruning shears shown can be adjusted by placing pin A at various ratchet positions on blade ACE. Knowing that 300-lb vertical forces are required to complete the pruning of a small branch, determine the magnitude P of the forces that must be applied to the handles when the shears
The truss shown is one of several supporting an advertising panel. Determine the force in each member of the truss for a wind load equivalent to the two forces shown. State whether each member is in tension or compression.
Determine the force in each member of the Pratt bridge truss shown. State whether each member is in tension or compression.
Using the method of joints, determine the force in each member of the truss shown. State whether each member is in tension or compression.
Solve Problem 6.19 assuming that the load applied at G has been removed.PROBLEM 6.19 Determine the force in each member of the Pratt bridge truss shown. State whether each member is in tension or compression.
Determine the force in each of the members located to the left of FG for the scissors roof truss shown. State whether each member is in tension or compression.
Determine the force in each member of the truss shown. State whether each member is in tension or compression.
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