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

  1. 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: $$ a = 6 \times 9.81 , \text{m/s}^2 = 58.86 , \text{m/s}^2 $$

  1. 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: $$ F = 90 , \text{kg} \times 58.86 , \text{m/s}^2 $$

  1. 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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