Question

# a. How much force does an 80 kg astronaut exert on his chair while sitting at rest on the launch pad? b. How much force does the astronaut exert on his chair while accelerating straight up at $10 \mathrm { m } / \mathrm { s } ^ { 2 }$?

Solution

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$\text{\underline{\textbf{Given values:}}}$

$m=80 \: \text{kg}$

$a=10 \: \dfrac{\text{m}}{\text{s}^2}$

$\textbf{a)}$ The force with which the astronaut acts on the chair is its weight:

\begin{align*} W&=mg\\ W&=80 \: \text{kg} \cdot \bigg(9.81 \: \dfrac{\text{m}}{\text{s}^2}\bigg)\\ W&=\boxed{784.8 \: \text{N}} \end{align*}

$\textbf{b)}$ If it moves rapidly, then by applying Newton's second law we have:

\begin{align*} F&=N-mg\\ ma&=N-mg\\ N&=ma +mg\\ N&=80 \: \text{kg} \cdot \bigg(10 \: \dfrac{\text{m}}{\text{s}^2}\bigg)+80 \: \text{kg} \cdot \bigg(9.81 \: \dfrac{\text{m}}{\text{s}^2}\bigg)\\ N&=\boxed{1584.8 \: \text{N}} \end{align*}

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