College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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![**Problem 8: Analyzing Forces on Mikey**
Mikey stops running and stands on a scale while checking out the scene. The scale reads 27.0 kg. Determine Mikey’s weight and the normal force exerted on him by the scale. (Include a free-body diagram.)
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To solve this problem, we need to consider the forces acting on Mikey when he stands on the scale. This involves understanding his weight and the normal force.
**Weight Calculation:**
1. Since the scale reads mass in kilograms, we can calculate Mikey's weight using the equation:
\[ \text{Weight} (W) = \text{mass} \times \text{gravity} \]
\[ W = 27.0 \, \text{kg} \times 9.8 \, \text{m/s}^2 \]
\[ W = 264.6 \, \text{N} \]
**Normal Force:**
- The normal force is the force exerted by the scale on Mikey. When Mikey is stationary and there are no other vertical forces, this force is equal in magnitude and opposite in direction to his weight. Therefore, the normal force is also 264.6 N.
**Free-Body Diagram: Explanation**
- A free-body diagram would show Mikey as a dot or box.
- Two main vertical forces act on him:
- **Weight (W):** Downward force represented by an arrow pointing down with the label \(264.6 \, \text{N}\).
- **Normal Force (N):** Upward force represented by an arrow pointing up with the label \(264.6 \, \text{N}\).
This setup confirms that Mikey is in equilibrium in the vertical direction, as his weight is balanced by the normal force.](https://content.bartleby.com/qna-images/question/4b08cbe3-b052-4a50-ae7b-da07c66e348c/f450707a-a321-4294-8336-5eb1a8e3c072/y3fulzv_processed.jpeg)
Transcribed Image Text:**Problem 8: Analyzing Forces on Mikey**
Mikey stops running and stands on a scale while checking out the scene. The scale reads 27.0 kg. Determine Mikey’s weight and the normal force exerted on him by the scale. (Include a free-body diagram.)
---
To solve this problem, we need to consider the forces acting on Mikey when he stands on the scale. This involves understanding his weight and the normal force.
**Weight Calculation:**
1. Since the scale reads mass in kilograms, we can calculate Mikey's weight using the equation:
\[ \text{Weight} (W) = \text{mass} \times \text{gravity} \]
\[ W = 27.0 \, \text{kg} \times 9.8 \, \text{m/s}^2 \]
\[ W = 264.6 \, \text{N} \]
**Normal Force:**
- The normal force is the force exerted by the scale on Mikey. When Mikey is stationary and there are no other vertical forces, this force is equal in magnitude and opposite in direction to his weight. Therefore, the normal force is also 264.6 N.
**Free-Body Diagram: Explanation**
- A free-body diagram would show Mikey as a dot or box.
- Two main vertical forces act on him:
- **Weight (W):** Downward force represented by an arrow pointing down with the label \(264.6 \, \text{N}\).
- **Normal Force (N):** Upward force represented by an arrow pointing up with the label \(264.6 \, \text{N}\).
This setup confirms that Mikey is in equilibrium in the vertical direction, as his weight is balanced by the normal force.
Expert Solution
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Step 1
Mikey is standing on the scale. The scale reads 27.0 kg. Determine Mikey's weight and the normal force exerted on him by the scale. Include a free-body diagram.
m = mass of Mikey = 27.0 kg
g = gravitational acceleration due to Earth = 9.81 m/s2
W = Mikey's weight = ?
N = normal force exerted on him by the scale = ?
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