Mass from Weight

Scales measure up weight, however to calculate body density we require mass. Part scales check out off mass, such as the digital scale in the image below, also though they in reality measure load as disputed in the previous chapter.

You are watching: The density of a human body can be calculated from its weight in air A food product sit on a digital weighing scale with options for displaying load in pounds or massive in kilograms or grams. The readout is 243 g. Photo Credit: “Digi-keukenweegschaal1284” by Algont via wikimedia commons.

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Mass have the right to be identified from a weight because weight is simply the force of gravity on the body and also force of gravity counts on fixed in a well-known way. Top top the surface of the Earth, the force gravity on things is pertained to its mass by the equation:

(1) The acceleration as result of gravity ~ above Earth, typically abbreviated tog, has actually a worth of 9.8 m/s2 and doesn’t readjust much end the whole surface of the Earth. Because of this we (and scales) have the right to measure weight and also then usage equation (1) over to calculation mass. Knowledge why the constant g is referred to as the acceleration because of gravity requires presenting acceleration, which we will execute in a later on unit, therefore for currently we acknowledge it as a consistent value that relates mass and also weight for objects ~ above the surface ar of Earth.

Force is a vector, so we must specify a direction because that the gravitational force, i beg your pardon is always down towards Earth’s center. We deserve to summarize the previous equation in prize form:

(2) ### Reinforcement Exercises: Helen Maroulis

Body Weight and also Mass ~ above the Moon

The worth ofgonly holds consistent near the surface of the Earth, and also therefore scale that use equation (1) to calculate mass indigenous measured load will review incorrect results. Because that example, her mass doesn’t readjust just due to the fact that you go to the moon (there no suddenly less matter inside you), yet your weight does change. In reality if youstood on a range on the moon it would certainly measure a weight around 1/6 the what the would review on Earth. The range wouldn’t understand you were on the moon rather of the Earth, so if the scale then tried to calculate your mass indigenous weight, the would read a mass the is 1/6 the actual value. Of course you didn’t shed 5/6 of yourself on the method there, for this reason that would not be correct.

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Universal regulation of Gravitation*

When you perform want to calculation the force of gravity and you space not near the surface ar of the planet then use the Universal legislation of Gravitation.

The Universal legislation of Gravitation states that the gravitational force between two objects relies on the fixed of every object ( and ) and also the distance in between their centers, ( ). To calculate the gravitational pressure we should multiply the 2 masses together, division by the distance in between them squared, and finally multiply by the universal gravitational constant , which always has the exact same value the . Written in equation form the universal law of gravitation is: