You are handed a spring that is 0.25 m0.25 m long. You hang the spring from a hook on the ceiling and attach a 0.70 kg0.70 kg mass to the other end of the spring. The stretched spring is 0.37 m0.37 m. k=WΔLk=WΔL

What is the spring constant? 

A.32.8 Nm32.8 Nm

B.64.1 Nm64.1 Nm

C.57.2 Nm57.2 Nm

D.9.80 Nm9.80 Nm


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.

You are handed a spring that is 0.25 m long. You hang the spring from a hook on the ceiling and attach a 0.70 kg mass to the other end of the spring. The stretched spring is 0.37 m. What is the spring constant?
A. 32.8 N/m
B. 64.1 N/m
C. 57.2 N/m
D. 9.80 N/m

Learn how to calculate the spring constant using Hooke's Law for a spring with an initial length of 0.25 m and a mass of 0.70 kg. The spring stretches to 0.37 m, and we use the formula F = kΔL to find the correct spring constant. Suitable for students in Grades 9-12.

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