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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 20-lb force is applied to the control rod AB as shown. Knowing that the length of the rod is 9 in. and that the moment of the force about B is 120 lb ∙ in. clockwise, determine the value of α.
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A 500-N force is applied to a bent plate as shown. Determine(a) An equivalent force-couple system at B,(b) An equivalent system formed by a vertical force at A and a force at B.
The tension in the cable attached to the end C of an adjustable boom ABC is 560 lb. Replace the force exerted by the cable at C with an equivalent force-couple system(a) At A,(b) At B.
The shearing forces exerted on the cross section of a steel channel can be represented by a 900-N vertical force and two 250-N horizontal forces as shown. Replace this force and couple with a single force F applied at Point C, and determine the distance x from C to line BD. (Point C is defined as
Three control rods attached to a lever ABC exert on it the forces shown.(a) Replace the three forces with an equivalent force-couple system at B.(b) Determine the single force that is equivalent to the force-couple system obtained in Part a, and specify its point of application on the lever.
Rod AB is held in place by the cord AC. Knowing that the tension in the cord is 1350 N and that c = 360 mm, determine the moment about B of the force exerted by the cord at point A by resolving that force into horizontal and vertical components applied(a) At point A,(b) At point C.
A 2.6-kip force is applied at Point D of the cast iron post shown. Replace that force with an equivalent force-couple system at the center A of the base section.
Replace the 150-N force with an equivalent force-couple system at A.
A 46-lb force F and a 2120-lbâ‹…in. couple M are applied to corner A of the block shown. Replace the given force-couple system with an equivalent force-couple system at corner H.
A 110-N force acting in a vertical plane parallel to the yz-plane is applied to the 220-mm-long horizontal handle AB of a socket wrench. Replace the force with an equivalent force-couple system at the origin O of the coordinate system.
An antenna is guyed by three cables as shown. Knowing that the tension in cable AB is 288 lb, replace the force exerted at A by cable AB with an equivalent force-couple system at the center O of the base of the antenna.
A gardener uses a 60-N wheelbarrow to transport a 250-N bag of fertilizer. What force must she exert on each handle?
Solve Problem 4.99, assuming that the small block C is moved and placed under edge DE at a point 0.15 m from corner E.PROBLEM 4.99An opening in a floor is covered by a 1×1.2-m sheet of plywood of mass 18 kg. The sheet is hinged at A and B and is maintained in a position slightly above the floor
Two steel pipes AB and BC, each having a mass per unit length of 8 kg/m, are welded together at B and supported by three wires. Knowing that a = 0.4 m, determine the tension in each wire.
For the pipe assembly of Problem 4.101, determine(a) The largest permissible value of a if the assembly is not to tip,(b) The corresponding tension in each wire.
The 24-lb square plate shown is supported by three vertical wires. Determine(a) The tension in each wire when a =10 in.,(b) The value of a for which the tension in each wire is 8 lb.
The table shown weighs 30 lb and has a diameter of 4 ft. It is supported by three legs equally spaced around the edge. A vertical load P of magnitude 100 lb is applied to the top of the table at D. Determine the maximum value of a if the table is not to tip over. Show, on a sketch, the area of the
A 10-ft boom is acted upon by the 840-lb force shown. Determine the tension in each cable and the reaction at the ball-and-socket joint at A.
The 6-m pole ABC is acted upon by a 455-N force as shown. The pole is held by a ball-and-socket joint at A and by two cables BD and BE. For a = 3 m, determine the tension in each cable and the reaction at A.
Solve Problem 4.106 for a = 1.5 m.PROBLEM 4.106The 6-m pole ABC is acted upon by a 455- N force as shown. The pole is held by a ball-and-socket joint at A and by two cables BD and BE. For a = 3 m, determine the tension in each cable and the reaction at A.
A 2.4-m boom is held by a ball-and-socket joint at C and by two cables AD and AE. Determine the tension in each cable and the reaction at C.
Solve Problem 4.108, assuming that the 3.6-kN load is applied at Point A.PROBLEM 4.108A 2.4-m boom is held by a ball-and socket joint at C and by two cables AD and AE. Determine the tension in each cable and the reaction at C.
For the beam of Prob. 4.10, determine the range of values of Q for which the loading is safe when P = 5 kN.
The 10-ft flagpole AC forms an angle of 30° with the z axis. It is held by a ball-and-socket joint at C and by two thin braces BD and BE. Knowing that the distance BC is 3 ft, determine the tension in each brace and the reaction at C.
A 48-in. boom is held by a ball-and-socket joint at C and by two cables BF and DAE; cable DAE passes around a frictionless pulley at A. For the loading shown, determine the tension in each cable and the reaction at C.
