# Question Video: Calculating the Mass of an Object Accelerated by a Constant Force

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 N is exerted, and an astronaut’s acceleration is measured to be 0.893 m/s². Calculate her mass.

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### Video Transcript

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.