4.125 The rigid L-shaped member ABF is supported by a ball-and-socketjoint at A and by

A gardener uses a 60-N wheelbarrow to transport a 250-N bag of fertilizer. What force must she exert on each handle?

The gardener of Prob. 4.1 wishes to transport a second 250-N bag of fertilizer at the same time as the first one. Determine the maxi- mum allowable horizontal distance from the axle A of the wheelbar- row to the center of gravity of the second bag if she can hold only 75 N with each arm.

A 2100-lb tractor is used to lift 900 lb of gravel. Determine the reaction at each of the two (a) rear wheels A, (b) front wheels B.

For the beam and loading shown, determine (a) the reaction at A, (b) the tension in cable BC.

A load of lumber of weight W 5 25 kN is being raised by a mobile crane. The weight of boom ABC and the combined weight of the truck and driver are as shown. Determine the reaction at each of the two (a) front wheels H, (b) rear wheels K.

A load of lumber of weight W 5 25 kN is being raised by a mobile crane. Knowing that the tension is 25 kN in all portions of cable AEF and that the weight of boom ABC is 3 kN, determine (a) the tension in rod CD, (b) the reaction at pin B.

A T-shaped bracket supports the four loads shown. Determine the reactions at A and B (a) if a 5 10 in., (b) if a 5 7 in.

For the bracket and loading of Prob. 4.7, determine the smallest distance a if the bracket is not to move.

Three loads are applied as shown to a light beam supported by cables attached at B and D. Neglecting the weight of the beam, determine the range of values of Q for which neither cable becomes slack when P 5 0.

For the beam of Prob. 4.10, determine the range of values of Q for which the loading is safe when P 5 5 kN.

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 allow- able value of each of the reactions is 25 kips and that the reaction at A must be directed upward.

The maximum allowable value of each of the reactions is 180 N. Neglecting the weight of the beam, determine the range of the dis- tance d for which the beam is safe.

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 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.

Two links AB and DE are connected by a bell crank as shown. Determine the maximum force that can 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 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.

For each of the plates and loadings shown, determine the reactions at A and B.

A rod AB, hinged at A and attached at B to cable BD, supports the loads shown. Knowing that d 5 200 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 5 150 mm, determine (a) the tension in cable BD, (b) the reaction at A.

Determine the reactions at A and B when (a) 5 0, (b) 5 90, (c) 5 30.

Determine the reactions at A and C when (a) 5 0, (b) 5 30.

Rod ABC is bent in the shape of an arc of circle of radius R. Know- ing that 5 30, determine the reaction (a) at B, (b) at C.

Neglecting friction, determine the tension in cable ABD and the reac- tion at C when 5 60.

Neglecting friction, determine the tension in cable ABD and the reac- tion at C when 5 45.

A force P of magnitude 90 lb is applied to member ACDE that 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 5 3 in., determine (a) the tension in the cable, (b) the reac- tion at D.

Solve Prob. 4.33 for a 5 6 in.

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. Deter- mine (a) the tension in cable BD, (b) the reaction at A, (c) the reac- tion 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 friction- less vertical walls. Determine the tension in cable BE and the reac- tions 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 5 30.

4.38 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 for which the equilibrium of the bracket is main- tained, (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.

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 5 15 lb, determine (a) the force each pin exerts on the plate, (b) the reaction at F.

For the plate of Prob. 4.41, the reaction at F must be directed down- ward, and its maximum value is 20 lb. Neglecting friction at the pins, determine the required range of values of P.

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 5 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 is (a) anchored at F as shown in the figure, (b) attached to the vertical member at a point located 1 ft above E.

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 maxi- mum 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 cou- ple at A may not exceed 500 N?m.

Knowing that the tension in wire BD is 1300 N, determine the reac- tion 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 5 100 lb, (b) W 5 90 lb.

For the beam and loading shown, determine the range of values of W for which the magnitude of the couple at D does not exceed 40 lb?ft.

A uniform rod AB with a length of l and weight of W is suspended from two cords AC and BC of equal length. Determine the angle corresponding to the equilibrium position when a couple M is applied to the rod.

Rod AD is acted upon by a vertical force P at end A and by two equal and opposite horizontal forces of magnitude Q at points B and C. Neglecting the weight of the rod, express the angle cor- responding to the equilibrium position in terms of P and Q.

A slender rod AB with a weight of W is attached to blocks A and B that move freely in the guides shown. The blocks are connected by an elastic cord that passes over a pulley at C. (a) Express the tension in the cord in terms of W and . (b) Determine the value of for which the tension in the cord is equal to 3W.

A vertical load P is applied at end B of rod BC. (a) Neglecting the weight of the rod, express the angle corresponding to the equilibrium position in terms of P, l, and the counterweight W. (b) Determine the value of corresponding to equilibrium if P 5 2W.

A vertical load P is applied at end B of rod BC. (a) Neglecting the weight of the rod, express the angle corresponding to the equilibrium position in terms of P, l, and the counterweight W. (b) Determine the value of corresponding to equilibrium if P 5 2W.

