## Weight Changes When Changes

On Earth, your weight is caused by the earths pull on you. In a future lesson we will see that weight is the result of the your mass, the earths mass, and the distance between you and Earth.

We will solve problems on this page using an average surface acceleration due to gravity

- More massive interstellar objects have a higher surface acceleration due to gravity .
- The higher the acceleration due to gravity the higher the weight

## Relationship Between Mass Weight And Gravity

The *gravity equation* shows the * relationship between mass, weight and acceleration due to gravity*.

The *mass* of an object is the amount of matter it contains, regardless of its volume or any forces acting on it. *Gravity* is a force that attracts objects toward the Earth. The *weight* of the object is defined as the force caused by *gravity* on a mass.

Weight can vary slightly at different places on the Earth, due to differences in the force from gravity at the various locations. The weight of an object is much different on various planets and moons.

Questions you may have include:

- What is the gravity equation?
- What are the units of measurement?
- What is weight on the Moon?

This lesson will answer those questions. Useful tool: Units Conversion

## How To Calculate Weight From Mass

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The **weight** of an object is the force of gravity exerted on that object. The **mass** of an object is the amount of matter it has, and it stays the same wherever you are, regardless of gravity.XResearch source That’s why an object that has 20 kilograms of mass on earth also has 20 kilograms of mass while on the moon, even though it would only weigh 1/6 as much. It weighs 1/6 as much on the moon because the force of gravity on the moon is 1/6 of what it is on Earth. Read on for information about and tips on calculating weight from mass.

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## Conversion From Mass To Weight

Newton’s second law is used to convert between weight and mass:

The equation for force is *F = ma* .

Here, *F* is the force due to gravity , *m* is the mass of the object in question, and *a* is the acceleration due to gravity, on Earth approximately 9.8 m/s² or 32.2 ft/s²).

In this context the same equation is often written as *W = mg*, with *W* standing for weight, and *g* for the acceleration due to gravity.

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People in the United States rarely describe objects using kilograms in daily life. Scientists and doctors use this term because it is the standard unit of mass in the metric system.

You can change an objects mass by removing some of its parts. When you take books out of your backpack at the end of a school day, youve decreased the backpacks mass. Mass can also change by adding more matter. When a child grows, their body is building longer bones and bigger organs. The childs mass will increase because they are transforming food energy into matter for their body.

Its important to know that mass doesnt change by varying its shape, location or size. Your bodys mass is the same when youre curled up on the sofa or when you stretch as high as you can. And its the same when youre at home or at the beach or at school! But your mass is a little bit more after youve eaten breakfast, compared with when you first wake up in the morning. Mass is a fundamental measurement of how much matter an object contains.

**Weight** is a measurement of the gravitational force on an object. It not only depends on the objects mass, but also on its location. Therefore, weight is actually a measure of force. In the United States, most people measure weight in pounds.

#### Explainer: Gravity and microgravity

#### Mass and weight are proportiona**l**

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## Relation Between Weight And Mass

Consider a body having large mass and large weight. Example of this situation is a large object which is hard to throw because the weight of this object is large.

Therefore, the relation between weight and mass can be derived with the help of Newtons second law which explains that the free falling object has an acceleration g as the magnitude.

If an object with a mass of 1kg falls with an acceleration of 9.8 ms-2, then the magnitude of the force is given as :F = ma

## Use Of Weight Vs Mass

In the physical sciences, the terms mass and weight are rigidly defined as separate measures in order to enforce clarity and precision. In everyday use, given that all masses on Earth have weight and this relationship is usually highly proportional, weight often serves to describe both properties, its meaning being dependent upon context. For example, in commerce, the net weight of retail products actually refers to mass and is properly expressed in pounds or kilograms. Conversely, the load index rating on automobile tires, which specifies the maximum structural load for a tire in kilograms, refers to weight that is, the force due to gravity.

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## W = M * G W=mgcomparing Mass And Weight

For the most part, when comparing mass and weight on Earthwithout moving!the values for mass and weight are the same. If you change your location with respect to gravity, mass will remain unchanged, but weight will not. For example, your body’s mass is a set value, but your weight is different on the Moon compared with on Earth.

Mass is a property of matter. The mass of an object is the same everywhere. | Weight depends on the effect of gravity. Weight increases or decreases with higher or lower gravity. |

Mass can never be zero. | Weight can be zero if no gravity acts upon an object, as in space. |

Mass does not change according to location. | Weight varies according to location. |

Mass is a scalar quantity. It has magnitude. | Weight is a vector quantity. It has magnitude and is directed toward the center of the Earth or other gravity well. |

Mass may be measured using an ordinary balance. | Weight is measured using a spring balance. |

Mass usually is measured in grams and kilograms. | Weight often is measured in newtons, a unit of force. |

## How Are The Terms Related

Weight and mass are related bodies with a lot of mass also have a lot of weight. A large object, for example, is difficult to throw due to its weight. To understand the weight-mass relationship, consider that a freely falling body has an acceleration of magnitude g.

