Solved: The horizontal beam is supported by springs at its

Draw the free-body diagram of the dumpster D of the truck, which has a mass of 2.5 Mg and a center of gravity at G . It is supported by a pin at A and a pin-connected hydraulic cylinder BC (short link). Explain the significance of each force on the diagram. (See Fig. 57 b .)

Draw the free-body diagram of member ABC which is supported by a smooth collar at A , rocker at B , and short link CD . Explain the significance of each force acting on the diagram. (See Fig. 57 b .)

Draw the free-body diagram of the beam which supports the 80-kg load and is supported by the pin at A and a cable which wraps around the pulley at D . Explain the significance of each force on the diagram. (See Fig. 57 b .)

Draw the free-body diagram of the hand punch, which is pinned at A and bears down on the smooth surface at B .

Draw the free-body diagram of the uniform bar, which has a mass of 100 kg and a center of mass at G . The supports A, B , and C are smooth.

Draw the free-body diagram of the beam, which is pin-supported at A and rests on the smooth incline at B

Draw the free-body diagram of the beam, which is pin connected at A and rocker-supported at B .

Draw the free-body diagram of the bar, which has a negligible thickness and smooth points of contact at A , B , and C . Explain the significance of each force on the diagram. (See Fig. 57 b .)

Draw the free-body diagram of the jib crane AB , which is pin connected at A and supported by member (link) BC

Determine the horizontal and vertical components of reaction at the pin A and the reaction of the rocker B on the beam

Determine the magnitude of the reactions on the beam at A and B . Neglect the thickness of the beam

Determine the components of the support reactions at the fixed support A on the cantilevered beam.

The 75-kg gate has a center of mass located at G . If A supports only a horizontal force and B can be assumed as a pin, determine the components of reaction at these supports.

The overhanging beam is supported by a pin at A and the two-force strut BC . Determine the horizontal and vertical components of reaction at A and the reaction at B on the beam

Determine the horizontal and vertical components of reaction at the pin at A and the reaction of the roller at B on the lever.

Determine the components of reaction at the supports A and B on the rod.

If the wheelbarrow and its contents have a mass of 60 kg and center of mass at G , determine the magnitude of the resultant force which the man must exert on each of the two handles in order to hold the wheelbarrow in equilibrium.

Determine the tension in the cable and the horizontal and vertical components of reaction of the pin A . The pulley at D is frictionless and the cylinder weighs 80 lb.

The shelf supports the electric motor which has a mass of 15 kg and mass center at Gm. The platform upon which it rests has a mass of 4 kg and mass center at Gp. Assuming that a single bolt B holds the shelf up and the bracket bears against the smooth wall at A , determine this normal force at A and the horizontal and vertical components of reaction of the bolt on the bracket.

The pad footing is used to support the load of 12 000 lb. Determine the intensities w1 and w2 of the distributed loading acting on the base of the footing for the equilibrium

When holding the 5-lb stone in equilibrium, the humerus H , assumed to be smooth, exerts normal forces FC and FA on the radius C and ulna A as shown. Determine these forces and the force FB that the biceps B exerts on the radius for equilibrium. The stone has a center of mass at G . Neglect the weight of the arm.

The smooth disks D and E have a weight of 200 lb and 100 lb, respectively. If a horizontal force of P = 200 lb is applied to the center of disk E , determine the normal reactions at the points of contact with the ground at A , B , and C .

The smooth disks D and E have a weight of 200 lb and 100 lb, respectively. Determine the largest horizontal force P that can be applied to the center of disk E without causing the disk D to move up the incline.

The man is pulling a load of 8 lb with one arm held as shown. Determine the force FH this exerts on the humerus bone H , and the tension developed in the biceps muscle B . Neglect the weight of the mans arm.

Determine the magnitude of force at the pin A and in the cable BC needed to support the 500-lb load. Neglect the weight of the boom AB.

The winch consists of a drum of radius 4 in., which is pin connected at its center C . At its outer rim is a ratchet gear having a mean radius of 6 in. The pawl AB serves as a two-force member (short link) and keeps the drum from rotating. If the suspended load is 500 lb, determine the horizontal and vertical components of reaction at the pin C .

