Determine the net force, in N, that a 90-kg man would experience in an aircraft whose acceleration is 6 g's.
Understand the Problem
The question is asking to determine the net force experienced by a 90-kg man in an aircraft accelerating at 6 g's. The key information provided includes the mass of the man and the acceleration in terms of g's. The quantity to be found is the net force in newtons (N).
Answer
The net force is \( 5297.4 \, \text{N} \).
Answer for screen readers
The net force experienced by the 90-kg man is ( 5297.4 , \text{N} ).
Steps to Solve
- Identify the known values
We know the mass of the man is ( m = 90 , \text{kg} ) and the acceleration is ( 6 , g ). The acceleration due to gravity is approximately ( g = 9.81 , \text{m/s}^2 ).
- Convert acceleration from g's to m/s²
To find the acceleration in standard units, we need to convert ( 6 , g ) to meters per second squared:
$$ a = 6 \cdot g = 6 \cdot 9.81 , \text{m/s}^2 = 58.86 , \text{m/s}^2 $$
- Use Newton's second law to calculate net force
According to Newton's second law, the net force ( F ) can be calculated using the formula:
$$ F = m \cdot a $$
Substituting the known values:
$$ F = 90 , \text{kg} \cdot 58.86 , \text{m/s}^2 $$
- Calculate the net force
Now, perform the multiplication:
$$ F = 90 \cdot 58.86 = 5297.4 , \text{N} $$
The net force experienced by the 90-kg man is ( 5297.4 , \text{N} ).
More Information
This calculation illustrates how forces increase with greater acceleration. A man in an aircraft accelerating at 6 g's experiences a force over 5,200 N, which is significantly more than his weight alone.
Tips
- Confusing the units of acceleration; always ensure to convert g's to m/s² correctly.
- Forgetting to apply Newton's second law properly; remember that net force is the product of mass and acceleration.
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