# Calculating Weight Using Different Gravity Loads

By Kathleen Cantor, 15 Oct 2020

One can define gravity as a universal force that acts between two objects. It tends to pull objects towards the center of the earth. Each body in the universe possesses a particular amount of matter. This is known as mass, which is defined as the amount of matter contained in a substance. Anything that occupies space and has weight is known as matter. The SI unit for mass is the kilograms (KG), although mass can also be expressed in grams(g), milligrams (mg), and even tones (t) and is measured using a beam balance.

## How to calculate weight using different gravity loads

When gravity acts on a body, it experiences a pull effect. This pull effect of gravity is known as weight. Weight is measured in Newton and changes depending on the place. The SI unit for weight is Newton (N). The difference between mass and weight is brought about by the presence of gravity in the latter. Weight is a vector quantity, and it has both magnitude and direction.

An astronomer's weight on earth slightly differs from the same astronomer's weight on a different planet, but the mass remains constant. Many people think it's fine to refer to mass and weight as the same thing, but a science student needs to understand the difference between them. Weight is directly proportional to the gravitational force available; thus, mathematically, this can be expressed as:

Weight = mass * gravity

W= mg

Lifting a 1-kilogram bag requires less physical effort compared to a 2-kilogram bag. This is because a 1-kilogram bag will weigh more than a 2-kilogram bag. The 1 Kg bag has a force of about 10 Newton acting on it, and the 2 Kg bag has a force of about 20 Newton acting on it; thus, the higher the mass, the larger the force required to carry it.

### How to calculate weight on the moon

A man on the moon weighs slightly lighter than he does on earth. The man's mass is constant on both the moon and earth; what brings about the difference in weight then? This is brought about by the different gravitational forces on both the earth and the moon's surface. The gravity at the surface of the moon is about 1/6th of the acceleration on earth. Thus, for a 2-kilogram bag of maize, a force of about 20 newton acts on it on earth, which translates to about 4 newton on the moon. This also happens because the moon is less heavy than the earth.

Even on the earth's surface, there are local variations in the gravitational force due to altitude, latitude, and geological structures. When a body is at rest, it experiences some acceleration due to its own weight and contents. To calculate the gravity load, one needs to get the product between the object's mass, the earth's gravitational acceleration, and the height above the ground in meters.

i.e. m*g which is (9.8 m/s2) * h

=mgh

Weight is the pull effect felt on a body due to gravity. The formulae for calculating weight as stated earlier is w = m * g ….. (i)

Where 'w' is the weight of the object, 'm' is the mass of the body measured in kilograms (Kg), and 'g' represents gravitational acceleration, which is 9.8 m/s2  when expressed in meters and 32.2 f/s2 when expressed in term of feet. Weight is a force; thus, the equation (i) above can also be written as F=mg.. .(ii)…this is expressed in Newton.

### How to calculate the magnitude of weight

When calculating weight, the mass of the object in question should always be converted to kilograms. You shouldn't mix up units of measurement; also, during the calculation, you should only use the scientific units available and convert them accordingly if need be. The next step is to figure out the gravitational acceleration depending on where gravity is acting from as the gravitation forces vary.

For example, the gravitation acceleration on the sun is about 274.0 m/s2. This is about 28 times the acceleration on earth. This means, for instance, if a man weighs 20 kilograms, he would have a weight force of 200 Newton on earth and 560 Newton on the sun. This is proof that the wrong estimated value of gravitational acceleration could lead to finding fault results; therefore, enough research must be done concerning this before proceeding with the math.

Lastly, once the mass and gravitational force with the right units have been noted, the values are then substituted in the equation (ii), i.e., F=mg accurately and the final weight force calculated.

Example:

Let's say an object has a mass of 90 Kg; what is its weight on earth?

I) identify the mass and convert it to kilograms

In this case, the mass is already in kilograms, and therefore it remains m=90 Kg

II) Identify the gravitational acceleration

In our case above, the space in question is the earth, which ah a gravitational acceleration of 9.8 m/s2

III) Finally, after identifying the 'g' and 'm,' substitute these values to equation [ii] above

F=m*g

=9.8 * 90 =882N

For this particular object, the weight is 882 Newton

A body has a mass of 100,000grams; what is its weight on the moon?.

In this above example, we have to convert the mass from grams to kilograms by diving by 1000

The mass, in this case, is 100 Kilograms. The gravitational acceleration on the moon is 1.6 m/s2

Therefore, the body's final weight after calculation is; 160 Newton after finding the product of the mass and the gravitational acceleration.

It should be noted that the gravity force in the moon and the earth are different.

Let's take into consideration the weight of a body in a lift. At rest, the weight of the body is  W=mg. During upward movement of the lift with an acceleration 'a,' then the weight becomes; W=m (a + g). and during downward movement of the lift with a deceleration  '-a' the weight becomes W= m ( g – a). This explains the elevator phenomenon where one feels lighter than usual when accelerating down and heavier than usual when accelerating upwards. In the upward movement, one feels heavy because of the force of moving upwards and the gravity acting on it. For the case of a freely falling lift, the weight is zero since there is no pressure on the feet or floor .i.e there is no support force.

In weight calculations, sometimes, one may be required to determine the gravity load of different structures. This load mainly comprises the weight of the structure and its occupants. The gravity load is majorly done for objects at rest. It is like determining the potential energy of a body, and it is measured in joules. Gravity load is determined by finding the products of mass, acceleration, and height. For a particular body, let's say a cuboid-shaped structure, made out of wood, you can determine the mass of this structure from the volume and density of the wood used. With the value of the cuboid's gravitational force and height, you can determine the gravitational load and weight.

### Conclusion

We can conclude that the calculations involving weight are not hard or tiresome; only two factors that is mass, and gravitational acceleration, are put into consideration. It is necessary, though, that one stays keen with the scientific units.

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