A spring has a spring constant of 63.4 N/m. The spring is stretched 0.9 m. What force was needed to stretch the spring? Show your work and use the correct units in your answer.(2 points)

Answer 1

To calculate the force needed to stretch a spring, we can use Hooke’s Law, which is given by the equation:

\[ F = k \cdot x \]

where:

• \( F \) is the force exerted by the spring (in Newtons, N),
• \( k \) is the spring constant (in Newtons per meter, N/m),
• \( x \) is the displacement of the spring from its equilibrium position (in meters, m).

Given:

• \( k = 63.4 , \text{N/m} \)
• \( x = 0.9 , \text{m} \)

Now, substituting the given values into the formula:

\[ F = 63.4 , \text{N/m} \times 0.9 , \text{m} \]

Calculating the force:

\[ F = 63.4 \times 0.9 = 57.06 , \text{N} \]

Thus, the force needed to stretch the spring is:

\[ \boxed{57.06 , \text{N}} \]