Answer :
The average normal strain in the string when stretched to the given position is approximately 0.028 or 2.8%.Therefore, the average normal strain in the string when stretched to the given position is approximately 4.23% or 0.0423.
1. We start by determining the change in length (ΔL) of the string, which is the difference between the final length (L_f) and the initial unstretched length (L_i).
2. Given that the unstretched length of the bowstring is 35.5 inches and the final length when stretched to the given position is 37 inches, we have ΔL = L_f - L_i = 37 in - 35.5 in.
3. Calculating ΔL gives us ΔL = 1.5 inches.
4. Next, we use the formula for strain (ε), which is the change in length (ΔL) divided by the original length (L_i).
5. Substituting the values into the formula, we have ε = ΔL / L_i = 1.5 in / 35.5 in.
6. Computing this gives us ε ≈ 0.0423.
7. To express the strain as a percentage, we multiply by 100.
8. Thus, ε = 0.0423 * 100 ≈ 4.23%.
9. However, it's essential to note that the question asks for the average normal strain, which involves taking measurements at multiple points along the string and averaging the strains.
10. Since we have only one measurement point provided in the question, we consider it as the average strain for simplicity.
11. Therefore, the average normal strain in the string when stretched to the given position is approximately 4.23% or 0.0423.
