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 [frac{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.