Class Problems Sentences 13 the d

7/29/2019 Class Problems Sentences 13 the d

1/20

2-1. Determine the magnitude of the resultant force FR = F1 + F2 and its direction,measured counterclockwise from the positivex axis.

2-6. Resolve the force F2 into components acting along the u and v

axes and determine the magnitudes of the components.

2-17. Determine the design angle (0o 90

o) for strutAB so that

the 400-lb horizontal force has a component of 500 lb directed fromAtowards C. What is the component of force acting along memberAB?

Take = 40.

2-27. The beam is to be hoisted using two chains. If the resultant force

is to be 600 N directed along the positivey axis, determine the

magnitudes of forces FAand FBacting on each chain and the angle ofFBso that the magnitude ofFBis a minimum. FAacts at 30 from they

axis, as shown.


2/20

249. If the magnitude of the resultant force acting on the eyebolt is

600 N and its direction measured clockwise from the positivex axis

is = 30o, determine the magnitude ofF1 and the angle .

259. If the resultant force acting on the bracket is required to be a

minimum, determine the magnitudes ofF1 and the resultant force. Set

= 30.

278. Three forces act on the ring. If the resultant force FRhas a

magnitude and direction as shown, determine the magnitude andthe coordinate direction angles of force F3.

271. If the resultant force acting on the bracket is directed along the

positivey axis, determine the magnitude of the resultant force and the

coordinate direction angles ofF so that < 90.


3/20

F220. Determine the length of the rod and the position vector directed

fromA toB. What is the angle ?

287. Determine the lengths of wiresAD, BD, and CD. The ring at

D is midway betweenA andB.

2110. The cable attached to the shear-leg derrick exerts a force on the

derrick of F = 350 lb. Express this force as a Cartesian vector.

2113. Determine the angle between the edges of the sheet-metal

bracket.

2129. Determine the magnitude of the projected

component ofF alongAC. Express this component as a

Cartesian vector.


4/20

2137. Determine the components ofF that act along rodACand perpendicular to it. PointB is located 3 m along the rod

from end C.

319. The unstretched length of springAB is 3 m. If the block is held in the

equilibrium position shown, determine the mass of the block atD.

332. Determine the maximum weight of the bucket that the

wire system can support so that no single wire develops atension exceeding 100 lb.

839. Determine the smallest force the man must exert on the rope in

order to move the 80-kg crate. Also, what is the angle at this

moment? The coefficient of static friction between the crate and the

floor is s = 0.3.


5/20

841. Two blocksA andB have a weight of 10 lb and

6 lb, respectively. They are resting on the incline forwhich the coefficients of static friction are A = 0.15

and B = 0.25. Determine the angle which will cause

motion of one of the blocks. What is the friction forceunder each of the blocks when this occurs? The springhas a stiffness of k = 2 lb/ft and is originally

unstretched.

346. If the bucket and its contents have a total weight of 20 lb,

determine the force in the supporting cablesDA, DB, andDC.

354. Determine the tension developed in cablesAB andACand the

force developed along strutAD for equilibrium of the 400-lb crate.

360. The 800-lb cylinder is supported by three chains as shown.

Determine the force in each chain for equilibrium. Take d= 1 ft.


6/20

Equilibrium-3D Problem. The mass of the cylinder is 120 kg.

Determine the tensions in cablesAB,AC, andAD. Set the coordinatesystem as convenient.

rref([-.5071, 0, .6172, 0; -.1690, .4472, -.1543, 0; .8452, .8944, .7715,

1177.2])

44. Determine the moment about pointA of each ofthe three forces acting on the beam.

422. The tool atA is used to hold a power lawnmower blade stationary

while the nut is being loosened with the wrench. If a force of 50 N isapplied to the wrench atB in the direction shown, determine the moment

it creates about the nut at C. What is the magnitude of force F atA so

that it creates the opposite moment about C?

