VECTOR MECHANICS FOR ENGINEERS W/CON >B
VECTOR MECHANICS FOR ENGINEERS W/CON >B
12th Edition
ISBN: 9781260804638
Author: BEER
Publisher: MCG
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Textbook Question
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Chapter 6.3, Problem 6.104P

Knowing that P = 25 lb and Q = 55 lb, determine the components of the forces exerted (a) on member BCDF at C and D, (b) on member ACEG at E.

Chapter 6.3, Problem 6.104P, Knowing that P = 25 lb and Q = 55 lb, determine the components of the forces exerted (a) on member

(a)

Expert Solution
Check Mark
To determine

The components of the forces exerted on member BCDF at C and D.

Answer to Problem 6.104P

The x component of force at D, Dx is 100lb_, y component of force at D, Dy is 20lb_, x component of force at C, Cx is 100lb_, y component of force at C , Cy is 60lb_, x component of force at E, Ex is 100lb_, and  the y component of force at E, Ey is 140lb_.

Explanation of Solution

Figure 1 is the free body diagram of the entire frame of the system.

VECTOR MECHANICS FOR ENGINEERS W/CON >B, Chapter 6.3, Problem 6.104P , additional homework tip  1

Write the equation to find the sum of the moments about point E.

ME=(P+Q)(25in)(P+Q)(15in)Dx(8in)=0 (I)

Here, P is the force acting on point A and F, Q is the force acting on point F and G, Dx is the x component of force at D.

Write the equation to find the sum of x components of force.

Fx=Ex+Dx=0 (II)

Here, Ex is the x component of force at E, and Dx is the x component of force at D.

Consider the member BCDF of the system.

Figure 2 shown below is the free body diagram of member BCDF.

VECTOR MECHANICS FOR ENGINEERS W/CON >B, Chapter 6.3, Problem 6.104P , additional homework tip  2

Write the equation to find the sum of x component of force.

Fx=Cx+Dx=0 (III)

Here, Cx is the x component of force at C, and Dx is the x component of force at point D.

Write the equation to find the sum of moments at D.

MD=Ex(4in)P(15in)+Q(25in)+Cy(10in)=0 (IV)

Here, Ex is the x component of force at E, P is the force at P, Q is the force at Q, and Cy is the y component of force at C.

Write the equation to find the sum of y components of force.

Fy=Dy+Cy=0 (V)

Here, Dy is the y component of force at D, and Cy is the y component of force at C.

Consider the free body diagram of member ACEG. The free body diagram of ACEG is given in figure 3.

VECTOR MECHANICS FOR ENGINEERS W/CON >B, Chapter 6.3, Problem 6.104P , additional homework tip  3

Write the equation to find the sum of y component of force.

Fy=EyCyPQ=0 (VI)

Here, Ey is the y component of force at E, Cy is the y component of force at C, P is the force at P, and Q is the force at Q.

Conclusion:

Solve equation (I) to get the value of Dx.

Dx=(P+Q)108

Substitute 25lb for P, and 55lb for Q to get Dx.

Dx=(25+55)108=100lb

Solve equation (III) to get the value of Cx.

Cx=Dx=(P+Q)108

Substitute 25lb for P, and 55lb for Q to get Cx.

Cx=(25+55)108=100lb

Substitute (P+Q)108 for Dx in equation (IV) to get Cy.

VECTOR MECHANICS FOR ENGINEERS W/CON >B, Chapter 6.3, Problem 6.104P , additional homework tip  4Substitute 25lb for P, and 55lb for Q to get Cy.

Cy=2(55)2(25)=60lb

Substitute 2Q2P for Cy in equation (V) to get Dy.

Dy+(2Q2P)=0PQ=0Dy=Q+3P

Substitute 25lb for P, and 55lb for Q to get Dy.

Dy=55+3(25)=20lb

Therefore, The x component of force at D, Dx is 100lb_, y component of force at D, Dy is 20lb_, x component of force at C, Cx is 100lb_, y component of force at C , Cy is 60lb_,

(b)

Expert Solution
Check Mark
To determine

The component of force on member ACEG at E.

Answer to Problem 6.104P

The x component of force at E, Ex is 100lb_, and  the y component of force at E, Ey is 140lb_.

Explanation of Solution

Rewrite equation (II) to find the x component of force at E.

Fx=Ex+Dx=0 (VII)

Here, Ex is the x component of force at E, and Dx is the x component of force at D.

Rewrite equation (VI) to get the y component of force at E.

Fy=EyCyPQ=0 (VIII)

Here, Ey is the y component of force at E, Cy is the y component of force at C, P is the force at P, and Q is the force at Q.

Conclusion:

Substitute (P+Q)108 for Dx in equation (VII) to get Ex.

Ex(P+Q)108=0Ex=(P+Q)108

Substitute 25lb for P, and 55lb for Q to get Ex.

Ex=(15+65)108=100lb

Substitute 2QP for Cy in equation (VIII) to get Ey.

Ey(2Q2P)PQ=0Ey=3QP

Substitute 25lb for P, and 55lb for Q to get Ey.

VECTOR MECHANICS FOR ENGINEERS W/CON >B, Chapter 6.3, Problem 6.104P , additional homework tip  5

Therefore, The x component of force at E, Ex is 100lb_, and  the y component of force at E, Ey is 140lb_.

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Chapter 6 Solutions

VECTOR MECHANICS FOR ENGINEERS W/CON >B

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