VECTOR MECH...,STAT.+DYNA.(LL)-W/ACCESS
VECTOR MECH...,STAT.+DYNA.(LL)-W/ACCESS
11th Edition
ISBN: 9781259633133
Author: BEER
Publisher: MCG
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Chapter 6.4, Problem 6.162P

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 with a magnitude of 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 crosspiece attached to shaft CF is horizontal, determine (a) the magnitude of the couple that must be applied to shaft AC at A to maintain equilibrium, (b) the reactions at B, D, and E. (Hint: The sum of the couples exerted on the crosspiece must be zero.)

Chapter 6.4, Problem 6.162P, Two shafts AC and CF, which lie in the vertical xy plane, are connected by a universal joint at C.

Fig. P6.161

*6.162 Solve Prob. 6.161 assuming that the arm of the crosspiece attached to shaft CF is vertical.

(a)

Expert Solution
Check Mark
To determine

The magnitude of the couple that must be applied to shaft AC at A to maintain equilibrium.

Answer to Problem 6.162P

The magnitude of the couple that must be applied to shaft AC at A to maintain equilibrium is 433lb.in.

Explanation of Solution

Take all vectors along the x axis , y axis and y axis as positive.

The free body diagram of the shaft DF is shown in figure 1.

VECTOR MECH...,STAT.+DYNA.(LL)-W/ACCESS, Chapter 6.4, Problem 6.162P , additional homework tip  1

Here, Cx , Cy and Cz are the component of force C at C , Dy and Dz are the y and z component of force at D , Ex,Ey and Ez are the x,yand z component force at E respectively.

At equilibrium total moment will be zero.

Write the expression for the equilibrium moment about x axis.

Mx=0 (I)

Here, Mx are the equilibrium moment of force about x axis.

The moment along the x axis are the moment of force about C and about E.

From free body diagram in figure1, write the complete equilibrium expression of moment about x for the shaft DF.

MC500lbin=0 VECTOR MECH...,STAT.+DYNA.(LL)-W/ACCESS, Chapter 6.4, Problem 6.162P , additional homework tip  2 (II)

Here, MC is the moment of force about the point C in the shaft DF.

The free body diagram of the shaft BC is shown in figure 1.

VECTOR MECH...,STAT.+DYNA.(LL)-W/ACCESS, Chapter 6.4, Problem 6.162P , additional homework tip  3

Here,x,y, z are the arbitrary axis with x along BC , Byj , Bzk are the component of force at B along yand z ,Exi,Eyjand Ezk are the component of force at E along arbitrary axes.

Write the expression for the equilibrium moment about C axis.

MC=0

Here, MC are the equilibrium moment of force about C.

Resolve (500lbin.) into components along x and y  axes.

MC=(500lbin.)(cos30°i+sin30°j)

From free body diagram in figure2, write the complete equilibrium expression of moment about C  for the shaft BC.

MAi(500lbin.)(cos30°i+sin30°j)+(5in.)i×(Byj+Bzk)=0VECTOR MECH...,STAT.+DYNA.(LL)-W/ACCESS, Chapter 6.4, Problem 6.162P , additional homework tip  4

MAi(433.35lbin.)i(250lbin.)j+(5Bylbin.)k+(5Bzlbin.)j=0 (III)

Here, MA is the moment of force about the point A in the shaft DF.

Calculation:

Rearrange equation (II) to get MC.

MC500lbin=0

MC=500lbin.

Equate coefficient of i in equation (III)to zero to get MA.

(MA(433lbin.))=0MA=433lb

Therefore, the magnitude of the couple that must be applied to shaft AC at A to maintain equilibrium is 433lb.in.

(b)

Expert Solution
Check Mark
To determine

The reaction at B,D and E.

Answer to Problem 6.162P

The reaction at B is equal to B=(50lb) , reaction at D is equal to D=(83.3lb)k and reaction at E is equal to E=(33.3lb)k.

Explanation of Solution

From free body diagram in figure2, write the complete equilibrium expression of moment about C for the shaft BC.

MAi(500lbin.)(cos30°i+sin30°j)+(5in.)i×(Byj+Bzk)=0VECTOR MECH...,STAT.+DYNA.(LL)-W/ACCESS, Chapter 6.4, Problem 6.162P , additional homework tip  5

MAi(433lbin.)i+(5Bylbin.)k(5Bzlbin.)j=0 (III)

Here, MA is the moment of force about the point A in the shaft DF.

