Question

Using Hooke's law, F s p r i n g = k Δ x , find the distance a spring with an elastic constant of 4 N/cm will stretch if a 2 newton force is applied to it.

Question 5 options:

Mathml image cm


2 cm


4 cm


8 cm

Answer 1

To find the distance a spring will stretch when a force is applied, we can use Hooke's law, which is given by the formula:

\[ F = k \Delta x \]

where:
- \( F \) is the force applied (in newtons),
- \( k \) is the spring constant (in N/cm),
- \( \Delta x \) is the distance the spring stretches (in cm).

Given:
- The spring constant \( k = 4 \, \text{N/cm} \)
- The applied force \( F = 2 \, \text{N} \)

We can rearrange Hooke's law to solve for \( \Delta x \):

\[ \Delta x = \frac{F}{k} \]

Now, plugging in the values:

\[ \Delta x = \frac{2 \, \text{N}}{4 \, \text{N/cm}} \]

\[ \Delta x = \frac{2}{4} \, \text{cm} \]

\[ \Delta x = 0.5 \, \text{cm} \]

Since the options you've provided are in whole centimeters, it appears there may be a misunderstanding or a typographical error in the question, as the computed stretch is 0.5 cm and does not match any of the provided options.

If you round or reconsider the values provided, please clarify the question further or check the data for any discrepancies.