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![### Ferris Wheel Physics Problem
**Scenario:**
A child rides on a Ferris wheel with a radius of 12.2 m at a constant speed of 2.75 m/s as shown in the figures. The child moves in a vertical circle.
**Figures:**
- **(a)** Shows the side view of a Ferris wheel with two positions: top and bottom for the child.
- **(b)** Top view indicating the forces acting on the child at different points of the path.
- Vector diagrams illustrating forces on the child at the top and bottom positions of the ride.
---
**Problem (a): Determine the force exerted by the seat on the child at the bottom of the ride. Express in terms of the child’s weight (mg).**
**Solution:**
**Conceptualize:**
- When the child is at the top of the Ferris wheel, gravitational force (weight) and the seat's normal force both act downwards.
- At the bottom, gravity acts downward and the seat’s normal force acts upward against the child’s weight.
**Using Uniform Circular Motion:**
- **Equation:** \(\sum F = m a_c\)
- Acceleration (\(a_c\)) at bottom (\(v^2/r\))
**Calculations:**
1. **Net Force at Bottom** \( N_{bottom} = mg + \frac{mv^2}{r} \)
**Substitute values:**
\[ N_{bottom} = mg + \frac{m (2.75)^2}{12.2} \]
**Magnitude of Normal Force:**
- Greater than the child’s weight at the bottom.
---
**Problem (b): Determine the force exerted by the seat on the child at the top of the ride.**
**Solution:**
**Using Uniform Circular Motion:**
- **Equation:** \(\sum F = m a_c\)
- At the top of the ride, the forces are \(N_{top}\) and weight:
**Calculations:**
1. **Net Force at Top** \( N_{top} = mg - \frac{mv^2}{r} \)
**Substitute values:**
\[ N_{top} = mg - \frac{m (2.75)^2}{12.2} \]
**Magnitude of Normal Force:**
- Less than the child’s weight at the top.
---
**Exercise:**
Calculate the force on](https://content.bartleby.com/qna-images/question/985fbb06-c2de-4830-a5c1-9e4f21ac13aa/d874631c-f0aa-4693-b2f1-e13b6d528256/tiujyap_processed.png)
Transcribed Image Text:### Ferris Wheel Physics Problem
**Scenario:**
A child rides on a Ferris wheel with a radius of 12.2 m at a constant speed of 2.75 m/s as shown in the figures. The child moves in a vertical circle.
**Figures:**
- **(a)** Shows the side view of a Ferris wheel with two positions: top and bottom for the child.
- **(b)** Top view indicating the forces acting on the child at different points of the path.
- Vector diagrams illustrating forces on the child at the top and bottom positions of the ride.
---
**Problem (a): Determine the force exerted by the seat on the child at the bottom of the ride. Express in terms of the child’s weight (mg).**
**Solution:**
**Conceptualize:**
- When the child is at the top of the Ferris wheel, gravitational force (weight) and the seat's normal force both act downwards.
- At the bottom, gravity acts downward and the seat’s normal force acts upward against the child’s weight.
**Using Uniform Circular Motion:**
- **Equation:** \(\sum F = m a_c\)
- Acceleration (\(a_c\)) at bottom (\(v^2/r\))
**Calculations:**
1. **Net Force at Bottom** \( N_{bottom} = mg + \frac{mv^2}{r} \)
**Substitute values:**
\[ N_{bottom} = mg + \frac{m (2.75)^2}{12.2} \]
**Magnitude of Normal Force:**
- Greater than the child’s weight at the bottom.
---
**Problem (b): Determine the force exerted by the seat on the child at the top of the ride.**
**Solution:**
**Using Uniform Circular Motion:**
- **Equation:** \(\sum F = m a_c\)
- At the top of the ride, the forces are \(N_{top}\) and weight:
**Calculations:**
1. **Net Force at Top** \( N_{top} = mg - \frac{mv^2}{r} \)
**Substitute values:**
\[ N_{top} = mg - \frac{m (2.75)^2}{12.2} \]
**Magnitude of Normal Force:**
- Less than the child’s weight at the top.
---
**Exercise:**
Calculate the force on
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