Question
John releases various objects from an identical height on Earth. The provided table displays his collected data.
Object | Mass (kg) | Gravitational Force on the Object (N)
1 | 1 | 9.8
2 | 10 | 98
3 | 100 | 980
4 | 1,000 | 9800
Object | Mass (kg) | Gravitational Force on the Object (N)
1 | 1 | 9.8
2 | 10 | 98
3 | 100 | 980
4 | 1,000 | 9800
Answers
GPT-4o mini
Based on John's collected data, we can observe how the gravitational force acting on each object scales with mass. The gravitational force (weight) on an object can be calculated using the formula:
\[ F = m \cdot g \]
where:
- \( F \) is the gravitational force (weight) in newtons (N),
- \( m \) is the mass of the object in kilograms (kg),
- \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \) on the surface of the Earth).
From the data in the table, we can confirm this relationship. Here are the details derived from the table:
1. For Object 1 (mass = 1 kg):
\[ F = 1 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 9.8 \, \text{N} \]
2. For Object 2 (mass = 10 kg):
\[ F = 10 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 98 \, \text{N} \]
3. For Object 3 (mass = 100 kg):
\[ F = 100 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 980 \, \text{N} \]
4. For Object 4 (mass = 1,000 kg):
\[ F = 1,000 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 9800 \, \text{N} \]
The data supports the conclusion that the gravitational force increases linearly with mass, and we can see that for every increase in mass by a factor of 10, the gravitational force also increases by a factor of 10.
Thus, John’s results are consistent with the physics of gravitational force on Earth, which is directly proportional to mass, governed by the constant \( g \).
\[ F = m \cdot g \]
where:
- \( F \) is the gravitational force (weight) in newtons (N),
- \( m \) is the mass of the object in kilograms (kg),
- \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \) on the surface of the Earth).
From the data in the table, we can confirm this relationship. Here are the details derived from the table:
1. For Object 1 (mass = 1 kg):
\[ F = 1 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 9.8 \, \text{N} \]
2. For Object 2 (mass = 10 kg):
\[ F = 10 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 98 \, \text{N} \]
3. For Object 3 (mass = 100 kg):
\[ F = 100 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 980 \, \text{N} \]
4. For Object 4 (mass = 1,000 kg):
\[ F = 1,000 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 9800 \, \text{N} \]
The data supports the conclusion that the gravitational force increases linearly with mass, and we can see that for every increase in mass by a factor of 10, the gravitational force also increases by a factor of 10.
Thus, John’s results are consistent with the physics of gravitational force on Earth, which is directly proportional to mass, governed by the constant \( g \).