Same situation as in the previous problem this time the magnet has mass 5.05 kg, the force pulling it to the right is 143.8 N, the cord has length 1.39 m and the ceiling is 3.39 m above the floor. How far to the right of its start point will the magnet have traveled when it hits the floor after the cord is cut? 12.80 m 16.207 m 8.53 m 4.27 m
Same situation as in the previous problem this time the magnet has mass 5.05 kg, the force pulling it to the right is 143.8 N, the cord has length 1.39 m and the ceiling is 3.39 m above the floor. How far to the right of its start point will the magnet have traveled when it hits the floor after the cord is cut? 12.80 m 16.207 m 8.53 m 4.27 m
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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4. Same situation as in the previous problem this time the magnet has mass 5.05 kg, the force pulling it to the right is 143.8 N, the cord has length 1.39 m and the ceiling is 3.39 m above the floor. How far to the right of its start point will the magnet have traveled when it hits the floor after the cord is cut?
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12.80 m
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16.207 m
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8.53 m
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||
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4.27 m
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![### Pendulum Motion Analysis
#### Diagram Explanation:
The diagram illustrates a simple pendulum model, which consists of the following components:
1. **Pendulum String (L):**
- This is represented by a straight solid line denoted by \( L \). It indicates the length of the pendulum string from the pivot point to the center of the pendulum bob.
2. **Pendulum Bob:**
- A small circle at the bottom end of the string represents the pendulum bob, which is the mass at the end of the pendulum.
3. **Angle of Displacement (\(\theta\)):**
- The dotted lines indicate the angle \(\theta\) from the vertical resting position to the displacement position of the pendulum. This angle shows how far the pendulum has been displaced from its equilibrium position.
4. **Restoring Force (\(F_m\)):**
- Represented by an arrow labeled \( F_m \) pointing horizontally. This force acts perpendicular to the length of the pendulum and is responsible for the motion of the pendulum as it swings back and forth.
#### Understanding Pendulum Motion:
A simple pendulum consists of a mass (bob) attached to the end of a string, which in turn is connected to a fixed point. When displaced from its equilibrium position and released, the pendulum will swing back and forth because of the force of gravity and the tension in the string.
- **Angle (\(\theta\))**:
This is the angle between the string of the pendulum and the vertical line passing through the fixed point. The larger the angle, the greater the initial potential energy.
- **Pendulum Length (L)**:
The length of the string is a crucial factor in determining the period of the pendulum. The period \( T \) of a simple pendulum is given by:
\[
T = 2\pi \sqrt{\frac{L}{g}}
\]
where \( g \) is the acceleration due to gravity. This formula assumes small angles of displacement where \(\sin(\theta) \approx \theta\).
- **Restoring Force (\(F_m\))**:
This is the force that brings the pendulum back to its equilibrium position. The restoring force for a pendulum is a component of the gravitational force acting on the bob. It varies with the angle \(\theta\).
This diagram is fundamental in understanding the principles](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29ba052e-ec8e-416d-9ba2-17490093bce9%2F47b67320-6742-4e02-9ce3-7ace942bca18%2Fmfbqhwe_processed.png&w=3840&q=75)
Transcribed Image Text:### Pendulum Motion Analysis
#### Diagram Explanation:
The diagram illustrates a simple pendulum model, which consists of the following components:
1. **Pendulum String (L):**
- This is represented by a straight solid line denoted by \( L \). It indicates the length of the pendulum string from the pivot point to the center of the pendulum bob.
2. **Pendulum Bob:**
- A small circle at the bottom end of the string represents the pendulum bob, which is the mass at the end of the pendulum.
3. **Angle of Displacement (\(\theta\)):**
- The dotted lines indicate the angle \(\theta\) from the vertical resting position to the displacement position of the pendulum. This angle shows how far the pendulum has been displaced from its equilibrium position.
4. **Restoring Force (\(F_m\)):**
- Represented by an arrow labeled \( F_m \) pointing horizontally. This force acts perpendicular to the length of the pendulum and is responsible for the motion of the pendulum as it swings back and forth.
#### Understanding Pendulum Motion:
A simple pendulum consists of a mass (bob) attached to the end of a string, which in turn is connected to a fixed point. When displaced from its equilibrium position and released, the pendulum will swing back and forth because of the force of gravity and the tension in the string.
- **Angle (\(\theta\))**:
This is the angle between the string of the pendulum and the vertical line passing through the fixed point. The larger the angle, the greater the initial potential energy.
- **Pendulum Length (L)**:
The length of the string is a crucial factor in determining the period of the pendulum. The period \( T \) of a simple pendulum is given by:
\[
T = 2\pi \sqrt{\frac{L}{g}}
\]
where \( g \) is the acceleration due to gravity. This formula assumes small angles of displacement where \(\sin(\theta) \approx \theta\).
- **Restoring Force (\(F_m\))**:
This is the force that brings the pendulum back to its equilibrium position. The restoring force for a pendulum is a component of the gravitational force acting on the bob. It varies with the angle \(\theta\).
This diagram is fundamental in understanding the principles
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