Question
What is the coefficient of elasticity of the material that must be placed on the heel of the 10 cm high clog, with a base area of 2 cm² so that it deforms only 2 cm when the force on it will be a maximum of 600 N.
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Answer to a math question What is the coefficient of elasticity of the material that must be placed on the heel of the 10 cm high clog, with a base area of 2 cm² so that it deforms only 2 cm when the force on it will be a maximum of 600 N.
Miles
4.969 Answers
To calculate the coefficient of elasticity (also known as Young's modulus), you can use the formula:
Young's Modulus (Y) = (Stress) / (Strain)
Where:
- Stress is the force applied (in newtons, N).
- Strain is the deformation or change in length (in meters, m).
- The coefficient of elasticity (Young's Modulus) has units of pascals (Pa).
In your case, you want to find the coefficient of elasticity (Y) for the material that must be placed on the heel of the clog. The height of the clog is 10 cm, and it deforms only 2 cm when a maximum force of 600 N is applied. First, let's convert the measurements to meters:
Height (h) = 10 cm = 0.1 m
Deformation (Δh) = 2 cm = 0.02 m
Force (F) = 600 N
Base area (A) = 2 cm² = 0.0002 m²
Now, calculate the stress (σ) and strain (ε):
Stress (σ) = Force (F) / Area (A)
σ = 600 N / 0.0002 m²
σ = 3,000,000 N/m² (or 3,000,000 Pa)
Strain (ε) = Deformation (Δh) / Original Length (h)
ε = 0.02 m / 0.1 m
ε = 0.2
Now, you can use Young's Modulus formula to find Y:
Young's Modulus (Y) = Stress (σ) / Strain (ε)
Y = 3,000,000 Pa / 0.2
Y = 15,000,000 Pa
So, the coefficient of elasticity (Young's Modulus) for the material that must be placed on the heel of the clog is 15,000,000 pascals (Pa).
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