Solve Problem 4.111, assuming that the 320-lb load is applied at A.PROBLEM 4.111A 48-in. boom is held by a ball-and socket joint at C and by two cables BF and DAE; cable DAE passes around a frictionless pulley at A. For the loading shown, determine the tension in each cable and the reaction at C.
A 10-kg storm window measuring 900 × 1500 mm is held by hinges at A and B. In the position shown, it is held away from the side of the house by a 600-mm stick CD. Assuming that the hinge at A does not exert any axial thrust, determine the magnitude of the force exerted by the stick and the
The lid of a roof scuttle weighs 75 lb. It is hinged at corners A and B and maintained in the desired position by a rod CD pivoted at C; a pin at end D of the rod fits into one of several holes drilled in the edge of the lid. For the position shown, determine (a) the magnitude of the force exerted
A 100-kg uniform rectangular plate is supported in the position shown by hinges A and B and by cable DCE that passes over a frictionless hook at C. Assuming that the tension is the same in both parts of the cable, determine (a) the tension in the cable, (b) the reactions at A and B. Assume that the
Solve Problem 4.117, assuming that cable DCE is replaced by a cable attached to Point E and hook C.PROBLEM 4.117A 100-kg uniform rectangular plate is supported in the position shown by hinges A and B and by cable DCE that passes over a frictionless hook at C. Assuming that the tension is the same
Solve Prob. 4.113, assuming that the hinge at A has been removed and that the hinge at B can exert couples about axes parallel to the x and y axes.PROBLEM 4.113A 10-kg storm window measuring 900 × 1500 mm is held by hinges at A and B. In the position shown, it is held away from the side of the
For the beam of Sample Prob. 4.2, determine the range of values of P for which the beam will be safe, knowing that the maximum allowable value of each of the reactions is 25 kips and that the reaction at A must be directed upward.
Solve Prob. 4.115, assuming that the hinge at B has been removed and that the hinge at A can exert an axial thrust, as well as couples about axes parallel to the x and y axes.PROBLEM 4.115The horizontal platform ABCD weighs 60 lb and supports a 240-lb load at its center. The platform is normally
The assembly shown is used to control the tension T in a tape that passes around a frictionless spool at E. Collar C is welded to rods ABC and CDE. It can rotate about shaft FG but its motion along the shaft is prevented by a washer S. For the loading shown, determine (a) the tension T in the tape,
The assembly shown is welded to collar A that fits on the vertical pin shown. The pin can exert couples about the x and z axes but does not prevent motion about or along the y-axis. For the loading shown, determine the tension in each cable and the reaction at A.
The rigid L-shaped member ABC is supported by a ball-and-socket joint at A and by three cables. If a 1.8-kN load is applied at F, determine the tension in each cable.
Solve Problem 4.123, assuming that the 1.8- kN load is applied at C.PROBLEM 4.123The rigid L-shaped member ABC is supported by a ball-and socket joint at A and by three cables. If a 1.8- kN load is applied at F, determine the tension in each cable.
Three rods are welded together to form a "corner" that is supported by three eyebolts. Neglecting friction, determine the reactions at A, B, and C when P = 240 lb, a =12 in., b = 8 in., and c =10 in.
Solve Problem 4.127, assuming that the force P is removed and is replaced by a couple M = +(600 lb ∙ in.)j acting at B.PROBLEM 4.127Three rods are welded together to form a "corner" that is supported by three eyebolts. Neglecting friction, determine the reactions at A, B, and C when P = 240
The maximum allowable value of each of the reactions is 180 N. Neglecting the weight of the beam, determine the range of the distance d for which the beam is safe.
Frame ABCD is supported by a ball-and socket joint at A and by three cables. Knowing that the 350-N load is applied at D (a = 300 mm), determine the tension in each cable and the reaction at A.
The assembly shown consists of an 80- mm rod AF that is welded to a cross consisting of four 200-mm arms. The assembly is supported by a ball-and socket joint at F and by three short links, each of which forms an angle of 45° with the vertical. For the loading shown, determine (a) the tension in
The uniform 10-kg rod AB is supported by a ball-and-socket joint at A and by the cord CG that is attached to the midpoint G of the rod. Knowing that the rod leans against a frictionless vertical wall at B, determine(a) The tension in the cord,(b) The reactions at A and B.
The frame ACD is supported by ball-and-socket joints at A and D and by a cable that passes through a ring at B and is attached to hooks at G and H. Knowing that the frame supports at Point C a load of magnitude P = 268 N, determine the tension in the cable.
Solve Prob. 4.133, assuming that cable GBH is replaced by a cable GB attached at G and B.PROBLEM 4.133The frame ACD is supported by ball and- socket joints at A and D and by a cable that passes through a ring at B and is attached to hooks at G and H. Knowing that the frame supports at Point C a
The bent rod ABDE is supported by ball-and-socket joints at A and E and by the cable DF. If a 60-lb load is applied at C as shown, determine the tension in the cable.
