Question
A spring has a spring constant of 63.4 N/m. The spring is stretched 0.9 m. What force was needed to stretch the spring? Show your work and use the correct units in your answer.(2 points)
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To calculate the force needed to stretch a spring, we can use Hooke’s Law, which is given by the equation:
\[
F = k \cdot x
\]
where:
- \( F \) is the force exerted by the spring (in Newtons, N),
- \( k \) is the spring constant (in Newtons per meter, N/m),
- \( x \) is the displacement of the spring from its equilibrium position (in meters, m).
Given:
- \( k = 63.4 \, \text{N/m} \)
- \( x = 0.9 \, \text{m} \)
Now, substituting the given values into the formula:
\[
F = 63.4 \, \text{N/m} \times 0.9 \, \text{m}
\]
Calculating the force:
\[
F = 63.4 \times 0.9 = 57.06 \, \text{N}
\]
Thus, the force needed to stretch the spring is:
\[
\boxed{57.06 \, \text{N}}
\]
\[
F = k \cdot x
\]
where:
- \( F \) is the force exerted by the spring (in Newtons, N),
- \( k \) is the spring constant (in Newtons per meter, N/m),
- \( x \) is the displacement of the spring from its equilibrium position (in meters, m).
Given:
- \( k = 63.4 \, \text{N/m} \)
- \( x = 0.9 \, \text{m} \)
Now, substituting the given values into the formula:
\[
F = 63.4 \, \text{N/m} \times 0.9 \, \text{m}
\]
Calculating the force:
\[
F = 63.4 \times 0.9 = 57.06 \, \text{N}
\]
Thus, the force needed to stretch the spring is:
\[
\boxed{57.06 \, \text{N}}
\]
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.