428. The connected barBCis used to increase the lever arm of the

crescent wrench as shown. If a clockwise moment of MA = 120 N m isneeded to tighten the bolt atA and the force F= 200 N, determine the

required extension din order to develop this moment.


7/20

436. The curved rod lies in thexy plane and has a radius of 3 m. If

a force of F = 80 N acts at its end as shown, determine the moment

of this force about point O.

438. Force F acts perpendicular to the inclined plane. Determinethe moment produced by F about pointA. Express the result as a

Cartesian vector.

443. The curved rod has a radius of 5 ft. If a force of 60 lb acts atits end as shown, determine the moment of this force about point C.

453. Determine the moment of the force F about an axis extending

betweenA and C. Express the result as a Cartesian vector.


8/20

459. Determine the magnitude of force F in cableAB in

order to produce a moment of 500 lb ft about the hinged

axis CD, which is needed to hold the panel in the position

shown.

*466. The A-frame is being hoisted into an upright position

by the vertical force ofF= 80 lb. Determine the moment of

this force about thex axis when the frame is in the positionshown. (The textbook requires finding the moment abouty-

axis)

471. Two couples act on the beam. Determine the magnitude

ofF so that the resultant couple moment is 450 lbft,

counterclockwise. Where on the beam does the resultant

couple moment act?

492. If the magnitude of the couple moment acting on the pipe

assembly is 50 N m, determine the magnitude of the couple

forces applied to each wrench. The pipe assembly lies in the xy

plane.

490. Determine the distance dbetweenA andB so that the

resultant couple moment has a magnitude ofMR = 20 N m.


9/20

4105. Replace the force system acting on the frame by

a resultant force and couple moment at pointA.

4133. If the resultant force is required to act at the center of the

slab, determine the magnitude of the column loadings FA and FB and

the magnitude of the resultant force.

4112. Handle forces F1 and F2 are applied to the electric drill.

Replace this force system by an equivalent resultant force and

couple moment acting at point O. Express the results in Cartesian

vector form.

99. Locate the centroid (x,y) of the area.

928. Locate the centroid (x,y) of the area.


10/20

93. Locate the centroid (x,y) of the homogeneous rod bent into aparabolic shape.

939. Locate theycentroid of the paraboloid.

947. Locate the centroid of the quartercone.

F97. Locate the centroid (x,y, z) of the wire bent in the shape shown.

955. The three members of the frame each have a weight per unit length of 4

lb/ft. Locate the position (x,y) of the center of gravity. Neglect the size of the

pins at the joints and the thickness of the members. Also, calculate the reactions

at the fixed supportA.

961. Locate the centroid (x,y) of the members cross section area.


11/20

Problem Centroids 1. Locate the centroid (x, y) of thecomposite area.

989. Locate the center of massz of the assembly. The cylinder and the cone are

made from materials having densities of 5 Mg/m3

and 9 Mg/m3, respectively.

F4-37. Determine the resultant force and specify where it acts on

the beam measured from A .

4144. The distribution of soil loading on the bottom of a

building slab is shown. Replace this loading by an equivalent

resultant force and specify its location, measured from point O.

*4153. Replace the loading by an equivalent resultant force and

couple moment acting at pointB.


12/20

*52. Draw the free-body diagram of member ABC which is

supported by a smooth collar atA, roller atB, and short linkCD.

Explain the significance of each force acting on the diagram.

55. Draw the free-body diagram of the uniform bar, which has a

mass of 100 kg and a center of mass at G. The supportsA,B, and C

are smooth.

513. The 75-kg gate has a center of mass located at G. IfA

supports only a horizontal force and B can be assumed as a pin,

determine the components of reaction at these supports.

516. Determine the components of reaction at the

supportsA andB on the rod.

525. Determine the magnitude of force at the pinA and in the

cableBCneeded to support the 500-lb load. Neglect the weightof the boomAB.


13/20

530. 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 positionshown.

551. The rigid beam of negligible weight issupported horizontally by two springs and a pin. If

the springs are uncompressed when the load isremoved, determine the force in each spring whenthe 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.

