## What Is The Weight Equation Through General Relativity

The gravitational force on your body, called your weight, pushes you down onto the floor.$$W=mg$$So, what is the weight equation through general relativity?

Start with the Schwarzschild metric $$ds^2 = c^2dt^2-^dr^2-r^2d\Omega^2 $$ where $$r_S=\frac $$ A particle at rest at radius $r$ and angular parameters zero from the centre of mass has worldline $$ x^=$$ Its four velocity is thus $$ u^=\frac}=^}, 0, 0, 0)$$ Its four-acceleration is $$a^= \frac}+\Gamma^_u^u^ $$ After looking up the Christoffel symbols, because I’m lazy, I get $$ a^ = $$ So the Lorentz norm squared of the four-acceleration is $$g_a^a^= \frac)}=\frac)}$$ Now the *proper acceleration* of an object at time t is the acceleration relative to an observer in free fall, who is momentarily at rest w.r.to the object at time t. The free fall guy is the one who is not accelerating – the object held at rest at radius r is the one who is accelerating. As we’ve shown, his acceleration is $$\frac\frac}} $$ So if you want to define a force, it would be $$F=ma=\frac\frac}} $$ As $c\rightarrow \infty$ we recover the Newtonian definition, but nobody bothers phrasing it in these terms.

Morally speaking, the formula is still obeyed in general relativity. However, both $W$ and $g$ become sort of obsolete quantities in general relativity, so we would never describe the behavior of the physical system in this way.

## 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.

## Weight Mass And Gravitational Field Strength

The weight of an object may be thought of as acting at a single point called its centre of mass. Depending on the object’s shape, its centre of mass can be inside or outside it.

The weight of an object and its mass are directly proportional. For a given gravitational field strength, the greater the mass of the object, the greater its weight.

weight = mass × gravitational field strength

- weight is measured in newtons
- mass is measured in kilograms
- gravitational field strength is measured in newtons per kilogram

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## 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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## 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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## Weight As Vector Weight Formula Units

Weight is a vector and therefore has magnitude, direction, and sense. In the vicinity of the earths surface, the weight is a vector in the vertical direction and the direction is always downwards.

The vertical direction is usually named as the *y* or *z* axis , and the downward direction is assigned a + or sign to distinguish it from the upward direction. The choice depends on the location of the origin. In the image below, the origin was chosen at the point from which the apple falls: weight formula units

The unit vector **j** , a vector of magnitude equal to 1, is used to mark and distinguish the vertical direction. In terms of this vector, the weight is written like this:

**W**= mg

Where a negative sign is assigned to the downward direction.

## Weight Calculation And Formula

The weight of an object is proportional to its mass. The greater the mass, the greater the weight. weight formula units

The formula to find the magnitude of the weight is very simple:

W = mg

Where **m** represents the mass of the object and W is the magnitude of the acceleration of gravity , approximately constant and whose value is taken as 9.81 m / s 2 for the most frequent calculations.

Weight is a vector and bold letters are used to distinguish between a vector and its magnitude. In this way, when we talk about W we understand that it is the numerical value and when we write W we refer to the vector: weight formula units

**W**= m **g**

The **g** with a bold letter is the Earths gravitational field, that is, the influence that the Earth exerts on the space that surrounds it, regardless of whether or not there is another body that perceives it. Any object with mass has its own gravitational field, be it small or large. weight formula units

The intensity of the Earths gravitational field **g** is not entirely constant. It has small variations that arise mainly because the Earth is not a perfect sphere and also due to local height and density differences . But for most applications, the value 9.81 m / s 2 works very well.

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## Apparent Weight In Lift

Lets check about the apparent weight of a man in a lift or elevator.

Assume that a boy of mass m is standing on a weighing machine placed in a lift. The actual weight of the man will be mg. This weight bears down on the machine. The machine also expends a reactionary force R on the boy in an upward direction where R = W . Hence, two forces are acting on the boy reactionary force R and gravity force mg. Seeing that, the two forces are in opposite directions, the net force on the boy is given by:

F = mg R

The person is at rest thus, the net force on him must be zero, that is

F = mg R = 0

## Difference Between Real And Apparent Weight

It implies real weight = true weight. True or real weight simply is weight. So, what is your true weight? It’s simply the mg. Mass multiplied by gravity.

Apparent weight is represented by WA. It’s described as

WA = N

In which, N denotes the normal force in the direction opposite to the direction of gravity. That is simply away from the centre of the earth. You may be standing and someone may be attempting to push you horizontally. That normal force of reaction doesn’t count. Only the vertical Normal Force is countable.

So assume that you jump from the top of the building since your cat died. You are falling and your ‘ Weight’ is simply mg. Your apparent weight will be 0. Because there is no normal force exerted on you presently .

Now assume that you are standing in an elevator at rest. The weight, of course, is mg. But the apparent weight is also mg. Since you are at rest, N = mg.

Elevator moving with constant speed: N = mg.

Assume that the magnitude of an elevator’s acceleration is: |a|.

Elevator going up and slowing down: N = mg m|a|.

Elevator going up, and increasing speed: N = mg + m|a|.

Elevator going downwards and slowing down: N = mg + m|a|.

Elevator going up, and growing speed: N = mg m|a|.

Note: Apparent weight is the weight you ‘feel’. When you are falling, you feel weightlessness. Thus, the Apparent Weight is 0. When in an elevator going upwards with growing speed, you feel heavier. Therefore, more is the Apparent Weight!

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## Differences Between Weight Mass And Volume Weight Formula Units

These three concepts are often confused, but reviewing the characteristics of weight, it is easy to differentiate it from mass and volume . weight formula units

To begin with, the weight depends on the gravitational field where the object is. For example, on Earth and on the Moon the same thing has a different weight, although the number of atoms that compose it remains constant.

