8/6/2019 How to weigh astronauts

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 S Astronauts spend long time in Earth-orbiting spacecraft. The international community has alarge spacecraft constantly circling the Earth(The International Space Station, ISS) where

astronauts spend many days, occasionally up to

200, performing tasks ranging frommaintenance of the craft toexperiments of interest to

humanity.

Because of this "weightlessness" astronauts will lose musclemass and is very important to control their

 weight during their stay at the ISS.

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8/6/2019 How to weigh astronauts

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How can we weigh astronauts on the ISS?Surely our first thought is to place a scale, such as those usedin our bathrooms, in the ship, but we need to think a littlemore about this.

 What would happen to the scale when placed on the

ship? The scale would float like the astronauts, so it would need tobe fixed like all objects. But once attached to the ship the as-tronaut could not stand on it as the astronaut floats.

In this experiment students of “Thader” and “Gabriel Miró”High Schools in Orihuela (Spain) have designed a system tomeasure the mass of the “weightless” astronaut. This consistsof a chair with wheels attached to several springs. The astro-naut sits in the chair and is swung in the chair. A motion sen-

sor picks up the swing and allows us to see the motiongraphics and get their period, as the period is related to themass of the astronaut through it we can use a simple calcula-tion to measure the mass.

 The value obtained in this way, and since we are not orbiting the Earth, we can compare with that traditionally obtained

 with the scale.

 The students arrived at system very similar to that used by 

NASA (U.S. Space Agency).

 To better understand how we may be able to weigh an astro-naut in this way, we may have to think further and ask a num-ber of questions:

 What is weight?Or rather, weight on Earth, according to any physics textbook it is the force with which the Earth attracts bodies. And theEarth attracts bodies because they have gravitational mass.Gravitational mass and weight are related in a simple W=mg g (where mg is the gravitational mass and g the accelerationof gravity).

 What do our weighing scale give us? All scales have an elastic element that deforms when we exert aforce on it, for example a spring. So when we stand on the scale

 we exercise a force on the spring (F) and it contracts, the markson the scale represent the degree of contraction of this spring and this we transform into a scale, either analog (needle) or digital(numbers).

 The scale offers over us another force(N) equal and opposite to F. These twoforces always have the same value ( Newton's Third Law). In addition andin accordance with Newton`s SecondLaw the sum of the force N and the

 weight (P) must be equal to the pro-duct of inertial mass by the accelera-tion which moves the person (N - P =

mi a). When we weigh on Earth, the accelera-tion is zero and therefore N = W andcontraction of spring marks our

 weight, but when we are orbiting theEarth the acceleration is g, therefore N= W - - mi g and N = mgg - mig andsince mi and mg have the same valueyou do not check the balance.

 The inertial mass and gravitationalmass are two different properties of the body, the inertial mass measuresthe inertia of the body to change its

motion status, while the gravitational mass is a property of bo-dies by which they are gravitationally attracted by other bodies,but they have the same value, so if we know the value of one weknow the value of another and this is what allows us to deter-mine the weight of the astronaut and why by another procedure,as in the oscillating chair, we measure the inertial mass.

But if we measure the period, how can we us it to me-asure the inertial mass?

 The period of an oscillatory motion is the time it takes the body to perform an oscillation, that is what is measured by the sensor,the time it takes the chair go back and forth. This time, the pe-riod squared is directly proportional to the inertial mass and so

 we can measure the inertial mass and through it the gravitationalmass and weight.

 With the educational program "DATA STUDIO" we get a graphof motion from which, after adjustments, we get the oscillationperiod. With the data we can use a simple Excel spreadsheet toconsider the weight of the chair, resulting in the astronaut's

 weight

 Weight = constant · Period2 - mass of the chair