Welcome to the article The spring in a retractable ballpoint pen is 1 8 cm long with a spring constant of tex 320 text N m tex When the. On this page, you will learn the essential and logical steps to better understand the topic being discussed. We hope the information provided helps you gain valuable insights and is easy to follow. Let’s begin the discussion!
Answer :
Certainly! Let's go through the problem step by step to understand how to find the energy required to extend the pen.
1. Understanding the System:
- We have a spring in a pen with a spring constant ([tex]\(k\)[/tex]) of [tex]\(320 \, \text{N/m}\)[/tex].
- When the pen is retracted, the spring is initially compressed by [tex]\(1.0 \, \text{mm}\)[/tex] (which is [tex]\(0.001 \, \text{m}\)[/tex]).
- When the button is clicked, the spring is compressed by an additional [tex]\(5.0 \, \text{mm}\)[/tex] (which is [tex]\(0.005 \, \text{m}\)[/tex]).
2. Calculate Total Compression when Extended:
- The total compression of the spring when the pen is extended is the initial compression plus the additional compression:
[tex]\[
\text{Total Compression} = 0.001 \, \text{m} + 0.005 \, \text{m} = 0.006 \, \text{m}
\][/tex]
3. Energy Stored in the Spring:
- The energy stored in a compressed spring is given by the formula:
[tex]\[
U = \frac{1}{2} k x^2
\][/tex]
- Initial Energy (when compressed by 1.0 mm):
- Using the initial compression [tex]\(x = 0.001 \, \text{m}\)[/tex]:
[tex]\[
U_{\text{initial}} = \frac{1}{2} \times 320 \, \text{N/m} \times (0.001)^2 = 0.00016 \, \text{J}
\][/tex]
- Total Energy (when compressed by 6.0 mm):
- Using the total compression [tex]\(x = 0.006 \, \text{m}\)[/tex]:
[tex]\[
U_{\text{total}} = \frac{1}{2} \times 320 \, \text{N/m} \times (0.006)^2 = 0.00576 \, \text{J}
\][/tex]
4. Energy Required to Extend the Pen:
- The energy required to compress the spring from the initial to the total state is the difference between the total energy and the initial energy:
[tex]\[
\text{Energy Required} = U_{\text{total}} - U_{\text{initial}} = 0.00576 \, \text{J} - 0.00016 \, \text{J} = 0.00560 \, \text{J}
\][/tex]
- Rounding this to three significant figures, we have:
[tex]\[
\text{Energy Required} = 0.006 \, \text{J}
\][/tex]
So, the energy required to extend the pen is [tex]\(0.006 \, \text{J}\)[/tex].
1. Understanding the System:
- We have a spring in a pen with a spring constant ([tex]\(k\)[/tex]) of [tex]\(320 \, \text{N/m}\)[/tex].
- When the pen is retracted, the spring is initially compressed by [tex]\(1.0 \, \text{mm}\)[/tex] (which is [tex]\(0.001 \, \text{m}\)[/tex]).
- When the button is clicked, the spring is compressed by an additional [tex]\(5.0 \, \text{mm}\)[/tex] (which is [tex]\(0.005 \, \text{m}\)[/tex]).
2. Calculate Total Compression when Extended:
- The total compression of the spring when the pen is extended is the initial compression plus the additional compression:
[tex]\[
\text{Total Compression} = 0.001 \, \text{m} + 0.005 \, \text{m} = 0.006 \, \text{m}
\][/tex]
3. Energy Stored in the Spring:
- The energy stored in a compressed spring is given by the formula:
[tex]\[
U = \frac{1}{2} k x^2
\][/tex]
- Initial Energy (when compressed by 1.0 mm):
- Using the initial compression [tex]\(x = 0.001 \, \text{m}\)[/tex]:
[tex]\[
U_{\text{initial}} = \frac{1}{2} \times 320 \, \text{N/m} \times (0.001)^2 = 0.00016 \, \text{J}
\][/tex]
- Total Energy (when compressed by 6.0 mm):
- Using the total compression [tex]\(x = 0.006 \, \text{m}\)[/tex]:
[tex]\[
U_{\text{total}} = \frac{1}{2} \times 320 \, \text{N/m} \times (0.006)^2 = 0.00576 \, \text{J}
\][/tex]
4. Energy Required to Extend the Pen:
- The energy required to compress the spring from the initial to the total state is the difference between the total energy and the initial energy:
[tex]\[
\text{Energy Required} = U_{\text{total}} - U_{\text{initial}} = 0.00576 \, \text{J} - 0.00016 \, \text{J} = 0.00560 \, \text{J}
\][/tex]
- Rounding this to three significant figures, we have:
[tex]\[
\text{Energy Required} = 0.006 \, \text{J}
\][/tex]
So, the energy required to extend the pen is [tex]\(0.006 \, \text{J}\)[/tex].
Thank you for reading the article The spring in a retractable ballpoint pen is 1 8 cm long with a spring constant of tex 320 text N m tex When the. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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Rewritten by : Brahmana