To determine the spring constant $k$, we can use Hooke's Law:

$F = k \Delta L$

Where:

• $F$ is the force applied to the spring,
• $k$ is the spring constant,
• $\Delta L$ is the change in length of the spring.

Step 1: Calculate the force $F$

The force applied to the spring is the weight of the mass hanging from it, which can be calculated using:

$F = mg$

Where:

• $m = 0.70 \, \text{kg}$ (mass),
• $g = 9.8 \, \text{m/s}^2$ (acceleration due to gravity).

$F = 0.70 \times 9.8 = 6.86 \, \text{N}$

Step 2: Calculate the change in length $\Delta L$

The change in length is the difference between the stretched length and the original length of the spring:

$\Delta L = 0.37 \, \text{m} - 0.25 \, \text{m} = 0.12 \, \text{m}$

Step 3: Calculate the spring constant $k$

Using Hooke's Law, rearrange for $k$:

$k = \frac{F}{\Delta L} = \frac{6.86}{0.12} = 57.17 \, \text{N/m}$

Step 4: Round the value

After rounding, we get $k \approx 57.2 \, \text{N/m}$.

Thus, the correct answer is:

C. 57.2 N/m

Would you like further details or have any questions?

Here are 5 related questions:

1. How does increasing mass affect the stretch of the spring?
2. What is Hooke's Law, and how does it apply to real-world scenarios?
3. How would the spring constant change if the mass were doubled?
4. What factors can affect the accuracy of calculating the spring constant in a real experiment?
5. How can you measure the spring constant experimentally?

Tip: Always ensure you use consistent units when working with formulas involving force, length, and mass.