A force of 10 N holds an ideal spring with a `20 N/m` spring constant in compression. The potential energy stored in the spring is

Options

A. `0.5`J
B. `2.5`J
C. `5`J
D. 10 J

Answer

To find the potential energy stored in the spring when a force is applied, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Force (F) = 10 N
- Spring constant (k) = 20 N/m

2. **Use Hooke's Law to Find Compression (x):**
Hooke's Law states that the force applied to a spring is proportional to its compression or extension:
\[ F = k \cdot x \]
Rearranging this gives:
\[ x = \frac{F}{k} \]
Substituting the known values:
\[ x = \frac{10 \, \text{N}}{20 \, \text{N/m}} = 0.5 \, \text{m} \]

3. **Calculate the Potential Energy (U) Stored in the Spring:**
The potential energy stored in a spring is given by the formula:
\[ U = \frac{1}{2} k x^2 \]
Substituting the values of k and x:
\[ U = \frac{1}{2} \cdot 20 \, \text{N/m} \cdot (0.5 \, \text{m})^2 \]
\[ U = \frac{1}{2} \cdot 20 \cdot 0.25 \]
\[ U = 10 \cdot 0.25 = 2.5 \, \text{J} \]

4. **Conclusion:**
The potential energy stored in the spring is:
\[ U = 2.5 \, \text{J} \]