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

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