An elastic change of all constant 2000permeter undergoes a strain of 0.02 Under a load of 20N.
What is the natural length of the strain?
50cm
Well, I'm no mathematician, but let's see if I can clown my way through this! So, we know that the strain is 0.02 and the load is 20N. Now, to find the natural length of the strain, we need to dig a bit deeper. Remember the equation E = (F/A)/Δx, where E is the elasticity constant, F is the load, A is the cross-sectional area, and Δx is the change in length?
If I put on my clown thinking cap, I'd say that since the elasticity constant is given as 2000permeter, and the strain is 0.02, we can use the equation E = Δx/lo, where lo is the natural length. Rearranging, we get Δx = E * lo. Plugging in the values of E = 2000permeter and Δx = 0.02, we can solve for lo! Let's crunch some numbers.
(2000permeter) * lo = 0.02
So, lo = 0.02 / (2000permeter)
Now, the tricky part is converting units! Let's imagine a circus trick where we convert permeter to just meter. Since "per" means division, we divide the value by 1000 to convert it. That means 2000permeter is just 2 meters!
Therefore, the natural length of the strain, lo, is 0.02 / 2 = 0.01 meter. Voila! I hope that somehow made sense in a clownish way.
To find the natural length of the strain, we can use Hooke's Law, which states that the strain in a material is directly proportional to the stress applied to it. The formula for Hooke's Law is given by:
Stress = Young's Modulus * Strain
Rearranging this formula, we can solve for the natural length of the strain:
Natural Length = Stress / Young's Modulus
We are given that the elastic constant is 2000 N/m and the strain is 0.02. The stress can be calculated using the formula:
Stress = Load / Area
The load is given as 20N, and the area is not provided. Without the area, we cannot calculate the stress and therefore cannot determine the natural length of the strain.
To find the natural length of the strain, we need to use Hooke's Law, which states that the strain in a material is directly proportional to the stress applied to it. The formula for Hooke's Law is:
σ = E ε
Where:
- σ is the stress applied to the material
- E is the Young's modulus (elastic constant) of the material
- ε is the strain experienced by the material
In this case, we are given the strain (ε) and the stress (σ) is not given directly, but we are given the load (force) applied (F = 20N) and the length (L = 2000m) of the material.
The stress (σ) can be calculated by dividing the force (F) applied by the cross-sectional area (A) of the material:
σ = F / A
Assuming that the cross-sectional area is constant and known, we can substitute the value of stress (σ) in the Hooke's Law equation:
F / A = E ε
We can rearrange this equation to solve for the strain (ε):
ε = F / (A E)
Now we can substitute the given values into the equation to find the strain (ε):
ε = 20N / (A * E)
Since the problem doesn't provide the value of the cross-sectional area (A), we can't determine the exact strain without that information.
However, we can calculate the natural length (Lo) of the material by using the following formula:
Lo = L + L * ε
Where:
- Lo is the natural length of the material
- L is the original length of the material
- ε is the strain experienced by the material
Substituting the given values in the equation, we can find the natural length (Lo):
Lo = 2000m + 2000m * 0.02
Lo = 2000m + 40m
Lo = 2040m
Therefore, the natural length of the strain is 2040 meters.