The sports car has a mass of 1.5 Mg and mass center at G . If the front two springs each have a stiffness of kA = 58 kN>m and the rear two springs each have a stiffness of kB = 65 kN>m, determine their compression when the car is parked on the 30 incline. Also, what friction force FB must be applied to each of the rear wheels to hold the car in equilibrium? Hint: First determine the normal force at A and B , then determine the compression in the springs.

The telephone pole of negligible thickness is subjected to the force of 80 lb directed as shown. It is supported by the cable BCD and can be assumed pinned at its base A . In order to provide clearance for a sidewalk right of way, where D is located, the strut CE is attached at C , as shown by the dashed lines (cable segment CD is removed). If the tension in CD is to be twice the tension in BCD , determine the height h for placement of the strut CE .

The floor crane and the driver have a total weight of 2500 lb with a center of gravity at G . If the crane is required to lift the 500-lb drum, determine the normal reaction on both the wheels at A and both the wheels at B when the boom is in the position shown.

The floor crane and the driver have a total weight of 2500 lb with a center of gravity at G . Determine the largest weight of the drum that can be lifted without causing the crane to overturn when its boom is in the position shown.

The mobile crane has a weight of 120 000 lb and center of gravity at G1; the boom has a weight of 30 000 lb and center of gravity at G2. Determine the smallest angle of tilt u of the boom, without causing the crane to overturn if the suspended load is W = 40 000 lb. Neglect the thickness of the tracks at A and B .

The mobile crane has a weight of 120 000 lb and center of gravity at G1; the boom has a weight of 30 000 lb and center of gravity at G2. If the suspended load has a weight of W = 16 000 lb, determine the normal reactions at the tracks A and B . For the calculation, neglect the thickness of the tracks and take u = 30.

The woman exercises on the rowing machine. If she exerts a holding force of F = 200 N on handle ABC , determine the horizontal and vertical components of reaction at pin C and the force developed along the hydraulic cylinder BD on the handle.

The ramp of a ship has a weight of 200 lb and a center of gravity at G . Determine the cable force in CD needed to just start lifting the ramp, (i.e., so the reaction at B becomes zero). Also, determine the horizontal and vertical components of force at the hinge (pin) at A .

The toggle switch consists of a cocking lever that is pinned to a fixed frame at A and held in place by the spring which has an unstretched length of 200 mm. Determine the magnitude of the resultant force at A and the normal force on the peg at B when the lever is in the position shown.

The worker uses the hand truck to move material down the ramp. If the truck and its contents are held in the position shown and have a weight of 100 lb with center of gravity at G , determine the resultant normal force of both wheels on the ground A and the magnitude of the force required at the grip B .

The boom supports the two vertical loads. Neglect the size of the collars at D and B and the thickness of the boom, and compute the horizontal and vertical components of force at the pin A and the force in cable CB . Set F1 = 800 N and F2 = 350 N.

The boom is intended to support two vertical loads, F1 and F2. If the cable CB can sustain a maximum load of 1500 N before it fails, determine the critical loads if F1 = 2F2. Also, what is the magnitude of the maximum reaction at pin A ?

The jib crane is pin connected at A and supported by a smooth collar at B. If x = 8 ft, determine the reactions on the jib crane at the pin A and smooth collar B. The load has a weight of 5000 lb

The jib crane is pin connected at A and supported by a smooth collar at B . Determine the roller placement x of the 5000-lb load so that it gives the maximum and minimum reactions at the supports. Calculate these reactions in each case. Neglect the weight of the crane. Require 4 ft x 10 ft.

The crane consists of three parts, which have weights of W1 = 3500 lb, W2 = 900 lb, W3 = 1500 lb and centers of gravity at G1, G2, and G3, respectively. Neglecting the weight of the boom, determine (a) the reactions on each of the four tires if the load is hoisted at constant velocity and has a weight of 800 lb, and (b), with the boom held in the position shown, the maximum load the crane can lift without tipping over

The cantilevered jib crane is used to support the load of 780 lb. If x = 5 ft , determine the reactions at the supports. Note that the supports are collars that allow the crane to rotate freely about the vertical axis. The collar at B supports a force in the vertical direction, whereas the one at A does not

The cantilevered jib crane is used to support the load of 780 lb. If the trolley T can be placed anywhere between 1.5 ft x 7.5 ft, determine the maximum magnitude of reaction at the supports A and B . Note that the supports are collars that allow the crane to rotate freely about the vertical axis. The collar at B supports a force in the vertical direction, whereas the one at A does not.

