How Do You Calculate Tension in a Cable and Compression in a Brace?

[copyfilew]

Homework Statement

A 235lb sign is supported from a wall by a cable inclined 37 degrees with the horizontal, and a brace perpendicular to the wall. Find the tension in the cable and the compression in the boom.

The answers are 390.5 and 311.9. But I have no idea how they got to those numbers. :S

Homework Equations

No idea?

The Attempt at a Solution

Tried to find the x/y components of the vectors, but I'm confused now.

 

[PhanthomJay]

Homework Statement

A 235lb sign is supported from a wall by a cable inclined 37 degrees with the horizontal, and a brace perpendicular to the wall. Find the tension in the cable and the compression in the boom.

The answers are 390.5 and 311.9. But I have no idea how they got to those numbers. :S

Homework Equations

No idea?

The Attempt at a Solution

Tried to find the x/y components of the vectors, but I'm confused now.

One way is to draw a free body diagram of the sign and identify the forces acting on it ...its weight down, the cable tension along the length of the cable (which has an x and a y component), and the brace compression along its length (x component only). Then use Newton 1 inthe x and y direction to solve for the components.

 

[m2003]

I would approach this problem by first drawing a free body diagram of the sign and the forces acting on it. From the problem statement, we know that there are two forces acting on the sign: the tension in the cable and the compression in the boom. The sign itself has a weight of 235lb, which can be represented as a downward force.

Next, I would use trigonometry to find the components of the forces acting on the sign. The tension in the cable can be broken down into horizontal and vertical components, with the vertical component opposing the weight of the sign. The horizontal component of the tension will be equal to the compression in the boom, as they are perpendicular to each other.

Using the given angle of 37 degrees, we can find the values of the horizontal and vertical components of the tension using basic trigonometric functions (sin, cos, tan). Once we have the values for the components, we can use the Pythagorean theorem to find the magnitude of the tension, which is equal to the compression in the boom.

The tension in the cable can then be found by adding the horizontal and vertical components together. This will give us a value of approximately 390.5lb. Similarly, the compression in the boom can be found by taking the square root of the sum of the squares of the horizontal and vertical components, which will give us a value of approximately 311.9lb.

In summary, the tension in the cable and the compression in the boom can be found by using trigonometry and the Pythagorean theorem to break down the forces and find their magnitudes. This approach is based on the principles of Newton's laws of motion and can be applied to various problems involving forces and their components.