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PROBLEM 4.105
A 10-ft boom is acted upon by the 840-lb force shown. Determine the tension in each cable and the reaction at the ball-and-socket joint at A.
The tension in each cable and the reaction at the ball and socket joint at A.
Answer to Problem 4.105P
The tension in cable BD is
Explanation of Solution
The free body diagram corresponding to the system of cable is shown in figure 1 plotted below.
A down ward force of magnitude
Write the equation to find the position vector
Here,
Write the equation to find the position vector
Here,
Write the equation to find the magnitude of
Here,
Write the equation to find the magnitude of
Here,
Write the equation to find the tension along cable BD.
Here,
Write the equation to find the tension along cable BE.
Here,
Write the equation to find the moments at point B due to force at D.
Here,
Write the equation to find the moment at point B due to force at point E.
Here,
Write the equation to find the moment of force at point B due to force at point C.
Here,
Write the equation to find the sum of moment of force at point B.
Here,
Substitute equation (VII), (VIII), and (IX) in equation (X) to find the
Substitute
Since sum of all external force acting on a body is zero, equate the equation for moments to zero.
Write the equation to find the sum of x components of force.
Write the equation to find the sum of y components of force.
Write the equation to find the sum of z component of forces.
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Equate the coefficients of unit vectors
Equate the coefficient of unit vector
Equate the coefficients of unit vector
Substitute
Substitute
Substitute
Therefore, the tension in cable BD is
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