The upper portion of the crane boom consists of the jib AB , which is supported by the pin at A , the guy line BC , and the backstay CD , each cable being separately attached to the mast at C . If the 5-kN load is supported by the hoist line, which passes over the pulley at B , determine the magnitude of the resultant force the pin exerts on the jib at A for equilibrium, the tension in the guy line BC , and the tension T in the hoist line. Neglect the weight of the jib. The pulley at B has a radius of 0.1 m

he device is used to hold an elevator door open. If the spring has a stiffness of k = 40 N>m and it is compressed 0.2 m, determine the horizontal and vertical components of reaction at the pin A and the resultant force at the wheel bearing B

Three uniform books, each having a weight W and length a , are stacked as shown. Determine the maximum distance d that the top book can extend out from the bottom one so the stack does not topple over.

The horizontal beam is supported by springs at its ends. Each spring has a stiffness of k = 5 kN>m and is originally unstretched when the beam is in the horizontal position. Determine the angle of tilt of the beam if a load of 800 N is applied at point C as shown.

The horizontal beam is supported by springs at its ends. If the stiffness of the spring at A is kA = 5 kN>m, determine the required stiffness of the spring at B so that if the beam is loaded with the 800-N force it remains in the horizontal position. The springs are originally constructed so that the beam is in the horizontal position when it is unloaded.

The wheelbarrow and its contents have a mass of m = 60 kg with a center of mass at G . Determine the normal reaction on the tire and the vertical force on each hand to hold it at u = 30 . Take a = 0.3 m , b = 0.45 m , c = 0.75 m and d = 0.1 m .

The wheelbarrow and its contents have a mass m and center of mass at G . Determine the greatest angle of tilt u without causing the wheelbarrow to tip over.

The rigid beam of negligible weight is supported horizontally by two springs and a pin. If the springs are uncompressed when the load is removed, determine the force in each spring when the load P is applied. Also, compute the vertical deflection of end C . Assume the spring stiffness k is large enough so that only small deflections occur. Hint: The beam rotates about A so the deflections in the springs can be related.

A boy stands out at the end of the diving board, which is supported by two springs A and B , each having a stiffness of k = 15 kN>m. In the position shown the board is horizontal. If the boy has a mass of 40 kg, determine the angle of tilt which the board makes with the horizontal after he jumps off. Neglect the weight of the board and assume it is rigid.

The uniform beam has a weight W and length l and is supported by a pin at A and a cable BC . Determine the horizontal and vertical components of reaction at A and the tension in the cable necessary to hold the beam in the position shown

Determine the distance d for placement of the load P for equilibrium of the smooth bar in the position u as shown. Neglect the weight of the bar.

If d = 1 m , and u = 30 , determine the normal reaction at the smooth supports and the required distance a for the placement of the roller if P = 600 N . Neglect the weight of the bar.

The disk B has a mass of 20 kg and is supported on the smooth cylindrical surface by a spring having a stiffness of k = 400 N>m and unstretched length of l0 = 1 m. The spring remains in the horizontal position since its end A is attached to the small roller guide which has negligible weight. Determine the angle u for equilibrium of the roller. 0.2

The beam is subjected to the two concentrated loads. Assuming that the foundation exerts a linearly varying load distribution on its bottom, determine the load intensities w1 and w2 for equilibrium if P = 500 lb and L = 12 ft

The beam is subjected to the two concentrated loads. Assuming that the foundation exerts a linearly varying load distribution on its bottom, determine the load intensities w1 and w2 for equilibrium in terms of the parameters shown.

The thin rod of length l is supported by the smooth tube. Determine the distance a needed for equilibrium if the applied load is P .

The 30-N uniform rod has a length of l = 1 m . If s = 1.5 m , determine the distance h of placement at the end A along the smooth wall for equilibrium.

The uniform rod has a length l and weight W . It is supported at one end A by a smooth wall and the other end by a cord of length s which is attached to the wall as shown. Determine the placement h for equilibrium.

The uniform load has a mass of 600 kg and is lifted using a uniform 30-kg strongback beam BAC and four ropes as shown. Determine the tension in each rope and the force that must be applied at A .

The 50-lb mulching machine has a center of gravity at G . Determine the vertical reactions at the wheels C and B and the smooth contact point A .

