The Young's modulus for a material is 2.0 x 1010 N/m2. The material is stretched to a strain of 5.0 x 10-3. How much elastic energy will be expended? (Express your answer in J/m3)
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
The Young's modulus for a material is 17.0 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)
answer is 340000
To calculate the elastic energy expended, we need to use the formula:
Elastic Energy (U) = 0.5 * Young's Modulus * (Strain)²
Given:
Young's Modulus (E) = 2.0 x 10^10 N/m²
Strain (ε) = 5.0 x 10^-3
Substituting these values into the formula:
U = 0.5 * (2.0 x 10^10 N/m²) * (5.0 x 10^-3)²
First, let's simplify the expression within the parenthesis:
U = 0.5 * (2.0 x 10^10 N/m²) * (5.0 x 10^-3)²
= 0.5 * (2.0 x 10^10 N/m²) * [5.0 x 10^-3)^2]
= 0.5 * (2.0 x 10^10 N/m²) * (5.0 x 10^-3) * (5.0 x 10^-3)
Now, multiply the coefficients and add the exponents:
U = 0.5 * 2.0 * 5.0 * 10^10 N/m² * 10^-3 * 5.0 * 10^-3
= 5.0 * 2.0 * 10^10 N/m² * 10^-3 * 10^-3
Now, multiply the coefficients:
U = 10 * 10^10 N/m² * 10^-3 * 10^-3
Combine the exponents:
U = 10 * 10^10 N/m² * 10^-6
= 10^5 N/m² * 10^-6
= 10^-1 N/m²
Finally, express the answer in J/m³:
1 N/m² = 1 J/m³
Therefore, the elastic energy expended is 10^-1 J/m³.