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 \( 50 , \text{N/m} \).