Explanation Given Information: On a beam there are three forces acting F 1 , F 2 and F 3 where, the equation representing the relation between the forces on a beam is as follows: 3 F 1 + F 2 − F 3 = 2 F 1 − 2 F 2 + F 3 = 0 4 F 1 − F 2 + F 3 = 3 Formula used: To solve for three variables in the problem, there is requirement of three equations to obtain the value of variables. Addition or Elimination method to solve a linear system of equations: Step1. Write the equations in the form of a x + b y + c z = d . Step2. Eliminate the one variable by using the any two equations by multiplying one or both equations by a constant, so that after adding the equations, there will be equation of two variables. Step3: Repeat the step2 with one different equation for eliminating the same variable. Step4. Write the both new equations in the form of a x + b y = c . Step5. Multiply one or both equations by a constant, so that after adding the equations, there will be only one variable. Step6. Add both the equations which will result in equation of one variable. Step7. Compute the equation obtained in step6 and find the value of one variable. Step8. Substitute the value obtained in step7 of one variable in any of the new equation of two variables to obtain other one. Step9. Substitute the value obtained in the step7 and step8 in any of the original equation to obtain the third one. Step10. Write the value of variables in correct order. Step11. Check the solution by putting the calculated value in all equations in the system. Calculation: Consider the three forces acting F 1 , F 2 and F 3 on a beam and equation representing the relation between the forces on a beam is as follows: 3 F 1 + F 2 − F 3 = 2 F 1 − 2 F 2 + F 3 = 0 4 F 1 − F 2 + F 3 = 3 Consider the system of equations: 3 F 1 + F 2 − F 3 = 2 …… ( 1 ) F 1 − 2 F 2 + F 3 = 0 …… ( 2 ) 4 F 1 − F 2 + F 3 = 3 …… ( 3 ) Use equation ( 1 ) and equation ( 2 ) to eliminate F 1 : Multiply equation ( 2 ) by − 3 , 3 F 1 + F 2 − F 3 = 2 − 3 F 1 + 6 F 2 − 3 F 3 = 0 _ 7 F 2 − 4 F 3 = 2 Therefore, the new equation will be, 7 F 2 − 4 F 3 = 2 …… ( 4 ) Use equation ( 2 ) and equation ( 3 ) to eliminate F 1 : Multiply equation ( 2 ) by − 4 , − 4 F 1 + 8 F 2 − 4 F 3 = 0 4 F 1 − F 2 + F 3 = 3 _ 7 F 2 − 3 F 3 = 3 Therefore, the new equation will be, 7 F 2 − 3 F 3 = 3 …… ( 5 ) Use equation ( 4 ) and equation ( 5 ) to eliminate F 2 and solve for F 3 : Multiply equation ( 4 ) by − 1 , − 7 F 2 + 4 F 3 = − 2 7 F 2 − 3 F 3 = 3 _ F 3 = 1 Thus, the value of F 3 is 1

Intermediate Algebra For College Students (10th Edition)

10th Edition

ISBN: 9780134758992

Author: Allen R. Angel, Dennis Runde

Publisher: PEARSON

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Chapter 4.3, Problem 62ES

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To calculate: The three forces acting on a beam. If on a beam there are three forces acting F1, F2 and F3 where, the equation representing the relation between the forces on a beam is as follows:

3F1+F2−F3=2F1−2F2+F3=04F1−F2+F3=3

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Chapter 4.3, Problem 61ES

Chapter 4.3, Problem 63ES

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The three forces acting on a beam. If on a beam there are three forces acting F 1 , F 2 and F 3 where, the equation representing the relation between the forces on a beam is as follows: 3 F 1 + F 2 − F 3 = 2 F 1 − 2 F 2 + F 3 = 0 4 F 1 − F 2 + F 3 = 3

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To calculate: The three forces acting on a beam. If on a beam there are three forces acting F1, F2 and F3 where, the equation representing the relation between the forces on a beam is as follows: 3F1+F2−F3=2F1−2F2+F3=04F1−F2+F3=3

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Chapter 4 Solutions

To calculate: The three forces acting on a beam. If on a beam there are three forces acting F1, F2 and F3 where, the equation representing the relation between the forces on a beam is as follows:

3F1+F2−F3=2F1−2F2+F3=04F1−F2+F3=3