Answer:
the work required is 0.163 J
Explanation:
Given;
Energy applied to the spring, E = 2 J
initial length of the spring, x₀ = 32 cm
final length of the spring, x₁ = 46 cm
Extension of the spring, Δx = x₁ - x₀ = 46 cm - 32 cm = 14 cm = 0.14 m
The spring constant is calculated as follows;
E = ¹/₂kΔx²
[tex]k = \frac{2E}{(\Delta x)^2} = \frac{2\times 2}{(0.14)^2} = 204.1 \ N/m^2[/tex]
The extension of the spring when it is stretched from 37 cm + 41 cm:
Δx = 41 cm - 37 cm = 4 cm = 0.04 m
The work required:
W = ¹/₂kΔx²
W = ¹/₂ x (204.1) x (0.04)²
W = 0.163 J
Therefore, the work required is 0.163 J
