Question

Using Hooke's law, F subscript s p r i n g end subscript equals k increment x, find the elastic constant of a spring that stretches 2 cm when a 4 newton force is applied to it.

Question 3 options:

1/2 image N/cm


2 N/cm


4 N/cm


8 N/cm

2.07 Quiz: Spring Force Pool 4
Question 4 (1 point)
Which statement is true according to Hooke's law?

Question 4 options:

If the force acting on a spring is doubled, the distance it stretches is halved.


If the force on a spring doubles, the distance it stretches doubles.


If the force on a spring doubles, the spring's length increases by some unknown amount.


If the force on a spring doubles, the spring's length decreases by some unknown amount.

2.07 Quiz: Spring Force Pool 5
Question 5 (1 point)
Using Hooke's law, F s p r i n g = k Δ x , find the force needed to stretch a spring 2 cm if it has an elastic constant of 3 N/cm.

Question 5 options:

2/3 image N


3/2 image N


3 N


6 N

Answer 1

Let's go through each question step by step using Hooke's law, which states that the force exerted by a spring is directly proportional to the distance it is stretched or compressed. This can be expressed mathematically as:

\[ F_{\text{spring}} = k \Delta x \]

where:
- \( F_{\text{spring}} \) is the force exerted by the spring,
- \( k \) is the elastic (spring) constant,
- \( \Delta x \) is the displacement from the spring's equilibrium position (the amount it is stretched or compressed).

### Question 3:
Find the elastic constant (\( k \)) of the spring that stretches 2 cm when a 4 newton force is applied.

1. Convert the displacement from cm to meters for standard SI units:
\[ \Delta x = 2 \, \text{cm} = 0.02 \, \text{m} \]

2. Rearrange Hooke's law to solve for \( k \):
\[ k = \frac{F_{\text{spring}}}{\Delta x} \]

3. Substitute the values:
\[ k = \frac{4 \, \text{N}}{0.02 \, \text{m}} = 200 \, \text{N/m} \]

To convert \( k \) into N/cm:
\[ 200 \, \text{N/m} = 200 \, \text{N}/100 \, \text{cm} = 2 \, \text{N/cm} \]

**Correct option for Question 3:** **2 N/cm**

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### Question 4:
Which statement is true according to Hooke's law?

- If the force acting on a spring is doubled, the distance it stretches is halved.
- **If the force on a spring doubles, the distance it stretches doubles.**
- If the force on a spring doubles, the spring's length increases by some unknown amount.
- If the force on a spring doubles, the spring's length decreases by some unknown amount.

**Correct option for Question 4:** **If the force on a spring doubles, the distance it stretches doubles.**

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### Question 5:
Find the force needed to stretch a spring 2 cm if it has an elastic constant of 3 N/cm.

1. Convert displacement from cm to meters:
\[ \Delta x = 2 \, \text{cm} = 0.02 \, \text{m} \]

2. Use Hooke's law to find \( F_{\text{spring}} \):
\[ F_{\text{spring}} = k \Delta x \]
Given \( k = 3 \, \text{N/cm} = 300 \, \text{N/m} \) (since 1 N/cm = 100 N/m),
Now substitute the values:
\[ F_{\text{spring}} = 3 \, \text{N/cm} \times 2 \, \text{cm} = 6 \, \text{N} \]

**Correct option for Question 5:** **6 N**