A diver of mass 75.6 kg stands on one end of a diving board of mass 39.1 kg, as shown in the diagram. Everything is in equilibrium (since nothing is moving). What is the magnitude of the support force on the opposite end of the diving board?
A diver of mass 75.6 kg stands on one end of a diving board of mass 39.1 kg, as shown in the diagram. Everything is in equilibrium (since nothing is moving). What is the magnitude of the support force on the opposite end of the diving board?
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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A diver of mass 75.6 kg stands on one end of a diving board of mass 39.1 kg, as shown in the diagram. Everything is in equilibrium (since nothing is moving). What is the magnitude of the support force on the opposite end of the diving board?2,345 N503 N1,675 N838 N
![**Physics of Diving Boards: Understanding Lever Mechanics**
In the illustration provided, we observe a diver standing at the end of a diving board. This image serves as a wonderful example to discuss the principles of lever mechanics and equilibrium in physics.
### Description of the Diagram:
1. **The Diving Board Setup**:
- The image features a diver standing on the far end of a horizontal diving board.
- The diving board is supported at a point 1.00 meter from the left end, and the distance from this support to where the diver stands is 2.00 meters.
- There is a vertical ladder or support structure back on the leftmost end of the board, which appears to be attached to the diving platform.
2. **Distance Measurements**:
- The distance between the end of the diving board furthest from the diver (the left end) and the support point is labeled as **1.00 meter**.
- The distance between the support point and the diver (standing to the right of the support) is labeled as **2.00 meters**.
### Explanation:
1. **Lever Arm & Fulcrum**:
- In this scenario, the diving board acts as a lever, with the support point acting as the fulcrum. The diver's weight provides a downward force at a distance of 2.00 meters from the fulcrum.
2. **Calculating Torques**:
- The torque \( \tau \) about the fulcrum due to the diver’s weight can be calculated using the formula:
\[
\tau = r \times F
\]
where \( r \) is the distance from the fulcrum, and \( F \) is the force (weight of the diver).
3. **Static Equilibrium**:
- For the diving board to be in equilibrium, the sum of the torques around the fulcrum must be zero. This involves considering torques produced by the diver’s weight and the reactive forces at the supports.
Understanding these principles is crucial in designing stable and safe diving boards, as it ensures they can withstand the forces applied by divers standing or jumping on them. This example illustrates the practical application of physics concepts such as lever mechanics, torque, and equilibrium in everyday structures and activities.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29ba052e-ec8e-416d-9ba2-17490093bce9%2Fae4f30cd-42a0-499d-b857-db02fe3e6e1e%2Furd51r8_processed.png&w=3840&q=75)
Transcribed Image Text:**Physics of Diving Boards: Understanding Lever Mechanics**
In the illustration provided, we observe a diver standing at the end of a diving board. This image serves as a wonderful example to discuss the principles of lever mechanics and equilibrium in physics.
### Description of the Diagram:
1. **The Diving Board Setup**:
- The image features a diver standing on the far end of a horizontal diving board.
- The diving board is supported at a point 1.00 meter from the left end, and the distance from this support to where the diver stands is 2.00 meters.
- There is a vertical ladder or support structure back on the leftmost end of the board, which appears to be attached to the diving platform.
2. **Distance Measurements**:
- The distance between the end of the diving board furthest from the diver (the left end) and the support point is labeled as **1.00 meter**.
- The distance between the support point and the diver (standing to the right of the support) is labeled as **2.00 meters**.
### Explanation:
1. **Lever Arm & Fulcrum**:
- In this scenario, the diving board acts as a lever, with the support point acting as the fulcrum. The diver's weight provides a downward force at a distance of 2.00 meters from the fulcrum.
2. **Calculating Torques**:
- The torque \( \tau \) about the fulcrum due to the diver’s weight can be calculated using the formula:
\[
\tau = r \times F
\]
where \( r \) is the distance from the fulcrum, and \( F \) is the force (weight of the diver).
3. **Static Equilibrium**:
- For the diving board to be in equilibrium, the sum of the torques around the fulcrum must be zero. This involves considering torques produced by the diver’s weight and the reactive forces at the supports.
Understanding these principles is crucial in designing stable and safe diving boards, as it ensures they can withstand the forces applied by divers standing or jumping on them. This example illustrates the practical application of physics concepts such as lever mechanics, torque, and equilibrium in everyday structures and activities.
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