Concept explainers
Three cables are connected at A, where the forces P and Q are applied as shown. Knowing that Q = 0, find the value of P for which the tension in cable AD is 305 N.
Fig.P2.107and P2.108
The value of
Answer to Problem 2.107P
The force
Explanation of Solution
The sketch of the cables connected at
Free body diagram at
Here,
The force
Let
Let
Write the equation of vector distance
Here,
Write the vector distance of the cable
Here,
Write the vector distance of the cable
Here,
Write the equation of tension in the cable
Here,
Write the equation of
Write the equation of tension in the cable
Here,
Write the equation of
Write the equation of tension in the cable
Here,
Write the equation of
Write the equation of force exerting at point
Here,
Write the equation of force exerting at point
Write the equilibrium condition for the forces at
Here, F is the force
The above equation implies that at equilibrium, total force acting on the cable at
Refer figure 2 and write the equation of total force.
Since
Conclusion:
Substitute
Calculate the magnitude of
Substitute
Calculate the magnitude of
Substitute
Calculate the magnitude of
Substitute
Substitute
Substitute
(VII) to get
Substitute
Substitute
Substitute
Substitute
Since total force is zero. Equate force along each direction as zero.
Multiply equation (XIII) by
Add above equation with equation (XIV) to get
Substitute
Substitute
Therefore, the force
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Chapter 2 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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