Formula and Calculation of Weight
The measure of the force of gravity that is acted upon a body is known as its weight. It is denoted by w. In mathematical terms, weight can be described as the product of mass and acceleration due to gravity.
W = mg
Since weight is considered a force, its SI unit is also considered as the same as that of force which is Newton (N). The weight of a body is dependent on two factors, according to the expression of weight, which are the mass which is constant, and acceleration due to gravity which might differ in different places.
What is Mass?
The mass of a body can be defined as the measure of the amount of matter that is present inside the body. Its SI unit is kilograms (kg). For a given body, the mass rarely changes for any given time. However, if a large amount of energy is taken out or given to the body, there may be a change in the mass of the body. For an instance, in the case of a nuclear reaction, a huge amount of energy is converted from a very little amount of energy which results in the reduction of mass of the substance.
Calculation of Weight from Mass
Suppose a body possesses a large mass and a large weight and this body is a very large object that is hard to throw because of its weight.
Therefore by using Newton’s second law which states that the magnitude of the acceleration is ‘g’ for an object which is freely falling.
Therefore, if the mass of an object is 1 kg which is falling with an acceleration of 9.8 ms⁻², the magnitude of the force will be given by-
F = ma
F =(1 kg) x (9.8 ms⁻²)
F = (9.8 kg.ms⁻²)
F = 9.8 N
Hence, it is clear that for an object with mass m= 1 kg, the weight of the object will be equal to 9.8 N.
Examples:
Question: For a freely falling object of mass 10Kg, an upward force of 20N is applied. Find the final acceleration. ( $g = 10 \, \text{m/s}^2$ )
Ans:
Net downward force = weight of the object = 100 N
Net upward force = 20N
Net force = 80N in the downward direction.
So, Net acceleration = \[\frac{80}{10}\] = 8Kg
Question: What will be the weight of an object on the moon, if its weight is 90N on earth.
Ans: Weight of an object on earth = 90N
Weight of object on moon =?
We know that gravitational force on the moon is equal to one-sixth of earth’s gravitational force.
Weight of a body on earth, \[W_{earth}\] = \[mg_{earth}\]
Weight of a body on the moon, \[W_{moon}\] = \[mg_{moon}\] == \[\frac{mg_{earth}}{6}\] = \[\frac{W_{earth}}{6}\] = \[\frac{90}{6}\] = 15N
Conclusion
This is how weight is defined and its formula is derived. Learn how the terms are used to define the concept and to calculate the weight. Find out the relation of mass with weight.
FAQs on Weight Formula
1. What are some of the differences between weight and mass?
The most primary difference between weight and mass is that mass can never be zero while weight can be equal to zero. Another key difference is that mass is a scalar quantity and possesses a magnitude while weight is a vector quantity that has magnitude along with a direction that is directed towards the centre of the earth.
The measurement of mass is most commonly done in kilograms while that of weight is done in Newtons. Location does not have an effect on the mass of the body while it does have an effect on the weight of the body. For example, in space, the weight of the body becomes zero since there is no gravity that is acting upon the object.
2. What is meant by the term weightlessness?
The condition that is experienced in free-fall where the effect of gravity gets canceled by the inertial force which further results in the orbital flight, this condition is known as weightlessness. This sensation is felt when there are no more effects of gravity.
For example, when the astronauts are in the international space station, it is felt by the astronauts that everything in the space station including them is falling indefinitely towards the earth. Then the weightlessness is felt by astronauts which makes them freely float in the space station.
3. What are the primary factors that affect the weight of the body?
The three primary factors that affect the weight of the body include the mass of the object, the place of existence of the object, and the distance between the object and the centre of the planet. If there is an increase in the mass of the object, the weight of the object increases as well while the weight of the object decrease, if there is a decrease in the gravitational force of the body as the distance of the body, is increased from the centre of the planet.
4. What are some of the differences between weight and density?
The most primary difference between weight and density is that the amount of matter present in an object is known as its weight while the amount of matter that is present in a unit volume is known as the density. The weight of a body has a direct relation with gravity while there is no effect of gravity on the density. The weight is an extensive property of an object while density is an intensive property.
