Question

A spring is compressed by 0.2 meters and it exerts a force of 10 N. What is the spring constant (k)? Show your work using the GUESS method. You may use the math tool if needed.

Answer 1

To find the spring constant (k) using the information given, we can apply Hooke's Law, which states that the force exerted by a spring is proportional to the displacement (compression or elongation) of the spring from its equilibrium position. The equation is given by:

\[
F = k \cdot x
\]

Where:
- \( F \) is the force exerted by the spring (10 N)
- \( k \) is the spring constant (what we want to find)
- \( x \) is the displacement from the equilibrium position (0.2 m)

We will use the GUESS method to solve for \( k \).

**G - Given:**
- Force, \( F = 10 \, \text{N} \)
- Displacement, \( x = 0.2 \, \text{m} \)

**U - Unknown:**
- Spring constant, \( k \)

**E - Equation:**
Using Hooke's Law:
\[
F = k \cdot x
\]
We can rearrange this to solve for \( k \):
\[
k = \frac{F}{x}
\]

**S - Substitute:**
Substituting the known values into the equation:
\[
k = \frac{10 \, \text{N}}{0.2 \, \text{m}}
\]

**S - Solve:**
Now we will perform the calculation:
\[
k = \frac{10}{0.2} = 50 \, \text{N/m}
\]

**Final Answer:**
The spring constant \( k \) is \( 50 \, \text{N/m} \).