Different young modulus of rod - Need a proper explanation?

In summary: So, you must find the stress that causes that much strain in the rod (in other words, the stress that causes the rod to stretch 3mm).In summary, the problem asks for the greatest tensile stress that can be applied to a rod made of two materials with the same cross-sectional area, before the rod breaks at a total extension of 3.0mm. This can be found using the Young's modulus, which relates stress and strain, and considering the combined stretch of both materials in the rod. The stress that causes the rod to stretch 3mm is equal to the maximum allowed tensile stress.
  • #1
PhysicStud01
174
0

Homework Statement


A rod is made up as shown [pic attached]
pic.png

Both have same cross-sectional area. Ep and En are Young modulus.
The rod breaks when total extension = 3.0mm
Greatest tensile stress that can be applied before rod breaks?

Homework Equations


Young modulus = stress / strain

The Attempt at a Solution


Ans: 5.7 x 10^6 Pa.
Won't it break when the one of the 2 materials breaks? Can you please tell me the concepts to be used. How to solve?
Thanks
 
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  • #2
PhysicStud01 said:

Homework Statement


A rod is made up as shown [pic attached]
View attachment 75901
Both have same cross-sectional area. Ep and En are Young modulus.
The rod breaks when total extension = 3.0mm
Greatest tensile stress that can be applied before rod breaks?

Homework Equations


Young modulus = stress / strain

The Attempt at a Solution


Ans: 5.7 x 10^6 Pa.
Won't it break when the one of the 2 materials breaks? Can you please tell me the concepts to be used. How to solve?
Thanks

The Young's modulus tells you how much the material stretches for a given applied tensile stress.

If you apply the same stress to the rod shown in the OP, which material is going to stretch more?

The problem is asking you to find how much stress can be applied to the rod so that the combined stretch of the nylon and the glass-reinforced plastic equals 3 mm. Remember, the strain is equal to the change in length of the material divided by the original length (unstretched).
 
  • #3
PhysicStud01 said:
Won't it break when the one of the 2 materials breaks?
Sure, but you don't care which breaks, or even the fact that it breaks. What matters is that the max allowed extension of the rod as a whole is 3mm.
 

Related to Different young modulus of rod - Need a proper explanation?

1. What is the young modulus of a rod?

The young modulus, also known as the modulus of elasticity or elastic modulus, is a measure of the stiffness of a material. It is the ratio of stress to strain within the elastic limit of the material.

2. How does the young modulus of a rod differ from other materials?

The young modulus of a rod depends on the material it is made of. For example, the young modulus of steel is much higher than that of rubber. This is because the atoms in steel are tightly packed, making it more difficult for the material to deform, while rubber has looser atomic bonds, allowing for easier deformation.

3. Why is the young modulus important for rods?

The young modulus is important for rods as it determines their ability to withstand stress and strain. A higher young modulus indicates that the material is stiffer and less likely to deform under a given amount of stress, making it more suitable for use in structural applications such as bridges or buildings.

4. How is the young modulus of a rod measured?

The young modulus is typically measured through a tensile test, which involves applying a controlled amount of stress to the material and measuring the resulting strain. The young modulus is then calculated by dividing the stress by the strain.

5. Can the young modulus of a rod change?

Yes, the young modulus of a rod can change under certain conditions. For example, extreme temperatures or exposure to certain chemicals can alter the atomic bonds within the material, affecting its stiffness and resulting in a change in the young modulus. Additionally, the manufacturing process and composition of the material can also impact its young modulus.

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