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Q4.3-4PE

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Found in: Page 161

### College Physics (Urone)

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/s2.(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.

See the step by step solution

## Step 1: Concept of Newton’s second law of motion

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 Fnet is the net force, m is the mass, and a is the acceleration.

## Step 2: Given Data

• Acceleration of the astronaut = 0.893 m/s2.
• Net external force = 50 N.

## Step 3: (a) Determine the mass of the astronaut

By putting values 50 N for Fnet and 0.893 m/s2 for a in equation (i) and we get,

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

Hence, the mass of the astronaut is 56 kg.

## Step 4: (b) Determine the relationship between the acceleration due to mass experienced by another source

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.