Convert 100 Newton’s to kilograms, then choose the correct answer. 1) 98 kg 2) 22.4809 kg O 3) 9.8 kg 4) 100 kg
The Correct Answer and Explanation is :
To convert Newtons (N) to kilograms (kg), we can use the formula based on Newton’s second law of motion:
[
F = m \cdot g
]
Where:
- ( F ) is the force in Newtons,
- ( m ) is the mass in kilograms,
- ( g ) is the acceleration due to gravity (approximately ( 9.81 \, \text{m/s}^2 ) on Earth).
To find the mass in kilograms from a force in Newtons, we can rearrange the formula:
[
m = \frac{F}{g}
]
In this case, we have ( F = 100 \, \text{N} ) and ( g = 9.81 \, \text{m/s}^2 ). Substituting these values into the formula gives:
[
m = \frac{100 \, \text{N}}{9.81 \, \text{m/s}^2} \approx 10.19 \, \text{kg}
]
Therefore, when we convert 100 Newtons to kilograms, we find that it is approximately 10.19 kg.
Now, let’s analyze the answer choices provided:
1) 98 kg – This is not correct, as it is far too high compared to our calculated value.
2) 22.4809 kg – Also incorrect; this value does not align with our calculations.
3) 9.8 kg – This is the closest approximation but still slightly lower than the calculated value of 10.19 kg.
4) 100 kg – Clearly incorrect, as it is significantly higher than any realistic conversion from Newtons to kilograms.
Given the provided options, none of them match the calculated value of approximately 10.19 kg. However, Option 3 (9.8 kg) is the closest approximation based on the standard gravitational force of approximately 9.81 m/s².
In summary, while the exact conversion of 100 N to kg is approximately 10.19 kg, the best choice among the provided options is 9.8 kg, as it reflects a common simplification in physics where ( g ) is often rounded to 10 m/s² for easier calculations.