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Question
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$0.893\textrm{ m/s}^2$ . (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.
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Final Answer
  1. $56.0 \textrm{ kg}$
  2. The acceleration of the astronaut with respect to the spacecraft is what's being measured. This will be greater than the acceleration of the astronaut with respect to an observer who is stationary. Stationary in this context means stationary with respect to the centre of mass of the astronaut-spacecraft system. In other words, the stationary observer is moving at constant speed in the same orbit as the spacecraft before it accelerated due to the force on the astronaut.

    A method in which the vehicle recoil is avoided is to have a heavy object floating in the vehicle which applies the known force. The object will recoil, but not the vehicle.

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OpenStax College Physics Solution, Chapter 4, Problem 4 (Problems & Exercises) (3:15)

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