Young's Modulus for Two Materials connected

In summary, the conversation discusses the calculation of the change in length for a rod made of aluminum and steel when pulled upon. The equation F = Y(delta-L/L-naught)A is used, with the first part for aluminum and the second part for steel. It is also mentioned that the aluminum section is twice as long as the steel section and the total change in length is 1mm. The equation is manipulated to get (2Fx)/A = (6.9E10)(delta-Laluminum) + (4E11)(delta-Lsteel) and it is stated that the force and area of the rod are unknown. The method of setting the two equations equal to each other and cancelling out the area is suggested.
  • #1
thursdaytbs
53
0
If Aluminum and steel are connected as one rod, and are attached to the wall and is pulled upon. How would the change in length for each material of the rod be calculated? I'm given that the Aluminum section is twice as long as the steel section, and the total change in length of the whole rod is 1mm.

So far, I've said:
F = Y(delta-L / L-naught)A + Y(delta-L / L-naught)A
*Where, the first part is for Aluminum, and the Second part is for Steel.

Manipulating this equation I got:

(2Fx)/A = (6.9E10)(delta-Laluminum) + (4E11)(delta-Lsteel)
and, delta-Aluminum + delta-steel = 0.001m
*where x = the length of steel, therefore aluminum = 2x.

This is where I'm stuck. I dont' know the Force applied, or the Area of the rod. What can i do? Thanks in advance for any help.
 
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  • #2
OK another thing I've thought up is saying...

F = Y(delta-Laluminum / L-naught)A
and
F = Y(delta-Lsteel / L-naught)A

since force is equal throughout?

Then set the two equations equal to one another, where A cancels out?

Can anyone confirm this is a way of doing it?
 
  • #3
Looks good to me. The stress (F/A) is the same throughout the rod. You'll also need to use the other facts given regarding total change in length and the ratio of the two original lengths.
 
  • #4
awsome, thanks a lot.
 

Related to Young's Modulus for Two Materials connected

1. What is Young's Modulus for Two Materials connected?

Young's Modulus for Two Materials connected refers to the measure of the stiffness or elasticity of a material or a system of materials when two different materials are joined together. It is a measure of how easily the connected materials can be stretched or compressed along the direction of the applied force.

2. How is Young's Modulus for Two Materials connected calculated?

The Young's Modulus for Two Materials connected is calculated by dividing the applied stress by the resulting strain. The stress is the force applied to the materials, while the strain is the amount of deformation that occurs in the materials as a result of the applied force.

3. What is the significance of Young's Modulus for Two Materials connected?

Young's Modulus for Two Materials connected is significant because it helps to determine the strength and flexibility of materials when they are joined together. It also provides valuable information for engineers and designers in selecting appropriate materials for specific applications.

4. Can Young's Modulus for Two Materials connected vary?

Yes, Young's Modulus for Two Materials connected can vary depending on factors such as the composition, structure, and temperature of the materials. It can also vary based on the type of connection between the materials, such as welding or bonding.

5. How does Young's Modulus for Two Materials connected affect the behavior of a material?

The Young's Modulus for Two Materials connected affects the behavior of a material by determining its stiffness and resistance to deformation under an applied force. Materials with a higher Young's Modulus are stiffer and less flexible, while materials with a lower Young's Modulus are more flexible and prone to deformation.

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