Problem 3.52 Part A Determine the tension developed in cable AB for equilibrium
ID: 1587607 • Letter: P
Question
Problem 3.52
Part A
Determine the tension developed in cable AB for equilibrium of the 350-lb crate.(Figure 1)
Express your answer to two significant figures and include the appropriate units.
FAB =
Part B
Determine the tension developed in cables AC for equilibrium of the 350-lb crate.
Express your answer to two significant figures and include the appropriate units.
FAC =
Part C
Determine the force developed along strut AD for equilibrium of the Express your answer to two significant figures and include the appropriate units.
FAD =
**I have tried making A the center of the diagram and working the problem from that point of view, and also the way it stands now. The way that I have worked out the problem is using the vector way ie F_b=T_b(2,0,4) building the sum of forces equations and working to find the correct answers without success. Thanks.**
2 ft 2 ft 4 ft 5.5 ft 2.5 ft 6 ftExplanation / Answer
The point of interest is A. Begin with setting up the free-body diagram of A, with the four forces acting at A. There are no moments to calculate, as all the forces pass through A.
The four forces are as follows:
Weight of the Box, down. (Let's call this W)
Tension of AB, toward B. (We'll call it Tb)
Tension of AC, toward C. (We'll call this Tc)
"Tension" from AD, from D. (And we'll call this D)
To begin with, calculate the unit vectors of AB, AC, and AD. The unit vector for W is <0,0,-1>. The unit vectors for the others are, as previously ordered, <-4/13,-12/13,3/13>, <2/7,-6/7,3/7>, and <0,12/13,5/13>.
Breaking the force vectors into their components, we are left with the following equations:
(1) Fx = 0 = -4/13*Tb + 2/7*Tc
(2) Fy = 0 = -12/13*Tb + -6/7*Tc + 12/13*D
(3) Fz = 0 = 3/13*Tb + 3/7*Tc + 5/13*D - W
From (1), we can solve for Tb in terms of Tc, such that Tb = 13/14*Tc
From (2), we can substitute our solution from (1) into Tb and then solve D in terms of Tc, D = 13/7*Tc
Then from (3), we can substitute (1) and (2) for Tb and D and put W in terms of Tc, W = 19/14*Tc.
From (1), we can see that Tb will be less than Tc, so Tc shall be equal to 350 lbs.
W thus shall equal 475 lbs
D will equal 650 lbs
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.