A collar B with a weight of W can move freely along the vertical rod shown. The constant of the spring is k, and the spring is unstretched when 5 0. (a) Derive an equation in , W, k, and l that must be satisfied when the collar is in equilibrium. (b) Knowing that W 5 300 N, l 5 500 mm, and k 5 800 N/m, determine the value of corresponding to equilibrium.

vertical load P is applied at end B of rod BC. The constant of the spring is k, and the spring is unstretched when 5 60. (a) Neglect- ing the weight of the rod, express the angle corresponding to the equilibrium position in terms of P, k, and l. (b) Determine the value of corresponding to equilibrium if P 5 1 4 kl.

A vertical load P is applied at end B of rod BC. The constant of the spring is k, and the spring is unstretched when 5 60. (a) Neglect- ing the weight of the rod, express the angle corresponding to the equilibrium position in terms of P, k, and l. (b) Determine the value of corresponding to equilibrium if P 5 1 4 kl.

Eight identical 500 3 750-mm rectangular plates, each of mass m 5 40 kg, are held in a vertical plane as shown. All connections consist of frictionless pins, rollers, or short links. In each case, deter- mine whether (a) the plate is completely, partially, or improperly constrained, (b) the reactions are statically determinate or indetermi- nate, (c) the equilibrium of the plate is maintained in the position shown. Also, wherever possible, compute the reactions.

A 500-lb cylindrical tank, 8 ft in diameter, is to be raised over a 2-ft obstruction. A cable is wrapped around the tank and pulled horizon- tally as shown. Knowing that the corner of the obstruction at A is rough, find the required tension in the cable and the reaction at A.

Determine the reactions at A and B when a 5 180 mm.

For the bracket and loading shown, determine the range of values of the distance a for which the magnitude of the reaction at B does not exceed 600 N.

The spanner shown is used to rotate a shaft. A pin fits in a hole at A, while a flat, frictionless surface rests against the shaft at B. If a 60-lb force P is exerted on the spanner at D, find the reactions at A and B.

Determine the reactions at B and C when a 5 30 mm. 60 mm 40 mm 100 mm

A 12-ft wooden beam weighing 80 lb is supported by a pin and bracket at A and by cable BC. Find the reaction at A and the tension in the cable.

Determine the reactions at B and D when b 5 60 mm.

For the frame and loading shown, determine the reactions at C and D.

A 50-kg crate is attached to the trolley-beam system shown. Know- ing that a 5 1.5 m, determine (a) the tension in cable CD, (b) the reaction at B.

For the boom and loading shown, determine (a) the tension in cord BD, (b) the reaction at C.

A 40-lb roller of 8-in. diameter, which is to be used on a tile floor, is resting directly on the subflooring as shown. Knowing that the thickness of each tile is 0.3 in., determine the force P required to move the roller onto the tiles if the roller is (a) pushed to the left, (b) pulled to the right.

A T-shaped bracket supports a 300-N load as shown. Determine the reactions at A and C when 5 45.

A T-shaped bracket supports a 300-N load as shown. Determine the reactions at A and C when 5 60.

Rod AB is supported by a pin and bracket at A and rests against a frictionless peg at C. Determine the reactions at A and C when a 170-N vertical force is applied at B.

Solve Prob. 4.75, assuming that the 170-N force applied at B is horizontal and directed to the left.

Member ABC is supported by a pin and bracket at B and by an inextensible cord attached at A and C and passing over a frictionless pulley at D. The tension may be assumed to be the same in portions AD and CD of the cord. For the loading shown and neglecting the size of the pulley, determine the tension in the cord and the reaction at B.

Using the method of Sec. 4.2B, solve Prob. 4.22.

Knowing that 5 30, determine the reaction (a) at B, (b) at C.

Determine the reactions at A and B when 5 50.

Determine the reactions at A and B when 5 80.

Rod AB is bent into the shape of an arc of circle and is lodged between two pegs D and E. It supports a load P at end B. Neglecting friction and the weight of the rod, determine the distance c corre- sponding to equilibrium when a 5 20 mm and R 5 100 mm.

A slender rod of length L is attached to collars that can slide freely along the guides shown. Knowing that the rod is in equilibrium, derive an expression for angle in terms of angle .

An 8-kg slender rod of length L is attached to collars that can slide freely along the guides shown. Knowing that the rod is in equilibrium and that 5 30, determine (a) the angle that the rod forms with the vertical, (b) the reactions at A and B.

A uniform rod AB of length 2R rests inside a hemispherical bowl of radius R as shown. Neglecting friction, determine the angle cor- responding to equilibrium.

A slender rod BC with a length of L and weight W is held by two cables as shown. Knowing that cable AB is horizontal and that the rod forms an angle of 40 with the horizontal, determine (a) the angle that cable CD forms with the horizontal, (b) the tension in each cable.

A thin ring with a mass of 2 kg and radius r 5 140 mm is held against a frictionless wall by a 125-mm string AB. Determine (a) the distance d, (b) the tension in the string, (c) the reaction at C.

A slender rod with a length of L and weight W is attached to a collar at A and is fitted with a small wheel at B. Knowing that the wheel rolls freely along a cylindrical surface of radius R, and neglecting friction, derive an equation in , L, and R that must be satisfied when the rod is in equilibrium.