Solve Problem 4.135, assuming that cable DF is replaced by a cable connecting B and F.PROBLEM 4.135The bent rod ABDE is supported by ball-and-socket joints at A and E and by the cable DF. If a 60-lb load is applied at C as shown, determine the tension in the cable.
Two rectangular plates are welded together to form the assembly shown. The assembly is supported by ball-and socket joints at B and D and by a ball on a horizontal surface at C. For the loading shown, determine the reaction at C.
The pipe ACDE is supported by ball-and-socket joints at A and E and by the wire DF. Determine the tension in the wire when a 640-N load is applied at B as shown.
Solve Problem 4.138, assuming that wire DF is replaced by a wire connecting C and F.PROBLEM 4.138The pipe ACDE is supported by ball-and socket joints at A and E and by the wire DF. Determine the tension in the wire when a 640-N load is applied at B as shown.
For the beam and loading shown, determine the range of the distance a for which the reaction at B does not exceed 100 lb downward or 200 lb upward.
Two 2 × 4-ft plywood panels, each of weight 12 lb, are nailed together as shown. The panels are supported by ball-and socket joints at A and F and by the wire BH. Determine (a) the location of H in the xy plane if the tension in the wire is to be minimum, (b) the corresponding minimum tension.
Solve Problem 4.140, subject to the restriction that H must lie on the y-axis.PROBLEM 4.140Two 2 × 4-ft plywood panels, each of weight 12 lb, are nailed together as shown. The panels are supported by ball-and-socket joints at A and F and by the wire BH. Determine (a) the location of H in the xy
A 3200-lb forklift truck is used to lift a 1700-lb crate. Determine the reaction at each of the two (a) front wheels A, (b) rear wheels B.
The lever BCD is hinged at C and attached to a control rod at B. If P = 100 lb, determine (a) the tension in rod AB, (b) the reaction at C.
Determine the reactions at A and B when (a) h = 0, (b) h = 200 mm.
Neglecting friction and the radius of the pulley, determine (a) the tension in cable ADB, (b) the reaction at C.
Bar AD is attached at A and C to collars that can move freely on the rods shown. If the cord BE is vertical (α = 0), determine the tension in the cord and the reactions at A and C.
A slender rod AB, of weight W, is attached to blocks A and B that move freely in the guides shown. The constant of the spring is k, and the spring is unstretched when θ = 0. (a) Neglecting the weight of the blocks, derive an equation in W, k, l, and θ that must be satisfied when the rod is in
Determine the reactions at A and B when a = 150 mm.
For the frame and loading shown, determine the reactions at A and C.
Two links AB and DE are connected by a bell crank as shown. Knowing that the tension in link AB is 720 N, determine(a) The tension in link DE,(b) The reaction at C.
A 200-mm lever and a 240-mm-diameter pulley are welded to the axle BE that is supported by bearings at C and D. If a 720-N vertical load is applied at A when the lever is horizontal, determine(a) The tension in the cord,(b) The reactions at C and D. Assume that the bearing at D does not exert any
The 45-lb square plate shown is supported by three vertical wires. Determine the tension in each wire.
The rectangular plate shown weighs 75 lb and is held in the position shown by hinges at A and B and by cable EF. Assuming that the hinge at B does not exert any axial thrust, determine (a) the tension in the cable, (b) the reactions at A and B.
A force P is applied to a bent rod ABC, which may be supported in four different ways as shown. In each case, if possible, determine the reactions at the supports.
Two links AB and DE are connected by a bell crank as shown. Determine the maximum force that may be safely exerted by link AB on the bell crank if the maximum allowable value for the reaction at C is 1600 N.
The required tension in cable AB is 200 lb. Determine(a) The vertical force P that must be applied to the pedal,(b) The corresponding reaction at C.
Determine the maximum tension that can be developed in cable AB if the maximum allowable value of the reaction at C is 250 lb.
The bracket BCD is hinged at C and attached to a control cable at B. For the loading shown, determine(a) The tension in the cable,(b) The reaction at C.
The gardener of Problem 4.1 wishes to transport a second 250-N bag of fertilizer at the same time as the first one. Determine the maximum allowable horizontal distance from the axle A of the wheelbarrow to the center of gravity of the second bag if she can hold only 75 N with each arm.PROBLEM 4.1 A
Solve Problem 4.19, assuming that a = 0.32 m.PROBLEM 4.19 The bracket BCD is hinged at C and attached to a control cable at B. For the loading shown, determine (a) the tension in the cable, (b) the reaction at C.
The 40-ft boom AB weighs 2 kips; the distance from the axle A to the center of gravity G of the boom is 20 ft. For the position shown, determine (a) the tension T in the cable, (b) the reaction at A.
