The first linear graph shows that the Force of Gravity depends is directly proportional to the mass of an object at a given location. The second linear graph shows that the Force of Gravity is proportional to the Inverse Square of the distance between two bodies. Research Newton’s Universal Law of Gravitation, and explain.
The first linear graph shows that the Force of Gravity depends is directly proportional to the mass of an object at a given location. The second linear graph shows that the Force of Gravity is proportional to the Inverse Square of the distance between two bodies. Research Newton’s Universal Law of Gravitation, and explain.
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The first linear graph shows that the Force of Gravity depends is directly proportional to the mass of an object at a given location. The second linear graph shows that the Force of Gravity is proportional to the Inverse Square of the distance between two bodies. Research Newton’s Universal Law of Gravitation, and explain.
Transcribed Image Text:**Vernier Graphical Analysis: Gravitational Force vs. Manipulated Variable**
This graph displays the relationship between Gravitational Force (N) and a manipulated variable. The graph presents a linear trend, indicated by a blue line, suggesting a direct proportionality between the two variables.
**Graph Details:**
- **Y-axis**: Gravitational Force (N), ranging from 0 to 8,000 N.
- **X-axis**: Manipulated Variable, ranging from 0.01 to 0.25.
**Data Table:**
The accompanying table provides specific data points plotted on the graph:
| Gravitational Force (N) | Manipulated Variable |
|-------------------------|----------------------|
| 320 | 0.010000 |
| 500 | 0.015600 |
| 888 | 0.027800 |
| 2000 | 0.062500 |
| 8000 | 0.250000 |
In this analysis, as the manipulated variable increases, the gravitational force also increases linearly, illustrating a strong linear relationship. This can be used to understand how changes in the manipulated variable affect gravitational force, likely in an experimental or simulation context.
**Mode**: The graph is in Manual Entry mode, allowing users to input their own data for analysis.
![**Vernier Graphical Analysis: Mass and Weight Relationship**
This graph represents the linear relationship between mass (in kilograms) and weight (in newtons). The data is plotted on a cartesian plane with mass on the x-axis and weight on the y-axis.
**Graph Title:** Untitled
**Axes:**
- **X-axis (Mass in kg):** Ranges from 5 to 25 kg
- **Y-axis (Weight in N):** Ranges from 50 to 250 N
**Data Points:**
1. (5, 49)
2. (10, 98)
3. (15, 147)
4. (20, 196)
5. (25, 245)
These points show a direct proportionality between mass and weight. The linear fit is represented by the equation \( y = mx + b \), where:
- **m (slope):** 9.8
- **b (y-intercept):** 0
- **r (correlation coefficient):** 1
- **RMSE (Root Mean Square Error):** \( 1.641 \times 10^{-14} \)
The slope of 9.8 is significant as it represents the acceleration due to gravity. The correlation coefficient, \( r = 1 \), indicates a perfect linear relationship. The RMSE value is extremely low, confirming the accuracy of this linear model.
**Observation Table:** Data Set 1
- **Mass (kg)**: [5, 10, 15, 20, 25]
- **Weight (N)**: [49, 98, 147, 196, 245]
This analysis illustrates the fundamental physics concept that weight is the force of gravity acting on an object's mass. The consistent increase in weight with mass exemplifies Newton's second law.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F80399807-3b71-459c-959c-a8e2ffcfbf7b%2Fc448f5bb-04cd-4226-b3e3-081fbba55213%2Fopzhw2f_processed.png&w=3840&q=75)
Transcribed Image Text:**Vernier Graphical Analysis: Mass and Weight Relationship**
This graph represents the linear relationship between mass (in kilograms) and weight (in newtons). The data is plotted on a cartesian plane with mass on the x-axis and weight on the y-axis.
**Graph Title:** Untitled
**Axes:**
- **X-axis (Mass in kg):** Ranges from 5 to 25 kg
- **Y-axis (Weight in N):** Ranges from 50 to 250 N
**Data Points:**
1. (5, 49)
2. (10, 98)
3. (15, 147)
4. (20, 196)
5. (25, 245)
These points show a direct proportionality between mass and weight. The linear fit is represented by the equation \( y = mx + b \), where:
- **m (slope):** 9.8
- **b (y-intercept):** 0
- **r (correlation coefficient):** 1
- **RMSE (Root Mean Square Error):** \( 1.641 \times 10^{-14} \)
The slope of 9.8 is significant as it represents the acceleration due to gravity. The correlation coefficient, \( r = 1 \), indicates a perfect linear relationship. The RMSE value is extremely low, confirming the accuracy of this linear model.
**Observation Table:** Data Set 1
- **Mass (kg)**: [5, 10, 15, 20, 25]
- **Weight (N)**: [49, 98, 147, 196, 245]
This analysis illustrates the fundamental physics concept that weight is the force of gravity acting on an object's mass. The consistent increase in weight with mass exemplifies Newton's second law.
Expert Solution
Step 1
Newton’s Universal Law of Gravitation states that every particle attracts every other particle in the universe with a force, that is directly proportional to the product of their masses and inversely proportional to the square of distance between them.
G is gravitational constant
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