Tensile stress given theta and force

[plz]

Tensile stress given theta and force (I'm kinda desperate)

Homework Statement

Aluminum wire is lightweight. You can hang a piece of it nearly horizontally with very little tension. After having done so, you then hang a HEAVY (25 kg) block from the wire. The wire sags to make an angle of 12 degrees with the horizontal. Determine the radius of the wire.

Homework Equations

Stress / Strain = Modulus

Stress = Force / area = 25*9.8 / (pi)r^2

Strain = Delta L/L = [(L/cos12) - L / L] ?

Young's Modulus for aluminum = 70 x 10^9

The Attempt at a Solution

(25)(9.8) / [(pi)(r^2)] = (0.022)(70*10^9)

r = 2.25 * 10^-4

This is wrong, Please give me solid advice and not simple hints please. I'm really tired of this problem and I'd like to solve it with as little guesswork as possible. I need to have a solution in a few answers. If you can help me I will love you till the ends of the earth.

 

[Chestermiller]

The tension in each of the two sections of the wire is not 25 kg. Assume that the weight is suspended from the mid point of the wire, and draw a free body diagram to get the tension in each of the two sections. The vertical components of the tensions must sum to the weight of the weight.

 

[Sheridans]

I had the same problem. Could someone just tell me where the 0.022 came from? That was the only part i was missing.

Anyway, like Chestermiller said, just do a free body. The force in the stress equation is tension, not the weight of the block.

 

[PhanthomJay]

I had the same problem. Could someone just tell me where the 0.022 came from? That was the only part i was missing.

It actually is all there in please's relevant equations, and represents the unit strain in the wire. The wire must stretch from its original length to the new length as measured along the diagonals of the wire in its loaded stretched position.

 

[Nickie]

First of all, it's important to take a step back and understand what is being asked for in this problem. Tensile stress is defined as the force per unit area that a material experiences when it is being pulled or stretched. In this case, the aluminum wire is experiencing a force (the weight of the block) and is being stretched to make an angle of 12 degrees with the horizontal.

To solve this problem, we can use the formula for stress, which is force divided by area. In this case, the force is given (25 kg) and the area is unknown, represented by the radius (r) of the wire. So, we can set up the equation as follows:

Stress = Force / Area

25 kg * 9.8 m/s^2 = 70 x 10^9 Pa * Area

Solving for area, we get:

Area = (25 kg * 9.8 m/s^2) / (70 x 10^9 Pa)

= 3.5 x 10^-8 m^2

Now, we need to find the radius of the wire using this area. The area of a circle is given by the formula A = πr^2. So, we can rearrange this formula to solve for the radius, which gives us:

Radius (r) = √(Area / π)

= √(3.5 x 10^-8 m^2 / π)

= 2.66 x 10^-4 m

So, the radius of the wire is approximately 2.66 x 10^-4 meters. It's important to note that this is an approximation and may vary slightly depending on the exact value of pi used.

I hope this explanation helps you understand the concept and solve the problem with confidence. Remember to always take a step back and understand what is being asked for in a problem before jumping into solving it. Good luck with your studies!