How Does the Cross Product Help Calculate Tension in a Cable?

In summary, the tension in the supporting cable for a horizontal boom supporting a sign weighing 150 N and a uniform construction weighing 50 N can be found using the cross product method and is equal to 350 N. However, in order to accurately determine the tension, the angle of the cable from the horizontal is necessary. Without this information, the problem cannot be solved. A diagram is also provided for reference.
  • #1
Shay10825
338
0
In the problem:
A horizontal boom supporting the sign is of uniform construction and weighs 50 N. If the sign weighs 150 N, the tension in the supporting cable is?

Could I use the cross product and if so how? The answer is 350 N.
 
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  • #2
Do you have a diagram? Is the cable at an angle, or is it vertical? Where's this sign you mention?
 
  • #3
http://img121.exs.cx/img121/4286/2882.jpg
 
  • #4
Hmmm...is that all the info? Do we have some lengths, or the angle of the cable from the horizontal?
 
  • #5
The tension in the cable definitely depends on the angle it makes with the horizontal, so we need to know that to solve the problem.
 

FAQ: How Does the Cross Product Help Calculate Tension in a Cable?

What is the cross product in statics?

The cross product, also known as the vector product, is a mathematical operation that results in a vector perpendicular to the two vectors being multiplied. In statics, it is used to calculate the moment of a force about a point or axis.

How is the cross product calculated?

The cross product is calculated by taking the determinant of a 3x3 matrix. The first row consists of the unit vectors i, j, and k, the second row contains the components of the first vector, and the third row contains the components of the second vector. The result is a vector in the direction perpendicular to the two vectors being multiplied.

What is the right-hand rule and how is it related to the cross product?

The right-hand rule is a method used to determine the direction of the resulting vector in a cross product. It states that if the fingers of your right hand curl in the direction of the first vector, and then straighten in the direction of the second vector, your thumb will point in the direction of the resulting vector. This rule is used because the cross product is a vector perpendicular to the two vectors being multiplied.

Can the cross product be used for non-perpendicular vectors?

No, the cross product is only defined for two vectors that are perpendicular to each other. If the vectors are not perpendicular, the result will be a zero vector.

What are some real-world applications of the cross product in statics?

The cross product is commonly used in engineering and physics to calculate the moment of a force about a point or axis. It is also used in computer graphics and 3D modeling to determine the orientation of objects and calculate lighting and shading effects. Additionally, the cross product is used in navigation and robotics for determining the orientation and movement of objects in space.

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