Newtons second law states that a force must be present for gravitational acceleration. For example, if a body of mass 1 kg falls with an acceleration of 9.8 meters per second square, the magnitude of the required force is given as

F=ma

=9.8N

The force that causes the body to accelerate downward is known as its weight.

Anyone with a mass of 1kg near the Earths surface must weigh 9.8 N to provide the acceleration.

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## What Is A Tension Force In Physics

Tension is defined as the force transmitted through a rope, string or wire when pulled by forces acting from opposite sides. The tension force is directed over the length of the wire and pulls energy equally on the bodies at the ends. Every physical object which is in contact exerts some force on one another.

## Newtons Laws Of Motion

- Explain the difference between mass and weight
- Explain why falling objects on Earth are never truly in free fall
- Describe the concept of weightlessness

Mass and weight are often used interchangeably in everyday conversation. For example, our medical records often show our weight in kilograms but never in the correct units of newtons. In physics, however, there is an important distinction. Weight is the pull of Earth on an object. It depends on the distance from the center of Earth. Unlike weight, mass does not vary with location. The mass of an object is the same on Earth, in orbit, or on the surface of the Moon.

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## The Mg Camp’s Definition Of Weight

Some physicists define the weight of an object to be the force of gravity on it irrespective of anythingelse: their definition is “The weight of an object equals its mass times the local acceleration due togravity.” This idea of weight is independent of the object’s state of motion and doesn’t consider anycontact force. It is *not* quite equal to the feeling of heaviness that you have right now as yousit in a chair reading this, unless you’re sitting at either the North or the South Pole. Physicists whouse this definition of weight will refer to the contact force as “apparent weight”. They’ll say thatwhen you’re freely falling you weigh as much as you do when you’re sitting in a chair, although they’ll addthat your apparent weight is zero in free fall. They’ll say that the astronauts floating in the SpaceShuttle or tethered outside the Hubble telescope have almost the same weight as they do on Earth , but that their apparent weight is zero. Andthey’ll say that the astronauts working hard to keep thinking straight during a rocket launch have the exactsame weight as they do at home in their kitchen, but that their apparent weight has increased.

In the picture at left, Earth pulls on the mass *m* with a force of “weight” , and the table supports the mass with the contact force labelled “apparent weight”. Applying Newton’s “*F = ma*” here gives

weight apparent weight =m× acceleration.

*not*

## What Are The Types Of Mass And Weight

From a scientific standpoint, understand that mass and weight are magnitudes with which the matter contained in a body and the force exerted by gravity on it are measured. The most well-known and widely used types are-

- Atomic mass- Atomic mass is the mass of an atom.
- Molar mass- It is the mass of one mole of a substance.
- Molecular mass- It is the mass of a molecule of a substance.
- Inertial mass- This physical magnitude denotes the resistance of a body to a change in speed.
- Body mass- It refers to a persons body mass.
- Atomic weight- This term refers to an elements average atomic mass.

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## Key Takeaways: Weight Definition In Science

- Weight is the product of mass multiplied by acceleration acting on that mass. Usually, it’s an object’s mass multiplied by the acceleration due to gravity.
- On Earth, mass and weight have the same value and units. However, weight has a magnitude, like mass, plus a direction. In other words, mass is a scalar quantity while weight is a vector quantity.
- In the United States, the pound is a unit of mass or weight. The SI unit of weight is the newton. The cgs unit of weight is the dyne.

## Measurement Of Mass Vs Weight

Weight is measured using a scale which effectively measures the pull on the mass exerted by the gravity of the earth. Mass of a body is measured by balancing it equally with another known amount of mass. Mass may be measured using a pan balance while Weight may be measured using a spring balance. Methods may be interchanged if gravity is known and constant, as it is on earth.

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## Mass Vs Weight: Comparing And Understanding The Differences

- Ph.D., Biomedical Sciences, University of Tennessee at Knoxville
- B.A., Physics and Mathematics, Hastings College

The terms “mass” and “weight” are used interchangeably in ordinary conversation, but the two words don’t mean the same thing. The difference between mass and weight is that mass is the amount of matter in a material, while weight is a measure of how the force of gravity acts upon that mass.

- Mass is the measure of the amount of matter in a body. Mass is denoted using m or M.
- Weight is the measure of the amount of force acting on a mass due to the acceleration due to gravity. Weight usually is denoted by W. Weight is mass multiplied by the acceleration of gravity .

## Weight Variance Across The Earth

Two factors change weight at different locations on the Earth. Increasing altitude decreases weight because it increases the distance between a body and the mass of the Earth. For example, a person who weighs 150 pounds at sea level would weigh about 149.92 pounds at 10,000 feet above sea level.

