Question

Since astronauts in orbit are apparently weightien, a clever method of measuring their masses is needed to monitor their man gains or losses to adjust diets. One way to do this is to exert a known force on an astronauts and measure the acceleration produced. Suppose a net external force of 50.0 N is exerted and the astronaut's acceleration 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. Proposed a method in which recoil of the vehicle is avoided.

Answer 1

(a) Mass:

$$a=\frac {F_\text{net}}{m}=56\text{ kg}.$$

(b) Yes, the magnitude of the measured acceleration will reduce. A method in which recoil of the vehicle is avoided may take conservation of momentum into account: the astronaut holds a gun that ejects a projectile of known momentum. By measuring the initial velocity of the astronaut, it is possible to determine the mass:

$$0=m_pv_p-m_av_a,\\\space\\ m_a=m_p\frac{v_p}{v_a}.$$