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 the recoil of the vehicle is avoided.
From Newton’s second law of motion, we know that
For this particular problem, we are solving for the mass. Hence, the formula for mass is
In symbols, that is
Substituting the given values and solving for the unknown, we have
The mass of the austronaut is about 55.9910 kilograms.
If the force could be exerted on the astronaut by another source other than the spaceship, then the spaceship would not experience a recoil.