The wing of the jet aircraft is subjected to a thrust of T = 8 kN from its engine and the resultant lift force L = 45 kN . If the mass of the wing is 2.1 Mg and the mass center is at G , determine the x, y, z components of reaction where the wing is fixed to the fuselage A .

Due to an unequal distribution of fuel in the wing tanks, the centers of gravity for the airplane fuselage A and wings B and C are located as shown. If these components have weights WA = 45 000 lb, WB = 8000 lb, and WC = 6000 lb, determine the normal reactions of the wheels D, E , and F on the ground

The air-conditioning unit is hoisted to the roof of a building using the three cables. If the tensions in the cables are TA = 250 lb , TB = 300 lb , and TC = 200 lb , determine the weight of the unit and the location ( x, y) of its center of gravity G .

The platform truck supports the three loadings shown. Determine the normal reactions on each of its three wheels.

Determine the force components acting on the ball-and-socket at A , the reaction at the roller B and the tension on the cord CD needed for equilibrium of the quarter circular plate.

The windlass is subjected to a load of 150 lb. Determine the horizontal force P needed to hold the handle in the position shown, and the components of reaction at the ball-and-socket joint A and the smooth journal bearing B . The bearing at B is in proper alignment and exerts only force reactions on the windlass.

The 100-lb door has its center of gravity at G . Determine the components of reaction at hinges A and B if hinge B resists only forces in the x and y directions and A resists forces in the x, y, z directions.

Determine the support reactions at the smooth collar A and the normal reaction at the roller support B .

The pole is subjected to the two forces shown. Determine the components of reaction of A assuming it to be a ball-and-socket joint. Also, compute the tension in each of the guy wires, BC and ED .

The boom AB is held in equilibrium by a ball-andsocket joint A and a pulley and cord system as shown. Determine the x, y, z components of reaction at A and the tension in cable DEC if F = {-1500k}lb .

The cable CED can sustain a maximum tension of 800 lb before it fails. Determine the greatest vertical force F that can be applied to the boom. Also, what are the x, y, z components of reaction at the ball-and-socket joint A ?

If the pulleys are fixed to the shaft, determine the magnitude of tension T and the x, y, z components of reaction at the smooth thrust bearing A and smooth journal bearing B

The boom AC is supported at A by a ball-andsocket joint and by two cables BDC and CE . Cable BDC is continuous and passes over a pulley at D . Calculate the tension in the cables and the x, y, z components of reaction at A if a crate has a weight of 80 lb.

A vertical force of 80 lb acts on the crankshaft. Determine the horizontal equilibrium force P that must be applied to the handle and the x, y, z components of reaction at the journal bearing A and thrust bearing B . The bearings are properly aligned and exert only force reactions on the shaft.

Member AB is supported by a cable BC and at A by a square rod which fits loosely through the square hole at the end joint of the member as shown. Determine the components of reaction at A and the tension in the cable needed to hold the 800-lb cylinder in equilibrium.

The bent rod is supported at A , B , and C by smooth journal bearings. Compute the x , y , z components of reaction at the bearings if the rod is subjected to forces F1 = 300 lb and F2 = 250 lb . F1 lies in the yz plane. The bearings are in proper alignment and exert only force reactions on the rod.

The bent rod is supported at A, B, and C by smooth journal bearings. Determine the magnitude of F2 which will cause the reaction Cy at the bearing C to be equal to zero. The bearings are in proper alignment and exert only force reactions on the rod. Set F1 = 300 lb .

The sign has a mass of 100 kg with center of mass at G . Determine the x , y , z components of reaction at the balland-socket joint A and the tension in wires BC and BD

Determine the tensions in the cables and the components of reaction acting on the smooth collar at A necessary to hold the 50-lb sign in equilibrium. The center of gravity for the sign is at G . z

Both pulleys are fixed to the shaft and as the shaft turns with constant angular velocity, the power of pulley A is transmitted to pulley B . Determine the horizontal tension T in the belt on pulley B and the x , y , z components of reaction at the journal bearing C and thrust bearing D if u = 0 . The bearings are in proper alignment and exert only force reactions on the shaft.

Both pulleys are fixed to the shaft and as the shaft turns with constant angular velocity, the power of pulley A is transmitted to pulley B . Determine the horizontal tension T in the belt on pulley B and the x , y , z components of reaction at the journal bearing C and thrust bearing D if u = 45 . The bearings are in proper alignment and exert only force reactions on the shaft.