Determine the elongation of the rod in if it is under a tension of 5.7E10^3 N.
The rod is made of aluminum and copper. From the aluminum to the copper section it measures 1.3m and from the copper section to the end it measures 2.6m with a radius of 0.2cm.
Can someone please help, I honestly don't know where to begin.
You can find Young's modulus values for many materials, including copper and aluminum, at
http://en.wikipedia.org/wiki/Young's_modulus
It is represented by the symbol E there, not Y.
For copper is it about 120* 10^9 N/m^2 .
They use the units of GigaPascals (GPa), which is 10^9 N/m^2.
Oh, don't worry! I'll try to help you with a dash of humor. Let's begin with the elongation of the rod, shall we?
Now, to calculate the elongation, we need to know a couple of things: the Young's modulus of the materials and the cross-sectional area of the rod.
Let's start with the cross-sectional area. The radius of the copper section is given as 0.2cm, so we can convert that to meters by using the magic spell of dimensional analysis. Ready? 0.2cm... Abracadabra... Poof! It becomes 0.002 meters!
Now, for the Young's modulus, we need to know the values for aluminum and copper. I don't have those numbers off the top of my clown wig, but you can find them in your favorite materials science book or a trustworthy online source.
Okay, now that you have those values, use Hooke's Law, which states that the elongation is proportional to the applied force and inversely proportional to the cross-sectional area and Young's modulus.
Plug those values into the equation, and voila! You'll have the elongation, which is how much the rod stretches under the tension force of 5.7E10^3 N.
Remember, laughter is the best stress reliever, so don't stress too much about this problem. Good luck!
To determine the elongation of the rod under tension, we need to use the concept of stress and strain.
The formula for stress is given by:
Stress = Force / Area
In this case, the force applied is the tension (5.7E10^3 N) and we need to calculate the cross-sectional area of the rod at various sections.
First, let's consider the aluminum section. To calculate its area, we need to know the radius of the aluminum section. Unfortunately, this information is missing from the question. Please provide the radius of the aluminum section so that we can continue with the calculation.
Add the elongations of the aluminum and copper sections. The elongation of each is
delta L = L * T/(AY)
Where L is the length of that material, A is the cross sectional area and Y is Young's modulus, which you will have to look up.
For copper:
L = 2.6 m
A = (pi)*(2*10^-3 m)^2
Your text should have Young's modulus values for aluminum and copper; otherwise try googling it.