4. A Ferris wheel of radius 15 m turns clockwise as shown. A man of mass 70 kg stands on a scale in the Ferris wheel car without slipping. At the time shown, the man is moving down at 4 m/s but speeding up at a rate of 1.5 m/s?. a. Draw the free body diagram showing the forces on the man. b. What is the static friction force acting on the man? c. What does the scale read at this time? d. Now assume that the man's shoes just start slipping on the scale at this time. What is the coefficient of static friction between the man shoes and the scale?

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**Problem 4: Analyzing a Ferris Wheel Scenario**

A Ferris wheel of radius 15 meters turns clockwise as shown. A man of mass 70 kg stands on a scale in the Ferris wheel car without slipping. At the time shown, the man is moving down at 4 m/s but speeding up at a rate of 1.5 m/s².

**Tasks:**

a. **Draw the free body diagram showing the forces on the man.**

- Diagram Explanation: The diagram should include the gravitational force (weight) acting downward, the normal force from the scale acting upward, and possibly a static friction force acting horizontally if necessary to prevent slipping, depending on the configuration of the Ferris wheel car.

b. **What is the static friction force acting on the man?**

- Calculation steps: To be determined based on forces in the vertical and, potentially, horizontal direction.

c. **What does the scale read at this time?**

- Explanation: The reading on the scale would be equivalent to the normal force exerted by the man, adjusted for the acceleration due to the motion of the Ferris wheel.

d. **Now assume that the man’s shoes just start slipping on the scale at this time. What is the coefficient of static friction between the man’s shoes and the scale?**

- Explanation and formula: The coefficient of static friction can be calculated using the maximum static friction force that prevented slipping initially, using the formula: 
   
   \[ F_{\text{friction, max}} = \mu_s \cdot F_{\text{normal}} \]

- To calculate: Identify the actual forces based on given values to determine \(\mu_s\).
Transcribed Image Text:**Problem 4: Analyzing a Ferris Wheel Scenario** A Ferris wheel of radius 15 meters turns clockwise as shown. A man of mass 70 kg stands on a scale in the Ferris wheel car without slipping. At the time shown, the man is moving down at 4 m/s but speeding up at a rate of 1.5 m/s². **Tasks:** a. **Draw the free body diagram showing the forces on the man.** - Diagram Explanation: The diagram should include the gravitational force (weight) acting downward, the normal force from the scale acting upward, and possibly a static friction force acting horizontally if necessary to prevent slipping, depending on the configuration of the Ferris wheel car. b. **What is the static friction force acting on the man?** - Calculation steps: To be determined based on forces in the vertical and, potentially, horizontal direction. c. **What does the scale read at this time?** - Explanation: The reading on the scale would be equivalent to the normal force exerted by the man, adjusted for the acceleration due to the motion of the Ferris wheel. d. **Now assume that the man’s shoes just start slipping on the scale at this time. What is the coefficient of static friction between the man’s shoes and the scale?** - Explanation and formula: The coefficient of static friction can be calculated using the maximum static friction force that prevented slipping initially, using the formula: \[ F_{\text{friction, max}} = \mu_s \cdot F_{\text{normal}} \] - To calculate: Identify the actual forces based on given values to determine \(\mu_s\).
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