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Q4.3-4PE

Expert-verifiedFound in: Page 161

Book edition
1st Edition

Author(s)
Paul Peter Urone

Pages
1272 pages

ISBN
9781938168000

**Since astronauts in orbit are apparently weightless, a clever method of measuring their masses is needed to monitor their mass gains or losses to adjust diets. One way to do this is to exert a known force on an astronaut and measure the acceleration produced. Suppose a net external force of 50.0 N is exerted and the astronaut’s acceleration is measured to be 0.893 m/s ^{2}.**

**(a) Calculate her mass.**

**(b) By exerting a force on the astronaut, the vehicle in which they orbit experiences an equal and opposite force. Discuss how this would affect the measurement of the astronaut’s acceleration. Propose a method in which recoil of the vehicle is avoided.**

(a) The mass of the astronaut is 56 kg.

(b) The vehicle will not recoil.

**The Newton’s second law of motion states that the acceleration of a system is directly proportional to the net external force acting on the system and is inversely proportional to the mass of the system. It is mathematically represented as:**

${{\mathbf{F}}}_{{\mathbf{net}}}{\mathbf{=}}{\mathbf{ma}}$ …….…….. (i)

** **

**where F _{net} is the net force, m is the mass, and a is the acceleration.**

- Acceleration of the astronaut = 0.893 m/s
^{2}. - Net external force = 50 N.

By putting values 50 N for F_{net} and 0.893 m/s^{2} for *a* in equation (i) and we get,

$\begin{array}{c}50\text{\hspace{0.33em}N}=m\times 0.893{\text{\hspace{0.33em}m/s}}^{\text{2}}\\ m=\frac{50\text{\hspace{0.33em}kg}\cdot {\text{m/s}}^{\text{2}}}{0.893{\text{\hspace{0.33em}m/s}}^{2}}\\ m=56\text{kg}\end{array}$

Hence, the mass of the astronaut is 56 kg.

Write the expression for determining the acceleration due to another source.

${a}_{meas}={a}_{astr.}+{a}_{vehicle}$

Here, ${a}_{meas}$is the acceleration due to mass experienced by another source, ${a}_{astr.}$. Is the acceleration of the astronaut, and ${a}_{vehicle}$ is the acceleration of the vehicle.

${a}_{vehicle}=\frac{{m}_{astr.}\cdot {a}_{astr.}}{{m}_{vehicle}}$

When the force is exerted by another source, then the vehicle will not be able to recoil. Hence, the vehicle will not recoil.

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