Weight also varies with latitude. A body weighs slightly more at the poles than at the equator. In part, this is due to the bulge of the Earth near the equator, which puts objects at the surface slightly further from the center of mass. The difference in centrifugal force at the poles compared to the equator also plays a role, where centrifugal force acts perpendicular to the axis of the Earth’s rotation.

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## Which Definition Is More Useful

Physics sometimes redefines commonly used words in a way that differs to their everyday usage. Oneobvious example is “work”: when you hold an object in your hand, you do no work on it, and yet yourarm is clearly getting tired. Your muscular system is certainly doing work, but this work is doneinternally and is not done *on* the object. So physics has a notion of doing work *on*something, because that idea turns out to be useful in mechanics. Definitions don’t pretend to be morethan they are there is no point in asking “Which definition of weight is correct, or more correct?”. Instead, we can only ask “Which definition is more *useful*?”.

Given the option of retaining the everyday use of “weight” or redefining it, what’s the best course? I think that if there’s no useful reason to redefine a word then we shouldn’t, especially when that word hasbeen in the public domain since time immemorial. That’s why I’m in the Contact Camp, because I find nouseful reason to discard the commonly understood meaning of “weight”. As it is, physicists find it hardenough communicating their ideas to non-physicists through a sometimes-esoteric language so must we alsoredefine commonly used words that don’t need redefining, just for the sake of it?

Here are two thought experiments to help you distinguish between the two definitions of weightand todecide for yourself which camp you’d like to be in.

## What Is The Formula Of Pulley

Basic Pulley System If the mass accelerates down, F is positive. Calculate the tension in the rope using the following equation: T = M x A. Four example, if you are trying to find T in a basic pulley system with an attached mass of 9g accelerating upwards at 2m/s² then T = 9g x 2m/s² = 18gm/s² or 18N .

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## The Two Are Related But Definitely Not The Same

All of the metal weights shown here are made from the same material. But gravity is pulling the right side of this balance scale farther down than the left side. This shows that the total mass of the metal weights on the right side is greater.

xefstock/E+/Getty Images Plus adapted by L. Steenblik Hwang

## Product Of Avoirdupois Pound And Standard Gravity

The pound-force is the product of one pound and the , 9.80665 m/s2 .

The standard values of acceleration of the standard gravitational field and the result in a pound-force equal to 4.4482216152605 N.

- 1 4.4482216152605 N 1\,}& =1\,}\times g_}\\& =1\,}\times 9.80665\,}}^}}/0.3048\,}}}\\& \approx 1\,}\times 32.174049\,\mathrm }} \\& \approx 32.174049\,\mathrm lb}}} \\1\,}& =1\,}\times 0.45359237\,}}}\times g_}\\& =0.45359237\,}\times 9.80665\,}}^}}\\& =4.4482216152605\,}\end}}

This definition can be rephrased in terms of the . A slug has a mass of 32.174049 lb. A pound-force is the amount of force required to accelerate a slug at a rate of 1 ft/s2, so:

- 1 s 2 1\,}& =1\,}\times 1\,}}^}}\\& =1\,}\cdot }}}^}}\end}}

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## Effect Of Gravity Of Mass And Weight

The weight of an object depends on the gravity at that place while Mass is always a constant at any place and any time. Eg., If an object’s mass is 60 kgs, then its Weight would be 600 Newtons but when taken to the Moon, this object will have a weight of 100 newton as the gravity of the moon is 1/6th that of the Earth. But the mass of that object will remain the same.

Mass can be a constant while Weight varies.

## Weight And Gravitational Force

When an object is dropped, it accelerates toward the center of Earth. Newtons second law says that a net force on an object is responsible for its acceleration. If air resistance is negligible, the net force on a falling object is the gravitational force, commonly called its **weight** \overset , or its force due to gravity acting on an object of mass *m*. Weight can be denoted as a vector because it has a direction *down* is, by definition, the direction of gravity, and hence, weight is a downward force. The magnitude of weight is denoted as *w*. Galileo was instrumental in showing that, in the absence of air resistance, all objects fall with the same acceleration *g*. Using Galileos result and Newtons second law, we can derive an equation for weight.

Consider an object with mass *m* falling toward Earth. It experiences only the downward force of gravity, which is the weight \overset . Newtons second law says that the magnitude of the net external force on an object is }_}=m\overset. We know that the acceleration of an object due to gravity is \overset, or \overset=\overset . Substituting these into Newtons second law gives us the following equations.

#### Weight

The gravitational force on a mass is its weight. We can write this in vector form, where \overset is weight and *m* is mass, as

In scalar form, we can write

Since g=9.80\,}^ on Earth, the weight of a 1.00-kg object on Earth is 9.80 N:

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