A lever AB is hinged at C and attached to a control cable at A. If the lever is subjected to a 500-N horizontal force at B, determine(a) The tension in the cable,(b) The reaction at C.
For each of the plates and loadings shown, determine the reactions at A and B.a.b.
For each of the plates and loadings shown, determine the reactions at A and B.(a)(b)
A rod AB hinged at A and attached at B to cable BD supports the loads shown. Knowing that d = 200 mm, determine(a) The tension in cable BD,(b) The reaction at A.
A rod AB, hinged at A and attached at B to cable BD, supports the loads shown. Knowing that d = 150 mm, determine(a) The tension in cable BD,(b) The reaction at A.
Determine the reactions at A and B when(a) α = 0,(b) α = 90°,(c) α = 30°.
Determine the reactions at A and C when(a) α = 0,(b) α = 30°.
Rod ABC is bent in the shape of an arc of circle of radius R. Knowing the θ = 30°, determine the reaction(a) At B,(b) At C.
Rod ABC is bent in the shape of an arc of circle of radius R. Knowing that θ = 60°, determine the reaction(a) At B,(b) At C.
Neglecting friction, determine the tension in cable ABD and the reaction at C when θ = 45°.
A force P of magnitude 90 lb is applied to member ACDE, which is supported by a frictionless pin at D and by the cable ABE. Since the cable passes over a small pulley at B, the tension may be assumed to be the same in portions AB and BE of the cable. For the case when a = 3 in., determine(a) The
Solve Problem 4.33 for a = 6 in.PROBLEM 4.33 A force P of magnitude 90 lb is applied to member ACDE, which is supported by a frictionless pin at D and by the cable ABE. Since the cable passes over a small pulley at B, the tension may be assumed to be the same in portions AB and BE of the cable. For
Bar AC supports two 400-N loads as shown. Rollers at A and C rest against frictionless surfaces and a cable BD is attached at B. Determine(a) The tension in cable BD,(b) The reaction at A,(c) The reaction at C.
A light bar AD is suspended from a cable BE and supports a 20-kg block at C. The ends A and D of the bar are in contact with frictionless vertical walls. Determine the tension in cable BE and the reactions at A and D.
The T-shaped bracket shown is supported by a small wheel at E and pegs at C and D. Neglecting the effect of friction, determine the reactions at C, D, and E when θ = 30°.
The T-shaped bracket shown is supported by a small wheel at E and pegs at C and D. Neglecting the effect of friction, determine(a) The smallest value of θ for which the equilibrium of the bracket is maintained,(b) The corresponding reactions at C, D, and E.
A movable bracket is held at rest by a cable attached at C and by frictionless rollers at A and B. For the loading shown, determine(a) The tension in the cable,(b) The reactions at A and B.
A light bar AB supports a 15-kg block at its midpoint C. Rollers at A and B rest against frictionless surfaces, and a horizontal cable AD is attached at A. Determine(a) The tension in cable AD,(b) The reactions at A and B.
Two slots have been cut in plate DEF, and the plate has been placed so that the slots fit two fixed, frictionless pins A and B. Knowing that P = 15 lb, determine(a) The force each pin exerts on the plate,(b) The reaction at F.
For the plate of Problem 4.41 the reaction at F must be directed downward, and its maximum allowable value is 20 lb. Neglecting friction at the pins, determine the required range of values of P.PROBLEM 4.41 Two slots have been cut in plate DEF, and the plate has been placed so that the slots fit
The rig shown consists of a 1200-lb horizontal member ABC and a vertical member DBE welded together at B. The rig is being used to raise a 3600-lb crate at a distance x = 12 ft from the vertical member DBE. If the tension in the cable is 4 kips, determine the reaction at E, assuming that the cable
For the rig and crate of Prob. 4.43, and assuming that cable is anchored at F as shown, determine(a) The required tension in cable ADCF if the maximum value of the couple at E as x varies from 1.5 to 17.5 ft is to be as small as possible,(b) The corresponding maximum value of the couple.
A 175-kg utility pole is used to support at C the end of an electric wire. The tension in the wire is 600 N, and the wire forms an angle of 15° with the horizontal at C. Determine the largest and smallest allowable tensions in the guy cable BD if the magnitude of the couple at A may not exceed
Knowing that the tension in wire BD is 1300 N, determine the reaction at the fixed support C of the frame shown.
Determine the range of allowable values of the tension in wire BD if the magnitude of the couple at the fixed support C is not to exceed 100 N · m.
Beam AD carries the two 40-lb loads shown. The beam is held by a fixed support at D and by the cable BE that is attached to the counterweight W. Determine the reaction at D when(a) W = 100 lb,(b) W = 90 lb.
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