Answer:
The elastic potential energy stored in a spring is given by the formula:
\[ E = \frac{1}{2}kx^2 \]
Where:
- \( E \) is the elastic potential energy,
- \( k \) is the spring constant, and
- \( x \) is the displacement (stretch or compression) from the equilibrium position.
If the spring's stretch is doubled, the displacement becomes \( 2x \). Substituting this into the formula:
\[ E_1 = \frac{1}{2}k(2x)^2 = 2^2 \times \frac{1}{2}kx^2 = 4E \]
So, the elastic potential energy increases by a factor of 4.
If the spring's stretch is tripled, the displacement becomes \( 3x \). Substituting this into the formula:
\[ E_2 = \frac{1}{2}k(3x)^2 = 3^2 \times \frac{1}{2}kx^2 = 9E \]
So, the elastic potential energy increases by a factor of 9.
