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Physics Topics can be both theoretical and experimental, with scientists using a range of tools and techniques to understand the phenomena they investigate.
What is the Value and SI unit of Gravitational Force?
Weight of a Body : Gravitational Unit of Force
Definition: Weight of a body is the force with which the earth attracts the body.
The earths attraction is the force of gravity; the acceleration produced by it is called the acceleration due to gravity, g, and it is always directed towards the centre of the earth.
Hence, using the relation \(\vec{F}\) = m\(\vec{a}\), the weight of a body of mass m is formulated as
\(\vec{W}\) = m\(\vec{g}\).
So, weight = mass × acceleration due to gravity at the place. The value of g varies at different places and hence the weight also changes. For example, a bowling ball of mass 7.2 kg weighs 71N on earth, but only 12N on the moon. The mass of the ball is the same on both earth and the moon but the free fall acceleration on the moon is only 1.6 m/s2. [Detailed discussion of this aspect has been provided in the chapter Gravitation.]
Gravitational unit of force: The force with which the earth pulls a body of unit mass, is the unit of gravitational force.
Gravitational Unit | Unit | Definition | |
CGS System | g-wt | 1 g-wt = 1 g × 981 cm ᐧ s-2 = 981 dyn | This is the weight of a body of mass 1 g, i.e., the force with which the earth attracts a body of mass 1 g towards its centre. |
SI | Kg-wt | 1 kg-wt = 1.9 × 9.8 m ᐧ s-2 = 9.8N | This is the weight of a body of 1 kg, i.e., the force with which the earth attracts a body of mass 1 kg towards its centre. |
Gravitational units are no longer accepted for use with the SI units by BIPM.
From the above definitions, we see that gravitational units depend on acceleration due to gravity which varies at different places. So we cannot use these units as standard. But accepting a value of g as standard, a standard gravitational unit of force can be defined. Kilogram force or kgf is the most commonly used standard unit.
1 kgf is the weight of a mass of 1 kg at a place where the acceleration due to gravity, g = 9.80665 m ᐧ s-2 and therefore
1 kgf = 1 kg × 9.80665m ᐧ s-2 = 9.80665N.
However, this unit has become almost obsolete at present.
Inertial Mass
Suppose, two small pieces, one of wood and the other of iron, are at rest on the floor. From experience we know that, on applying the same amount of force, the piece of wood will have an acceleration greater than that of the iron piece. Conversely, to produce the same acceleration on both the pieces, the force applied on the iron piece will have to be greater. So, the inertia of rest for the iron piece is more than that for the piece of wood. Thus, the mass of a body is a measure of inertia of rest.
This is also true for inertia of motion. For instance, to stop a bicycle and a truck, moving with the same velocity within the same distance, i.e., to produce the same Retardation, the force applied on the truck has to be greater. So, in this case too, masses of the vehicles give measure of their inertia of motion.
Therefore, to produce the same acceleration in any two dif-ferent objects, at rest or in motion, force required will be dif-ferent if their masses are unequal. Thus, the mass of an object is the measure of its inertia. So mass is also called inertial mass. The mass m in the equation \(\vec{F}\) = m\(\vec{a}\), is the inertial mass.
Numerical Examples
Example 1.
A paratrooper of mass 75 kg falls with a constant velocity. Find the air resistance acting on him.
Solution:
As the acceleration is zero, there is no resultant force acting on the paratrooper. The weight acting downwards = 75 × 9.8 = 735 N .
Therefore, the air resistance, acting upwards, is R = 735 N.