Since the net force at the shaft BC is zero. Write the expression for the net force.

F=0BC=0 (IV)

Using free body diagram in figure1, apply the equilibrium condition for moment about D.

MD=0 (V)

Here, MD is the net moment at D.

From figure1, write the complete expression of moment MD about D

(500lbin.)i(500lbin.)i+(6in.)i×(Exi+Eyj+Ezk)(4in.)i×(50lb)k=0(200lbin.)j+(6in.)Eyk(6in.)Ezj=0 (VI)

Since net force at shaft DF is zero, write the expression for the net force.

F=0

C+Dyj+Dzk+Exi+Ezk=0 (VII)

Calculation:

Equate coefficient of j in equation (III)to zero to get Bz.

250lbin.-(5in.)Bz=0

Equate coefficient of k in equation (III)to zero to get By.

By=0

Therefore,

B=(0lb)j+(50lb)k=0=(50lb)k

Substitute 50lb for B in equation (III) to get C.

50lbC=0C=50lb

Equate coefficient of j in equation (VI) to get Ez.

(200lbin.)(6in.)Ez=0Ez=33.3lb

Equate coefficient of k in equation (VI) to zero to get Ey.

Ey=0

Equate coefficient of i in equation (VII) to zero to get Ex.

Ex=0

Therefore, net reaction at E is equal to, E=Exi+Eyj+Ezk=(33.3lb)k.

Substitute 50lbk for C , (33.3lb)k for E and equate coefficient of k in equation (VII) to zero to get Dz.

50lb+Dz+(33.3lb)=0Dz=83.3lb

Equate coefficient of j in equation (VII) to zero to get Dy.

Dy=0

Therefore, total reaction at D equal to D=83.3lbk

Therefore, the reaction at B is equal to B=(50lb) , reaction at D is equal to D=(83.3lb)k and reaction at E is equal to E=(33.3lb)k.