Two transmission belts pass over a double-sheaved pulley that is attached to an axle supported by bearings at A and D. The radius of the inner sheave is 125 mm and the radius of the outer sheave is 250 mm. Know- ing that when the system is at rest, the tension is 90 N in both portions of belt B and 150 N in both portions of belt C, determine the reactions at A and D. Assume that the bearing at D does not exert any axial thrust.

Solve Prob. 4.91, assuming that the pulley rotates at a constant rate and that TB 5 104 N, T B 95 84 N, and TC 5 175 N.

A small winch is used to raise a 120-lb load. Find (a) the magnitude of the vertical force P that should be applied at C to maintain equi- librium in the position shown, (b) the reactions at A and B, assuming that the bearing at B does not exert any axial thrust.

A 4 3 8-ft sheet of plywood weighing 34 lb has been temporarily placed among three pipe supports. The lower edge of the sheet rests on small collars at A and B and its upper edge leans against pipe C. Neglecting friction at all surfaces, determine the reactions at A, B, and C.

A 250 3 400-mm plate of mass 12 kg and a 300-mm-diameter pulley are welded to axle AC that is supported by bearings at A and B. For 5 30, determine (a) the tension in the cable, (b) the reactions at A and B. Assume that the bearing at B does not exert any axial thrust.

Solve Prob. 4.95 for 5 60.

The 20 3 20-in. square plate shown weighs 56 lb and is supported by three vertical wires. Determine the tension in each wire.

The 20 3 20-in. square plate shown weighs 56 lb and is supported by three vertical wires. Determine the weight and location of the lightest block that should be placed on the plate if the tensions in the three wires are to be equal.

An opening in a floor is covered by a 1 3 1.2-m sheet of plywood with a mass of 18 kg. The sheet is hinged at A and B and is main- tained in a position slightly above the floor by a small block C. Determine the vertical component of the reaction (a) at A, (b) at B, (c) at C.

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 vertical wires. Knowing that a 5 0.4 m, determine the tension in each wire.

For the pipe assembly of Prob. 4.101, determine (a) the largest per- missible 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 5 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 sup- ported by three legs equally spaced around the edge. A vertical load P with a magnitude of 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 table over which P can act without tipping the table.

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 5 3 m, determine the tension in each cable and the reaction at A.

Solve Prob. 4.106 for a 5 1.5 m.

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 Prob. 4.108, assuming that the 3.6-kN load is applied at point A.

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 Prob. 4.111, assuming that the 320-lb load is applied at A.

A 10-kg storm window measuring 900 3 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 components of the reactions at A and B.

The bent rod ABEF is supported by bearings at C and D and by wire AH. Knowing that portion AB of the rod is 250 mm long, determine (a) the tension in wire AH, (b) the reactions at C and D. Assume that the bearing at D does not exert any axial thrust.

The horizontal platform ABCD weighs 60 lb and supports a 240-lb load at its center. The platform is normally held in position by hinges at A and B and by braces CE and DE. If brace DE is removed, determine the reactions at the hinges and the force exerted by the remaining brace CE. The hinge at A does not exert any axial thrust.

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 5 50, determine (a) the magnitude of the force exerted by rod CD, (b) the reactions at the hinges. Assume that the hinge at B does not exert any axial thrust.

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 hinge at B does not exert any axial thrust.

Solve Prob. 4.117, assuming that cable DCE is replaced by a cable attached to point E and hook C.

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.

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, (b) the reaction at C.

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 Prob. 4.123, assuming that the 1.8-kN load is applied at C.

4.125 The rigid L-shaped member ABF is supported by a ball-and-socket joint at A and by three cables. For the loading shown, determine the tension in each cable and the reaction at A.

Solve Prob. 4.125, assuming that the load at C has been removed.

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 5 240 lb, a 5 12 in., b 5 8 in., and c 5 10 in.

Solve Prob. 4.127, assuming that the force P is removed and is replaced by a couple M 5 1 (600 lb?in.)j acting at B.

Frame ABCD is supported by a ball-and-socket joint at A and by three cables. For a 5 150 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 frame 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 load- ing shown, determine (a) the tension in each link, (b) the reaction at F.

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 5 268 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.

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 Prob. 4.135, assuming that cable DF is replaced by a cable connecting B and F.

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 Prob. 4.138, assuming that wire DF is replaced by a wire connecting C and F.

Solve Prob. 4.140, subject to the restriction that H must lie on the y axis.

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 5 100 lb, determine (a) the tension in rod AB, (b) the reaction at C.

Determine the reactions at A and B when (a) h 5 0, (b) h 5 200 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 ( 5 0), determine the tension in the cord and the reactions at A and C.

A slender rod AB, with a weight of 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 5 0. (a) Neglecting the weight of the blocks, derive an equation in W, k, l, and that must be satisfied when the rod is in equilibrium. (b) Determine the value of when W 5 75 lb, l 5 30 in., and k 5 3 lb/in.

Determine the reactions at A and B when a 5 150 mm.

For the frame and loading shown, determine the reactions at A and C.

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.