Mass is a scalar quantity, related to the number of atoms that make up the object and is evidenced by the resistance that the object has to change its motion, a property called *inertia* .

For its part, volume is the measure of the space that an object occupies, another scalar quantity. Two objects with the same volume do not weigh the same, for example an iron cube weighs much more than a polystyrene cube of the same dimensions.

In summary: weight formula units

- Mass is related to the amount of matter that a body has.
- Weight is the force exerted by the Earth on this mass, proportional to it.
- Volume is the space occupied by matter.

It should be noted that being scalar quantities, neither mass nor volume have direction or sense, but only numerical value and an adequate unit. On the other hand, the weight, being a vector, must always be expressed correctly indicating the magnitude, the unit, the direction and the sense, as in the previous section.

## What Is The Equation For Apparent Weight

**The equation for measuring apparent weight is F = mg + ma.** F represents apparent weight in newtons, m is the mass of the object, g is the acceleration due to gravity and a is the acceleration of the object.

The apparent weight of an object when it is at rest, free falling or moving at constant speed is equal to its normal weight because the object’s acceleration is zero. When the object is moving upward, for example in an elevator, the object’s apparent weight is heavier. This is due to the additional force necessary to push the object up, represented by mass times acceleration with positive acceleration value. If the object is moving downward, its apparent weight is lighter, since the object is actually decelerating and thus has a negative acceleration value.

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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 |
---|

## 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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## Formula Of Apparent Weight

Lets learn how to calculate the apparent weight. Your apparent weight is the sum of your real weight and a fictitious force related to your acceleration.

Usually, an object’s apparent weight is its mass multiplied by the vector difference between the acceleration of the object and the gravitational acceleration. This definition means that apparent weight is a vector that can make a move in any direction, not just vertically.

Thus, apparent weight formula a = dv/dt

## What Is Weight In Physics

We are giving a detailed and clear sheet on all Physics Notes that are very useful to understand the Basic Physics Concepts.

**Weight Definition Physics :**It is a field force. It is the force with which a body is pulled towards the centre of the earth due to gravity. It has the magnitude mg, where m is the mass of the body and g is the acceleration due to gravity.

w = mg

**Normal Reaction**It is a contact force. It is the force between two surfaces in contact, which is always perpendicular to the surfaces in contact.

**Tension**

- Tension force always pulls a body.
- Tension is a reactive force. It is not an active force.
- Tension across a massless pulley or frictionless pulley remains constant.
- Rope becomes slack when tension force becomes zero.

**Apparent Weight in Lift** When a lift is at rest or moving with a constant speed, then

The weighing machine will read the actual weight.

When a lift is accelerating upwards, then apparent weight

R1 = m

The weighing machine will read the apparent weight, which is more than the actual weight.

When a lift is accelerating downwards, then apparent weight

R2 = m

The weighing machine will read the apparent weight, which is less than the actual weight.

When lift is falling freely under gravity, then

R2 = m = 0

The apparent weight of the body becomes zero.

If lift is accelerating downward with an acceleration greater than g, then body will be lifted from floor to the ceiling of the lift.

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## Solved Examples On Force Formula

**Example 1.** A constant force acting on a body of mass 3.0 kg changes its speed from 2.0 m/s to 3.5m/s in 25 s. The direction of the motion of the body does not changes. What is the magnitude and what is the direction of the force?

**Solution**

Mass of the body, m = 3 kgInitial speed of body, u = 2 m/sFinal speed of body, v = 3.5 m/sTime, t = 25 s

Using the first equation of motion, the acceleration produced in the body can be calculated as:

v = u+at

F = ma

= 3 × 0.06 = 0.18 N

Since the application of the force does not change the direction of the body, the net force acting on the body goes in the direction of its motion.

**Example 2.** A stream of water flowing horizontally with a speed \ of gushes out of a tube of cross-sectional area \, and hits a vertical wall nearby. What is the force exerts on the wall by the waters impact, assuming it does not rebound?

**Solution**

Speed of water stream, v = 15 m/sThe cross-sectional area of the tube, A = 10 mThe volume of water that comes out through the pipe per second,V = A x v = 15 x 10 m /sDensity of water, = 10 kg/mMass of water that flows out in the pipe per second = density V = 150 kg/sThe water hits the wall and doesnt rebound. Therefore, the force that the water exerts on the wall is given by

Newtons second law of motion as:F = Rate of change of momentum = P / t.= mv / t= 150 x 15 = 2250 N

## Example On Weight Formula

**Example 1:** The mass of the body is 50 kg. Calculate the weight using the weight formula. (Hint: use g = 9.8 m/s2.

**Solution:**

To find the weight of the body.Mass = 50 kg Using the formula to find weight,W = mgW = 490 N

**Answer:** The weight of the body is 490 N

**Example 2:** If the weight of the body on the moon is 500N, find its mass. The value of g in the moon is 1.62 m/s2.

**Solution:**

To find the mass of the body.Weight of the body on the moon = 500 N Using the formula to find weight,W = mgMass of the body = W/gMass of the body = 500/1.62Mass of the body = 308.64 kg

**Answer:** Mass of the body is 308.64 kg

**Example 3:** The mass of the body is 50 kg and the weight of the body is 490 N. With the help of the weight formula prove that g = 9.8 m/s2.

**Solution:**

To prove, g = 9.8 m/s2 Weight of the body = 490 N Mass = 50 kg Using the formula to find weight,W = mg

Hence Proved g = 9.8 m/s2

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