### Static Electricity and Forces – Educational Scenario #### Scenario Description: In the image, Zoey is trying to hold up the weight of her body using a balloon she rubbed on her head. She uses the balloon's static electricity to cling to the ceiling. This is a creative way to explore static electricity and the forces at play. #### Detailed Explanation: Zoey decides to test if static electricity is strong enough to hold her weight. She rubs a balloon on her head, transferring electrons from her hair to the balloon. She then holds it up to the ceiling, hoping the attraction between the negatively charged balloon and the positively charged ceiling can support her. #### Problem to Solve: **Given Data:** - Zoey weighs 600N. - The charge on the balloon (\( q_1 \)) is \( 5 \times 10^{-9} \) C. - The distance (\( r \)) between the balloon and the ceiling is \( 4.0 \times 10^{-3} \) m. **Question:** What must be the charge on the ceiling (\( q_2 \)) to create a force of static electricity equal to Zoey's weight? **Solution:** Using Coulomb’s Law: \[ F = k \frac{|q_1 \cdot q_2|}{r^2} \] Where: - \( F \) is the force (600N). - \( k \) is Coulomb's constant (\( 8.99 \times 10^9 \, \text{N} \cdot \text{m}^2 / \text{C}^2 \)). - \( q_1 \) is the charge on the balloon. - \( q_2 \) is the charge on the ceiling we need to find. - \( r \) is the distance between the charges. Rearranging for \( q_2 \): \[ q_2 = \frac{F \cdot r^2}{k \cdot q_1} \] Substitute the known values: \[ q_2 = \frac{600 \cdot (4.0 \times 10^{-3})^2}{(8.99 \times 10^9) \cdot (5 \times 10^{-9})} \] Simplify the values: \[ q_2 = \frac{600 \cdot 16 \times 10^{-
### Static Electricity and Forces – Educational Scenario #### Scenario Description: In the image, Zoey is trying to hold up the weight of her body using a balloon she rubbed on her head. She uses the balloon's static electricity to cling to the ceiling. This is a creative way to explore static electricity and the forces at play. #### Detailed Explanation: Zoey decides to test if static electricity is strong enough to hold her weight. She rubs a balloon on her head, transferring electrons from her hair to the balloon. She then holds it up to the ceiling, hoping the attraction between the negatively charged balloon and the positively charged ceiling can support her. #### Problem to Solve: **Given Data:** - Zoey weighs 600N. - The charge on the balloon (\( q_1 \)) is \( 5 \times 10^{-9} \) C. - The distance (\( r \)) between the balloon and the ceiling is \( 4.0 \times 10^{-3} \) m. **Question:** What must be the charge on the ceiling (\( q_2 \)) to create a force of static electricity equal to Zoey's weight? **Solution:** Using Coulomb’s Law: \[ F = k \frac{|q_1 \cdot q_2|}{r^2} \] Where: - \( F \) is the force (600N). - \( k \) is Coulomb's constant (\( 8.99 \times 10^9 \, \text{N} \cdot \text{m}^2 / \text{C}^2 \)). - \( q_1 \) is the charge on the balloon. - \( q_2 \) is the charge on the ceiling we need to find. - \( r \) is the distance between the charges. Rearranging for \( q_2 \): \[ q_2 = \frac{F \cdot r^2}{k \cdot q_1} \] Substitute the known values: \[ q_2 = \frac{600 \cdot (4.0 \times 10^{-3})^2}{(8.99 \times 10^9) \cdot (5 \times 10^{-9})} \] Simplify the values: \[ q_2 = \frac{600 \cdot 16 \times 10^{-
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
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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![### Static Electricity and Forces – Educational Scenario
#### Scenario Description:
In the image, Zoey is trying to hold up the weight of her body using a balloon she rubbed on her head. She uses the balloon's static electricity to cling to the ceiling. This is a creative way to explore static electricity and the forces at play.
#### Detailed Explanation:
Zoey decides to test if static electricity is strong enough to hold her weight. She rubs a balloon on her head, transferring electrons from her hair to the balloon. She then holds it up to the ceiling, hoping the attraction between the negatively charged balloon and the positively charged ceiling can support her.
#### Problem to Solve:
**Given Data:**
- Zoey weighs 600N.
- The charge on the balloon (\( q_1 \)) is \( 5 \times 10^{-9} \) C.
- The distance (\( r \)) between the balloon and the ceiling is \( 4.0 \times 10^{-3} \) m.
**Question:**
What must be the charge on the ceiling (\( q_2 \)) to create a force of static electricity equal to Zoey's weight?
**Solution:**
Using Coulomb’s Law:
\[ F = k \frac{|q_1 \cdot q_2|}{r^2} \]
Where:
- \( F \) is the force (600N).
- \( k \) is Coulomb's constant (\( 8.99 \times 10^9 \, \text{N} \cdot \text{m}^2 / \text{C}^2 \)).
- \( q_1 \) is the charge on the balloon.
- \( q_2 \) is the charge on the ceiling we need to find.
- \( r \) is the distance between the charges.
Rearranging for \( q_2 \):
\[ q_2 = \frac{F \cdot r^2}{k \cdot q_1} \]
Substitute the known values:
\[ q_2 = \frac{600 \cdot (4.0 \times 10^{-3})^2}{(8.99 \times 10^9) \cdot (5 \times 10^{-9})} \]
Simplify the values:
\[ q_2 = \frac{600 \cdot 16 \times 10^{-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F207e939d-794f-42c8-b3db-71aa5db8695e%2F75719fb0-3856-4784-80dd-293596eefd1d%2Fey5p6y_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Static Electricity and Forces – Educational Scenario
#### Scenario Description:
In the image, Zoey is trying to hold up the weight of her body using a balloon she rubbed on her head. She uses the balloon's static electricity to cling to the ceiling. This is a creative way to explore static electricity and the forces at play.
#### Detailed Explanation:
Zoey decides to test if static electricity is strong enough to hold her weight. She rubs a balloon on her head, transferring electrons from her hair to the balloon. She then holds it up to the ceiling, hoping the attraction between the negatively charged balloon and the positively charged ceiling can support her.
#### Problem to Solve:
**Given Data:**
- Zoey weighs 600N.
- The charge on the balloon (\( q_1 \)) is \( 5 \times 10^{-9} \) C.
- The distance (\( r \)) between the balloon and the ceiling is \( 4.0 \times 10^{-3} \) m.
**Question:**
What must be the charge on the ceiling (\( q_2 \)) to create a force of static electricity equal to Zoey's weight?
**Solution:**
Using Coulomb’s Law:
\[ F = k \frac{|q_1 \cdot q_2|}{r^2} \]
Where:
- \( F \) is the force (600N).
- \( k \) is Coulomb's constant (\( 8.99 \times 10^9 \, \text{N} \cdot \text{m}^2 / \text{C}^2 \)).
- \( q_1 \) is the charge on the balloon.
- \( q_2 \) is the charge on the ceiling we need to find.
- \( r \) is the distance between the charges.
Rearranging for \( q_2 \):
\[ q_2 = \frac{F \cdot r^2}{k \cdot q_1} \]
Substitute the known values:
\[ q_2 = \frac{600 \cdot (4.0 \times 10^{-3})^2}{(8.99 \times 10^9) \cdot (5 \times 10^{-9})} \]
Simplify the values:
\[ q_2 = \frac{600 \cdot 16 \times 10^{-
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