Mass from Weight

Scales measure weight, yet to calculation body thickness we need mass. Some scales read off mass, such as the digital scale in the photo below, also though they actually measure load as questioned in the vault chapter.

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A food product sit on a digital weighing range with alternatives for displaying weight in pounds or massive in kilograms or grams. The readout is 243 g. Image Credit: “Digi-keukenweegschaal1284” by Algont via wikimedia commons.

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Mass have the right to be established from a weight because weight is just the force of heaviness on the body and also force that gravity counts on massive in a well-known way. On the surface ar of the Earth, the force gravity on an object is concerned its massive by the equation:

(1)

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The acceleration as result of gravity on Earth, commonly abbreviated tog, has actually a value of 9.8 m/s2 and doesn’t readjust much end the whole surface that the Earth. Because of this we (and scales) deserve to measure weight and also then usage equation (1) over to calculation mass. Understanding why the constant g is referred to as the acceleration because of gravity requires presenting acceleration, which we will perform in a later on unit, for this reason for currently we identify it together a consistent value that relates mass and also weight because that objects top top the surface of Earth.

Force is a vector, therefore we should specify a direction because that the gravitational force, i beg your pardon is always down towards Earth’s center. We can summarize the ahead equation in price form:

(2)

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Body Weight and Mass top top the Moon

The value ofgonly holds constant near the surface of the Earth, and therefore scales that use equation (1) to calculate mass indigenous measured weight will check out incorrect results. For example, her mass doesn’t adjust just since you walk to the moon (there isn’t suddenly less matter within you), but your weight does change. In reality if youstood ~ above a scale on the moon it would certainly measure a weight around 1/6 of what the would review on Earth. The scale wouldn’t understand you were on the moon instead of the Earth, therefore if the scale then tried come calculate her mass from weight, it would check out a mass that is 1/6 the yes, really value. Of food you didn’t shed 5/6 of you yourself on the method there, so that would not be correct.

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Universal regulation of Gravitation*

When you perform want to calculation the pressure of gravity and you room not close to the surface ar of the earth then use the Universal law of Gravitation.

The Universal legislation of Gravitation says that the gravitational force in between two objects depends on the massive of every object (

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and also
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) and the distance in between their centers, (
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). To calculation the gravitational pressure we have to multiply the two masses together, division by the distance in between them squared, and also finally multiply by the global gravitational consistent
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, which constantly has the very same value that
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. Composed in equation kind the universal law of gravitation is: