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:
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
From Force And Acceleration
The property of mass is also understood as the measure of a physical objects resistance to being accelerated by the application of an external force. This concept of mass is sometimes referred to as inertial mass. Inertia is the tendency for a moving body to continue in a constant state of motion, so inertial mass is a measure of how much inertia a body has and how difficult it is to change its state of motion. The relationship between mass, force, and acceleration is expressed by Newtons second law of motion F=ma. This mathematical relationship tells us that, in the face of a constant force, a more massive body will accelerate more slowly. By measuring the force applied to a body and measuring the observed acceleration, we can calculate the mass of the body.
For example, say that we apply a 748 N force to a metal cube, and we measure its acceleration as 21m/s2. What is the mass of the metal cube? We can figure calculate the mass by dividing the magnitude of the force by the magnitude of acceleration so:
m=F/a
So we know that the metal cube must have a mass of 35.62 kg.
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Solved Examples On Weight Formula
Q1. A persons mass happens to be 70 kg, while the gravity on Earth is 9.8 m/s2. Find out the weight of this person?
A1 In order to determine the formula of weight, one has to apply the weight formula.Here m = 70 kg and g = 9.8 m/s2
W = mgW = 637 Nw
Hence, the weight of the person is 637 Nw.
Q2. An individual weighs 250 Nw on the moon. Calculate the mass of the individual considering the gravity on the mass as 1.6 m/s2?
A2 Here, w = 250 Nw and g = 1.6 m/s2
W = mg
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Differences Between Mass And Weight
Here are some differences between these two physical quantities in tabular form
| SL. No. | ||
| It gives the amount of matter in an object. | It gives the force exerted by a body due to its mass. | |
| 2 | Mass is a Scalar quantity. | Weight is a vector quantity. |
| 3 | It is a fundamental physical quantity. | It is a compound physical quantity. |
| 4 | SI unit of Mass is Kilogram . | SI unit of Weight is Newton . |
How is the mass different from the weight?
Variables In The Weight Equation
The Weight Calculator uses the formula W = mg, or weight W is equal to mass m times gravity g. Note that the standard units for weight calculations are N, kg and m/s2. If you enter other units of measure for your calculation the calculator will do the units conversion for you.
Weight is a force and gravity can be thought of as an acceleration due to the pull of gravity. The equation W = mg is a special case of Newton’s second law of motion, F = ma, where force F equals mass m times acceleration a.
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How To Calculate Weight From Mass
wikiHow is a wiki, similar to Wikipedia, which means that many of our articles are co-written by multiple authors. To create this article, 63 people, some anonymous, worked to edit and improve it over time.There are 8 references cited in this article, which can be found at the bottom of the page. This article has been viewed 1,174,131 times.Learn more…
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.
What Is The Formula For Mass
Alex BolanoPRO INVESTOR
Mass is a property of physical objects and a measure of how resistant that body is to acceleration. One can consider the mass of an object as a measure of how much physical stuff makes up that object.
Unlike relational properties such as position, velocity, or potential energy, which always must be defined with respect to another object or a reference point, mass is an intrinsic property that an object has independently of its relation to other things. The mass of an object can be calculated in a number of different ways:
- mass=density×volume . Density is a measure of mass per unit of volume, so the mass of an object can be determined by multiplying density by volume.
- mass=force÷acceleration . According to Newtons second law , the acceleration of an object is directly proportional to the force applied to it. Consequently, the amount of acceleration accompanying the application of a constant force is inversely proportional to the mass.
- mass=weight÷gravitational acceleration . Weight is the product of the acceleration of mass in a gravitational field. Depending on the strength of gravitational acceleration, the weight will be different.
All three of these formulae are a way of determining the mass of an object. Since mass is a fundamental property, It is not defined in terms of other units, like the joule of newton are. There are other ways to calculate the mass of an object, but these three formulae are the most common ones.
m=V
m=F/a
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Acceleration Due To Gravity
Enter the acceleration due to gravity for your geographical location in metres per second per second or feet per second per second .
The local gravity on earth is dependent on several factors such as latitude, height above sea-level, local geological density, etc refer to your national geological survey data for your location or use this local gravity calculator to determine a close approximation. The default value is set to 9.80665 ms-2 which is the standard acceleration due to earths gravity.
You can also enter acceleration due to the pull of gravity for other places in the solar system such as , Moon , Titan or Europa for example.
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Relative Weights On The Earth And Other Celestial Bodies
The table below shows comparative gravitational accelerations at the surface of the Sun, the Earth’s moon, each of the planets in the solar system. The âsurfaceâ is taken to mean the cloud tops of the gas giants . For the Sun, the surface is taken to mean the . The values in the table have not been de-rated for the centrifugal effect of planet rotation and therefore, generally speaking, are similar to the actual gravity that would be experienced near the poles.
| Body |
|---|
How To Calculate Weight Of An Object Orbiting Another Object
How do we calculate weight of an object which is orbiting another bigger object in the space?
For example, comparing the pair of Sun-Earth, Earth is orbiting Sun due to the force applied by Sun on Earth. Earth is undergoing non-uniform acceleration.
Does Earth has weight? I think it has weight, but no sensation of it since it is in free fall. Is the weight of Earth changing every moment? Why it is believed popularly that Earth doesn’t have weight?
- $\begingroup$Yes, I know. That is reflected in the question. no where, I mentioned mass.$\endgroup$ KawaiKxNov 10, 2018 at 15:38
- $\begingroup$Okay, then let me ask: what is your weight if you were floating around in space?$\endgroup$ SteevenNov 10, 2018 at 16:28
- $\begingroup$There is no floating around in space exactly. You would be pulled to the nearest big object. Either you go straight toward it or orbit around it if you other velocities too. So called ‘free fall’ is due to weight only.$\endgroup$ KawaiKxNov 10, 2018 at 18:18
- $\begingroup$And if no other big objects existed in any significant nearby location? Then you would free float, right? What would the weight then be?$\endgroup$
Weight and mass are two different things:
So, what about the earth?
-
The earth has an enormous mass. Many, many, many kilograms.
-
The earth, regarded as a single object, is in free-fall around the sun. Therefore, regarded as a single object, the earth is weightless.
In summary:
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The Imperial British Gravitational System
The British Gravitational System of units is used by engineers in the English-speaking world with the same relation to the foot – pound – second system as the meter – kilogram – force second system has to the meter – kilogram – second system. For engineers who deals with forces, instead of masses, it’s convenient to use a system that has as its base units length, time, and force, instead of length, time and mass.
The three base units in the Imperial system are foot, second and pound-force.
In the BG system the mass unit is the slug and is defined from the Newton’s Second Law . The unit of mass, the slug, is derived from the pound-force by defining it as the mass that will accelerate with 1 foot per second per second when a 1 pound-force acts upon it:
1 lbf =
In other words, 1 lbf acting on 1 slug of mass will give the mass an acceleration of 1 ft/s2.
The weight of the mass can be calculated from equation in BG units as
Fg = m ag
With standard gravity – ag = 32.17405 ft/s2 – the weight of 1 slug mass can be calculated as
Fg =
= 32.17405 lbf
The English Engineering System
In the English Engineering system of units the primary dimensions are are force, mass, length, time and temperature. The units for force and mass are defined independently
- the basic unit of mass is pound-mass
- the unit of force is the pound alternatively pound-force .
In the EE system 1 lbf of force will give a mass of 1 lbm a standard acceleration of 32.17405 ft/s2.
Since the EE system operates with these units of force and mass, the Newton’s Second Law can be modified to
F = m a / gc
where
or transformed to weight
Fg = m ag / gc
The proportionality constant gc makes it possible to define suitable units for force and mass. We can transform to
1 lbf = / gc
gc = /
Since 1 lbf gives a mass of 1 lbm an acceleration of 32.17405 ft/s2 and a mass of 1 slug an acceleration of 1 ft/s2, then
1 slug = 32.17405 lbm
The mass of a car is 1644 kg. The weight can be calculated:
Fg =
= 16122.7 N
– there is a force of 16.1 kN between the car and the earth.
- 1 kg gravitation force = 9.81 N = 2.20462 lbf
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How To Get Weight From Mass
Weight and Mass are not the same physical quantity. They have different units and dimensions also. However, we can relate to them. In this article, Im going to explain how is weight different from Mass and how to get weight from the mass of an object. This article is basically for students of basic physics.
Measuring the Mass
How To Calculate The Weight Of An Object
The weight of an object is the force of attraction that the object has to the Earth. It is the product of the mass of the object, multiplied by the acceleration due to gravity. You may choose to calculate the weight of an object to solve a physics problem. It is a basic calculation and it is often a fundamental step to solving other, more complicated problems. You can calculate the weight by identifying what given information you have, and putting the numbers into the designated equation.
Write down your given information for the weight problem. The problem will provide you with the mass of the object and the acceleration due to gravity. For example, the mass may be 3 g, and the acceleration due to gravity may be 9.81 meters per second per second.
Find the equation that needs to be used to solve the problem. The equation used to calculate the weight of an object is F = ma. “F” is the force in Newtons, “m” is the mass in grams and “a” is the acceleration due to gravity.
Put the values of the problem into the equation. For example, multiply the mass of the object times the acceleration due to gravity, or F=. You should receive an answer of 29.4 Newtons.
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From Density And Volume
The density of an object, sometimes represented by the Greek letter , is a measure of mass per unit volume. Essentially, density tells you how tightly packed the mass of an object is. The denser an object is, the more mass per unit of volume it has.
For example, water has a density of 977 kg/m3 at standard temperatures and pressures. That is, one cubic meter of water has a mass of 977 kg. If we know the density and volume of a substance, we can also figure out the mass of that substance. Say we have a 0.7m3 sample of water. How much mass does that sample have?
Solving for mass gives us:
m=V
m= = 683 kg
0.5 cubic meters of water at standard temperature and pressure would have a mass of 683 kg.
Some objects are incredibly dense. A neutron star, for example, has an average density of 1.1 x 1018 kg/m3. A single teaspoon of a neutron star would weigh about 100 million tons on Earth.
Mass becomes immobile it cannot manoeuvre and therefore cannot win victories, it can only crush by sheer weight. Hans Von Seeckt