The Young's modulus for a material is 8.0 x 1010 N/m2. The material is stretched to a strain of 2.0 x 10-3. How much elastic energy will be expended? (Express your answer in J/m3)
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The Young's modulus for a material is 11.0 x 1010 N/m2. The material is stretched to a strain of 3.0 x 10-3. How much elastic energy will be expended?
answer is 495000.0
To calculate the elastic energy expended, we can use the formula for elastic potential energy:
Elastic Energy (U) = (1/2) x Young's Modulus (Y) x Strain (ε)²
Given:
Young's Modulus (Y) = 8.0 x 10¹⁰ N/m²
Strain (ε) = 2.0 x 10⁻³
Let's substitute these values into the formula:
U = (1/2) x (8.0 x 10¹⁰ N/m²) x (2.0 x 10⁻³)²
First, let's square the strain:
ε² = (2.0 x 10⁻³)² = 4.0 x 10⁻⁶
Now, substitute this value back into the equation:
U = (1/2) x (8.0 x 10¹⁰ N/m²) x (4.0 x 10⁻⁶)
To simplify the calculation further, let's express Young's Modulus in scientific notation:
U = (1/2) x (8.0 x 10¹⁰) x (4.0 x 10⁻⁶)
To multiply numbers in scientific notation, we multiply the coefficients and add the exponents:
U = (1/2) x (32 x 10⁴)
Now, let's simplify the expression:
U = 16 x 10⁴ J/m³
Therefore, the elastic energy expended is 16 x 10⁴ J/m³.