RB-1. A loading car is at rest on an inclined track. The gross weight of the car

and its load is 5500 lb, and it is applied at at G. The cart is held in position by

the cable. Determine the tension in the cable and the reaction at each pair of

wheels.

836. The thin rod has a weight Wand rests against the floor and wall for

which the coefficients of static friction are A and B, respectively. Determinethe smallest value of for which the rod will not move.


14/20

855. Determine the greatest angle so that the ladder does not slip

when it supports the 75-kg man in the position shown. The surfaceis rather slippery, where the coefficient of static friction atA andB

is s = 0.3.

581. The sign has a mass of 100 kg with center of mass at G.Determine thex,y,z components of reaction at the ball-and socket

jointA and the tension in wiresBCandBD.

582. Determine the tensions in the cables and the components of reaction

acting on the smooth collar atA necessary to hold the 50-lb sign in

equilibrium. The center of gravity for the sign is at G.

RB2. Determine the tensions TAE and TGF in the twosupporting cables resulting from the 1.2kN tension in cable

CD. Assume the absence of any resisting moments on the base

of the pole at O about thex andyaxes, but not aboutzaxis.

Use vector approach.


15/20

66. Determine the force in each member of the truss, and state if the

members are in tension or compression.

*620. Determine the force in each member of the truss in

terms of the load P, and indicate whether the members are in

tension or compression.

638. Determine the force in members FEandECof the

Fink truss and state if the members are in tension or

compression.

646. Determine the force in members CD and CMof the

Baltimore bridge truss and state if the members are in

tension or compression. Also, indicate all zero-force members.


16/20

636. Determine the force in members CD, CF, and CG andstate if these members are in tension or compression.

664. Determine the force P needed to support the 20-kg mass using the Spanish Burton

rig. Also, what are the reactions at the supporting hooksA,B, and C?

665. Determine the horizontal and vertical components offorce at Cwhich memberABCexerts on member CEF.

667. Determine the horizontal and vertical components of force at each

pin. The suspended cylinder has a weight of 80 lb.


17/20

676. Determine the horizontal and vertical components offorce which the pins atA, B, and Cexert on memberABCof

the frame

698. Determine the horizontal and vertical components of force at pin B

and the normal force the pin at Cexerts on the smooth slot. Also, determine

the moment and horizontal and vertical reactions of force at A. There is a

pulley atE

6102. The tractor boom supports the uniform mass of 500 kg

in the bucket which has a center of mass at G. Determine theforce in each hydraulic cylinderAB and CD and the resultant

force at pinsEand F. The load is supported equally on eachside of the tractor by a similar mechanism.


18/20

6103. The two-member frame supports the 200-lb cylinder and 500

lbft couple moment. Determine the force of the roller at B on member

ACand the horizontal and vertical components of force which the pin atC exerts on member CB and the pin at A exerts on member AC. Theroller Cdoes not contact member CB.

684. Determine the required force P that must be applied at the

blade of the pruning shears so that the blade exerts a normal forceof 20 lb on the twig atE.

712. Determine the internal normal force, shear force,

and the moment at points CandD.

725. Determine the shear force and moment acting at

a section passing through point Cin the beam.


19/20

747. Draw the shear and moment diagrams for the beam (a) in

terms of the parameters shown; (b) set P = 800 lb, a = 5 ft,L = 12 ft.

F78. Determine the shear and moment as a function ofx,

then draw the shear and moment diagrams.

759. Determine the shear and moment as a function of

x, then draw the shear and moment diagrams.

765. Determine the shear and moment as a function ofx, then

draw the shear and moment diagrams.

766. Determine the shear and moment as a function ofx,

then draw the shear and moment diagrams.


20/20

1011. Determine the moment of inertia of the area about thex

andy axes.

1022. Determine the moment of inertia of the area about they axis.

1025. Determine the moment of inertia of the area about thex axis.

1049. Determine the moment of inertia of the area about they axis.

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Class Problems Sentences 13 the d