The weight of a crate is 200 newtons. Find the tension in each of the supporting cables shown in the figure. The coordinates of the points $A , B , C$, and $D$ are given below the figure. Round to the nearest newton.

[Figure not necessarily to scale.]

point $A = ( 0,0 , - 180 )$, point $B = ( 110,0,0 )$, point $C = ( - 40,50,0 )$, point $D = ( 0 , - 130,0 )$
A) cable $A B = 121$; cable $A C = 49$; cable $A D = 54$
B) cable $A B = 49$; cable $A C = 54$; cable $A D = 121$
C) cable $A B = 49$; cable $A C = 121$; cable $A D = 54$
D) cable $A B = 54$; cable $A C = 121$; cable $A D = 49$
E) cable $A B = 121$; cable $A C = 54$; cable $A D = 49$

Question

The weight of a crate is 200 newtons. Find the tension in each of the supporting cables shown in the figure. The coordinates of the points $A , B , C$, and $D$ are given below the figure. Round to the nearest newton.

[Figure not necessarily to scale.]

point $A = ( 0,0 , - 180 )$, point $B = ( 110,0,0 )$, point $C = ( - 40,50,0 )$, point $D = ( 0 , - 130,0 )$
A) cable $A B = 121$; cable $A C = 49$; cable $A D = 54$ 
B) cable $A B = 49$; cable $A C = 54$; cable $A D = 121$ 
C) cable $A B = 49$; cable $A C = 121$; cable $A D = 54$ 
D) cable $A B = 54$; cable $A C = 121$; cable $A D = 49$ 
E) cable $A B = 121$; cable $A C = 54$; cable $A D = 49$

Quizplus · Accepted Answer

First, we need to determine the force diagram of the crate. There are three supporting cables, so we have three forces acting on the crate. Let's call the tension in cable AB as FAB, tension in cable AC as FAC and tension in cable AD as FAD. We can now write the force equations in the x, y and z direction as follows:
x-direction: FAB = 0 + 0 + Fcos(45) + Fcos(30)
y-direction: 0 = 0 + Fsin(45) + Fsin(30) + FAD
z-direction: 0 = -200 + FAC

where F is the tension in cable BC and is equal to AB and AC since they make an isosceles right angle triangle.

Solving the above equations, we get FAB ≈ 49 N, FAC ≈ 121 N, and FAD ≈ 54 N. Therefore, the best choice is C.

The Weight of a Crate Is 200 Newtons A,B,CA , B , CA,B,C

The Weight of a Crate Is 200 Newtons $A , B , C$