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 us to calculate the net force experienced by a 90-kg man in an aircraft that accelerates at 6 times the acceleration due to gravity (6 g's). To solve this, we will use Newton's second law (F = ma) where 'm' is the mass in kilograms and 'a' is the acceleration in meters per second squared. The acceleration can be calculated by multiplying the standard gravity (approximately 9.81 m/s²) by 6.
Answer
$5297.4 \, \text{N}$
Answer for screen readers
The net force experienced by the man is approximately $5297.4 , \text{N}$.
Steps to Solve
- Calculate the acceleration The acceleration experienced by the man can be calculated by multiplying the acceleration due to gravity by 6.
Using the standard gravity of approximately $9.81 , \text{m/s}^2$, we find: $$ a = 6 \times 9.81 , \text{m/s}^2 = 58.86 , \text{m/s}^2 $$
- Apply Newton's second law According to Newton's second law, the net force can be calculated using the formula $F = ma$, where ( m ) is the mass and ( a ) is the acceleration.
Substituting the values we have: $$ F = 90 , \text{kg} \times 58.86 , \text{m/s}^2 $$
- Calculate the net force Now, we can compute the net force: $$ F = 90 \times 58.86 = 5297.4 , \text{N} $$
The net force experienced by the man is approximately $5297.4 , \text{N}$.
More Information
This calculation shows that when an aircraft accelerates at 6 times the force of gravity, a 90-kg man would experience a force equivalent to over 5,290 newtons. This illustrates how acceleration forces impact objects in a non-inertial frame of reference, such as an accelerating aircraft.
Tips
- Not converting the acceleration due to gravity correctly (using a value other than $9.81 , \text{m/s}^2$).
- Forgetting to multiply the mass by the acceleration when applying Newton's second law.
- Miscalculating the final force value due to arithmetic errors.
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