5. (II) When an object such as a plastic comb is charged by rubbing it with a cloth, the net charge is typically a few microcoulombs. If that charge is 3.0 μC, by what percentage does the mass of a 9.0-g comb change during charging?
5. (II) When an object such as a plastic comb is charged by rubbing it with a cloth, the net charge is typically a few microcoulombs. If that charge is 3.0 μC, by what percentage does the mass of a 9.0-g comb change during charging?
College Physics
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Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![### Problem 5: Charging and Mass Change in a Plastic Comb
**Problem Statement:**
When an object such as a plastic comb is charged by rubbing it with a cloth, the net charge is typically a few microcoulombs. If that charge is 3.0 µC, by what percentage does the mass of a 9.0-g comb change during charging?
**Detailed Explanation:**
This problem involves understanding the relationship between charge and mass in the context of charging a plastic comb by rubbing it with a cloth. Here’s a systematic approach to solving this problem:
1. **Identify the Charge and Mass:**
- Charge acquired by the comb: 3.0 µC (microcoulombs)
- Mass of the plastic comb: 9.0 g (grams)
2. **Understanding Charge and Mass Change:**
- The charge, measured in coulombs, indicates the amount of electric charge the comb has acquired.
- The mass change is due to the transfer of electrons (or the removal of them) from or to the comb. Each electron has a small mass, hence we need to calculate the total mass change due to the transferred electrons.
3. **Calculate the Number of Electrons Transferred:**
- Use the elementary charge (e) which is approximately \(1.602 \times 10^{-19}\) C (coulombs).
- Number of electrons (\(N\)) can be obtained by dividing the total charge (\(Q\)) by the elementary charge (\(e\)):
\[
N = \frac{Q}{e} = \frac{3.0 \times 10^{-6} \ \text{C}}{1.602 \times 10^{-19} \ \text{C/electron}} \approx 1.87 \times 10^{13} \ \text{electrons}
\]
4. **Calculate the Mass Change:**
- The mass of one electron is approximately \(9.109 \times 10^{-31} \ \text{kg}\).
- The total mass change (\(\Delta m\)) is the number of electrons times the mass of a single electron:
\[
\Delta m = N \times m_e = (1.87 \times 10^{13} \ \text{electrons}) \times (9.109 \times 10^{-31} \ \text](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F22536c29-fcc1-4871-92e0-85fb58db97f7%2F2c976063-66b8-49a6-ba4a-05994eb7a1a7%2F23z7c7r_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem 5: Charging and Mass Change in a Plastic Comb
**Problem Statement:**
When an object such as a plastic comb is charged by rubbing it with a cloth, the net charge is typically a few microcoulombs. If that charge is 3.0 µC, by what percentage does the mass of a 9.0-g comb change during charging?
**Detailed Explanation:**
This problem involves understanding the relationship between charge and mass in the context of charging a plastic comb by rubbing it with a cloth. Here’s a systematic approach to solving this problem:
1. **Identify the Charge and Mass:**
- Charge acquired by the comb: 3.0 µC (microcoulombs)
- Mass of the plastic comb: 9.0 g (grams)
2. **Understanding Charge and Mass Change:**
- The charge, measured in coulombs, indicates the amount of electric charge the comb has acquired.
- The mass change is due to the transfer of electrons (or the removal of them) from or to the comb. Each electron has a small mass, hence we need to calculate the total mass change due to the transferred electrons.
3. **Calculate the Number of Electrons Transferred:**
- Use the elementary charge (e) which is approximately \(1.602 \times 10^{-19}\) C (coulombs).
- Number of electrons (\(N\)) can be obtained by dividing the total charge (\(Q\)) by the elementary charge (\(e\)):
\[
N = \frac{Q}{e} = \frac{3.0 \times 10^{-6} \ \text{C}}{1.602 \times 10^{-19} \ \text{C/electron}} \approx 1.87 \times 10^{13} \ \text{electrons}
\]
4. **Calculate the Mass Change:**
- The mass of one electron is approximately \(9.109 \times 10^{-31} \ \text{kg}\).
- The total mass change (\(\Delta m\)) is the number of electrons times the mass of a single electron:
\[
\Delta m = N \times m_e = (1.87 \times 10^{13} \ \text{electrons}) \times (9.109 \times 10^{-31} \ \text
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