The weight of a crate is 300 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 $A = ( 0,0 , - 130 )$, point $B = ( 90,0,0 )$, point $C = ( - 40,40,0 )$, point $D = ( 0 , - 180,0 )$
A) cable $A B = 196$; cable $A C = 97$; cable $A D = 68$
B) cable $A B = 97$; cable $A C = 68$; cable $A D = 196$
C) cable $A B = 97$; cable $A C = 196$; cable $A D = 68$
D) cable $A B = 68$; cable $A C = 196$; cable $A D = 97$
E) cable $A B = 196$; cable $A C = 68 ;$ cable $A D = 97$ )

Question

The weight of a crate is 300 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 $A = ( 0,0 , - 130 )$, point $B = ( 90,0,0 )$, point $C = ( - 40,40,0 )$, point $D = ( 0 , - 180,0 )$
A) cable $A B = 196$; cable $A C = 97$; cable $A D = 68$ 
B) cable $A B = 97$; cable $A C = 68$; cable $A D = 196$ 
C) cable $A B = 97$; cable $A C = 196$; cable $A D = 68$ 
D) cable $A B = 68$; cable $A C = 196$; cable $A D = 97$ 
E) cable $A B = 196$; cable $A C = 68 ;$ cable $A D = 97$ )

Quizplus · Accepted Answer

To find the tension in each cable, we need to analyze the forces acting on the crate. Since the crate is not accelerating, the net force in each direction (x, y, and z) must be zero.

In the z-direction, the weight of the crate is the only force, so the tension in cable AD must be equal to the weight, which is 300 N.

In the x-direction, the tension in cable AB must balance the component of the weight that is in the x-direction, which is given by:

(Weight)(cos 45) = (300 N)(0.707) = 212.1 N

Since cable AB is horizontal, the tension in cable AB must be equal to this value.

Finally, in the y-direction, the tension in cable AC must balance the component of the weight that is in the y-direction, which is given by:

(Weight)(sin 45) = (300 N)(0.707) = 212.1 N

Since cable AC makes a 45-degree angle with the y-axis, the tension in cable AC can be found using the Pythagorean theorem:

tension AC = sqrt[(212.1 N)^2 + (-130 N)^2] = 196 N

Therefore, the tension in each cable is AB = 212 N, AC = 196 N, and AD = 300 N, which matches choice C.

The Weight of a Crate Is 300 Newtons A,B,CA , B , CA,B,C

The Weight of a Crate Is 300 Newtons $A , B , C$