Chapter 4, Problem 1P

To determine

The net force that acts on the plane's 78-kg pilot.

Answer to Problem 1P

  $93.093 \text{N}$ .

Explanation of Solution

Given:

The airplane's mass is $m_{\text{plane }}=3.1\times {10}^4 \text{kg}$ .

The net force that acts on the plane is ${\displaystyle \sum F}=3.7\times {10}^4 \text{N}$ .

Mass of pilot is 78-kg

Formula used:

As per Newton's second law,

  ${\displaystyle \sum F}=ma$

As per Newton's third law,

  $F_{AB}=-F_{BA}$

Calculation:

Solve for the plane case:

  ${\displaystyle \sum F}=ma$

  $=3.7\times {10}^4 \text{N}$

  $=3.1\times {10}^4 \text{kg}\cdot a$

Rearrange and solve for the acceleration:

  $a=\frac{{\displaystyle \sum F}}{m}$

  $=\frac{3.7\times {10}^4 \text{N}}{3.1\times {10}^4 \text{kg}}$

  $=1.1935 \text{m}/{\text{s}}^2$

Solve for the pilot case:

  $\begin{array}{c}{\displaystyle \sum F}=ma\\ =78 \text{kg}\times 1.1935 \text{m}/{\text{s}}^2\\ =93.093 \text{N}\end{array}$

Conclusion:

Thus, the net force that acts on the plane's 78-kg pilot is $93.093 \text{N}$ .