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Chapter 6 Solutions

VECTOR MECH...,STAT.+DYNA.(LL)-W/ACCESS

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6.29 Determine whether the trusses of Probs....Ch. 6.1 - 6.30 Determine whether the trusses of Probs....Ch. 6.1 - Prob. 6.31PCh. 6.1 - Prob. 6.32PCh. 6.1 - For the given loading, determine the zero-force...Ch. 6.1 - Prob. 6.34PCh. 6.1 - Prob. 6.35PCh. 6.1 - Prob. 6.36PCh. 6.1 - The truss shown consists of six members and is...Ch. 6.1 - The truss shown consists of nine members and is...Ch. 6.1 - The truss shown consists of nine members and is...Ch. 6.1 - Solve Prob. 6.39 for P = 0 and Q = (900 N)k. 6.39...Ch. 6.1 - The truss shown consists of 18 members and is...Ch. 6.1 - The truss shown consists of 18 members and is...Ch. 6.2 - 6.43 A Mansard roof truss is loaded as shown....Ch. 6.2 - 6.44 A Mansard roof truss is loaded as shown....Ch. 6.2 - Determine the force in members BD and CD of the...Ch. 6.2 - Determine the force in members DF and DG of the...Ch. 6.2 - Prob. 6.47PCh. 6.2 - Prob. 6.48PCh. 6.2 - Determine the force in members CD and DF of the...Ch. 6.2 - Determine the force in members CE and EF of the...Ch. 6.2 - Determine the force in members DE and DF of the...Ch. 6.2 - Prob. 6.52PCh. 6.2 - Determine the force in members DF and DE of the...Ch. 6.2 - Prob. 6.54PCh. 6.2 - Prob. 6.55PCh. 6.2 - 6.56 A monosloped roof truss is loaded as shown....Ch. 6.2 - A Howe scissors roof truss is loaded as shown....Ch. 6.2 - A Howe scissors roof truss is loaded as shown....Ch. 6.2 - Determine the force in members AD, CD, and CE of...Ch. 6.2 - Determine the force in members DG, FG, and FH of...Ch. 6.2 - 6.61 Determine the force in members DG and FI of...Ch. 6.2 - Prob. 6.62PCh. 6.2 - Prob. 6.63PCh. 6.2 - Prob. 6.64PCh. 6.2 - The diagonal members in the center panels of the...Ch. 6.2 - The diagonal members in the center panels of the...Ch. 6.2 - Prob. 6.67PCh. 6.2 - Prob. 6.68PCh. 6.2 - Classify each of the structures shown as...Ch. 6.2 - Classify each of the structures shown as...Ch. 6.2 - Prob. 6.71PCh. 6.2 - 6.70 through 6.74 classify as determinate or...Ch. 6.2 - 6.70 through 6.74 classify as determinate or...Ch. 6.2 - 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Prob. 6.112PCh. 6.3 - 6.111, 6.112, and 6.113 Members ABC and CDE are...Ch. 6.3 - Prob. 6.114PCh. 6.3 - Solve Prob. 6.112 assuming that the force P is...Ch. 6.3 - Prob. 6.116PCh. 6.3 - Prob. 6.117PCh. 6.3 - Prob. 6.118PCh. 6.3 - 6.119 through 6.121 Each of the frames shown...Ch. 6.3 - 6.119 through 6.121 Each of the frames shown...Ch. 6.3 - 6.119 through 6.121 Each of the frames shown...Ch. 6.4 - An 84-lb force is applied to the toggle vise at C....Ch. 6.4 - For the system and loading shown, draw the...Ch. 6.4 - Prob. 6.7FBPCh. 6.4 - The position of member ABC is controlled by the...Ch. 6.4 - The shear shown is used to cut and trim...Ch. 6.4 - A 100-lb force directed vertically downward is...Ch. 6.4 - Prob. 6.124PCh. 6.4 - The control rod CE passes through a horizontal...Ch. 6.4 - Solve Prob. 6.125 when (a) = 0, (b) = 6. Fig....Ch. 6.4 - The press shown is used to emboss a small seal at...Ch. 6.4 - The press shown is used to emboss a small seal at...Ch. 6.4 - Prob. 6.129PCh. 6.4 - The pin at B is attached to member ABC and can...Ch. 6.4 - Arm ABC is connected by pins to a collar at B and...Ch. 6.4 - Arm ABC is connected by pins to a collar at B and...Ch. 6.4 - The Whitworth mechanism shown is used to produce a...Ch. 6.4 - Prob. 6.134PCh. 6.4 - Prob. 6.135PCh. 6.4 - Prob. 6.136PCh. 6.4 - 6.137 and 6.138 Rod CD is attached to the collar D...Ch. 6.4 - 6.137 and 6.138 Rod CD is attached to the collar D...Ch. 6.4 - Two hydraulic cylinders control the position of...Ch. 6.4 - Prob. 6.140PCh. 6.4 - Prob. 6.141PCh. 6.4 - Prob. 6.142PCh. 6.4 - Prob. 6.143PCh. 6.4 - Prob. 6.144PCh. 6.4 - The pliers shown are used to grip a...Ch. 6.4 - 6.146 Determine the magnitude of the gripping...Ch. 6.4 - In using the bolt cutter shown, a worker applies...Ch. 6.4 - Prob. 6.148PCh. 6.4 - Prob. 6.149PCh. 6.4 - and 6.150 Determine the force P that must be...Ch. 6.4 - Prob. 6.151PCh. 6.4 - Prob. 6.152PCh. 6.4 - 6.153 The motion of the bucket of the front-end...Ch. 6.4 - Prob. 6.154PCh. 6.4 - The telescoping arm ABC is used to provide an...Ch. 6.4 - The telescoping arm ABC of Prob. 6.155 can be...Ch. 6.4 - The motion of the backhoe bucket shown is...Ch. 6.4 - Prob. 6.158PCh. 6.4 - Prob. 6.159PCh. 6.4 - In the planetary gear system shown, the radius of...Ch. 6.4 - Two shafts AC and CF, which lie in the vertical xy...Ch. 6.4 - Two shafts AC and CF, which lie in the vertical xy...Ch. 6.4 - The large mechanical tongs shown are used to grab...Ch. 6 - Using the method of joints, determine the force in...Ch. 6 - Using the method of joints, determine the force in...Ch. 6 - A stadium roof truss is loaded as shown. Determine...Ch. 6 - A stadium roof truss is loaded as shown. Determine...Ch. 6 - Determine the components of all forces acting on...Ch. 6 - Prob. 6.169RPCh. 6 - Knowing that the pulley has a radius of 50 mm,...Ch. 6 - For the frame and loading shown, determine the...Ch. 6 - For the frame and loading shown, determine the...Ch. 6 - Water pressure in the supply system exerts a...Ch. 6 - A couple M with a magnitude of 1.5 kNm is applied...Ch. 6 - Prob. 6.175RP
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