Astronauts in orbit are apparently
weightless. This means that a clever method of
measuring the mass of astronauts is needed to monitor their mass gains or losses and
adjust their diet. 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 newtons is exerted and an astronaut’s acceleration is measured to be 0.893
metres per second squared, calculate her mass.
Knowing the force exerted on an
astronaut as well as the astronaut’s resulting acceleration, we want to calculate
the astronaut’s mass. If we call that mass we want to
solve for 𝑚 and record the force and acceleration as 𝐹 and 𝑎, respectively, we
can recall from Newton’s second law of motion that an object’s mass is equal to the
net force acting on it divided by its acceleration. For our scenario, we can write that
𝑚 is equal to 𝐹 divided by 𝑎. And when we plug in for these two
values and calculate this fraction, we find it’s equal to 56.0 kilograms. That’s the measured mass of the
astronaut based on the astronaut’s response to an applied force.