Question
Three metallic objects were released in a vacuum chamber from a height of 4.0 meters. The following data illustrates the mass of each object and the force exerted by each object upon colliding with the chamber floor.
Object | Force (N) | Mass (kg)
1 | 19.6 | 2.0
2 | 78.4 | 8.0
3 | 156.8 | 16.0
Which of the provided statements accurately characterizes the correlation between the mass of the descending objects (measured in kilograms) and the force exerted by these objects (measured in newtons)?
A. If the mass of a falling object doubles, the force exerted by the object is reduced by half.
B. The force exerted by each object varies inversely with its mass.
C. The force exerted by each object is directly linked to its mass.
D. If the mass of a falling object doubles, the force exerted by the object increases fourfold.
Object | Force (N) | Mass (kg)
1 | 19.6 | 2.0
2 | 78.4 | 8.0
3 | 156.8 | 16.0
Which of the provided statements accurately characterizes the correlation between the mass of the descending objects (measured in kilograms) and the force exerted by these objects (measured in newtons)?
A. If the mass of a falling object doubles, the force exerted by the object is reduced by half.
B. The force exerted by each object varies inversely with its mass.
C. The force exerted by each object is directly linked to its mass.
D. If the mass of a falling object doubles, the force exerted by the object increases fourfold.
Answers
GPT-4o mini
To analyze the relationship between mass and force exerted upon collision, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a):
\[
F = m \cdot a
\]
In the case of these objects falling under the influence of gravity, the acceleration (a) is equal to the acceleration due to gravity (\(g \approx 9.8 \, \text{m/s}^2\)).
Now, we can find the relationship between mass and the force each object exerts upon hitting the ground. The force of impact when the object hits the ground can be represented as follows, assuming they are in free fall:
1. For object 1:
- Mass = 2.0 kg
- Force = 19.6 N
- \(F_1 = 2.0 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 19.6 \, \text{N}\)
2. For object 2:
- Mass = 8.0 kg
- Force = 78.4 N
- \(F_2 = 8.0 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 78.4 \, \text{N}\)
3. For object 3:
- Mass = 16.0 kg
- Force = 156.8 N
- \(F_3 = 16.0 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 156.8 \, \text{N}\)
As we can see, the forces exerted by the objects upon impact are directly proportional to their masses.
Looking at the provided statements:
A. **False** - Doubling the mass does not reduce the force; it increases it.
B. **False** - The force does not vary inversely with mass; it varies directly.
C. **True** - The force exerted by each object is directly linked to its mass.
D. **False** - If the mass doubles, the force also doubles, not increases fourfold.
Therefore, the correct statement that characterizes the correlation between mass and force is:
**C. The force exerted by each object is directly linked to its mass.**
\[
F = m \cdot a
\]
In the case of these objects falling under the influence of gravity, the acceleration (a) is equal to the acceleration due to gravity (\(g \approx 9.8 \, \text{m/s}^2\)).
Now, we can find the relationship between mass and the force each object exerts upon hitting the ground. The force of impact when the object hits the ground can be represented as follows, assuming they are in free fall:
1. For object 1:
- Mass = 2.0 kg
- Force = 19.6 N
- \(F_1 = 2.0 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 19.6 \, \text{N}\)
2. For object 2:
- Mass = 8.0 kg
- Force = 78.4 N
- \(F_2 = 8.0 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 78.4 \, \text{N}\)
3. For object 3:
- Mass = 16.0 kg
- Force = 156.8 N
- \(F_3 = 16.0 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 156.8 \, \text{N}\)
As we can see, the forces exerted by the objects upon impact are directly proportional to their masses.
Looking at the provided statements:
A. **False** - Doubling the mass does not reduce the force; it increases it.
B. **False** - The force does not vary inversely with mass; it varies directly.
C. **True** - The force exerted by each object is directly linked to its mass.
D. **False** - If the mass doubles, the force also doubles, not increases fourfold.
Therefore, the correct statement that characterizes the correlation between mass and force is:
**C. The force exerted by each object is directly linked to its mass.**