Coupon Accepted Successfully!


Newton’s Second Law Of Motion

Let us take an example and understand Newton’s second law of motion. Consider a massive car and a light toy car. In order to move the massive car, a large force is required, and a small force is required to move the light toy car. So, for a given acceleration, force is proportional to mass. You would have experienced that even if you push a large rock with all your strength, it will not budge while a small marble needs only a gentle push.
F  m
Consider a ball kept on a horizontal floor. When we push this ball gently, the ball gains some speed in the direction of push; if we push with a heavier force the ball gains a higher speed. Thus, large forces cause large acceleration and small forces cause small acceleration. So, for a body of given mass, force is directly proportional to acceleration
F ∝ a
Therefore, we can write, F ∝ ma or F = kma, where k is the constant of proportionality. The value of constant of proportionality can be made unity by choosing proper units for force and other variables. Then,
F = ma

The above discussion is summarised in Newton’s second law.
The force on a body is equal to the product of its mass and the acceleration produced in the body.
Force = Mass  Acceleration
Therefore, Newton’s second law can also be stated as, ‘the acceleration of a body is directly proportional to the net force acting upon it and inversely proportional to the mass of the object.

Absolute and Gravitational Units of Force

The SI unit of force is newton and is denoted by N.

If a force acting on a body of mass 1 kg produces an acceleration of 1 m s−2 in it, the force is called one newton.
1 newton = 1 kg  1 m s−2
 1 N = 1 kg m s−2

In the CGS system, the unit of force is dyne. If a force acting on a body of mass of 1 g produces an acceleration of 1 cm s−2 in it, then the force is called one dyne.
1 dyn = 1 g  1 cm s−2
∴ 1 dyn = 1 g cm s−2
From the equation F = ma, we can write
1 N = 1 kg  1 m s−2
= 1000 g  100 cm s−2 = 105 g m s−2
= 105 dyne
∴ 1 N = 105 dyne

Newton and dyne are called the absolute units of force.
Gravitational force on an object of unit mass is known as a gravitational unit of force.
In the MKS system, the gravitational unit of force is the kilogram force (kgf). In the CGS system, the gravitational unit of force is the gram force (gf).
1 kgf = 1000 gf (or 103 gf).

Relationship Between kgf and Newton

By definition,
1 kgf = Force due to gravity on 1 kg mass
= 1 kg mass × acceleration due to gravity
= 1 kg × g m s−2 = g newton
= 9.8 newton [because g = 9.8 m s−2]
∴ 1 kg f = 9.8 newton (or 9.8 N)

Similarly, we can show that
1 gram force = 980 dyne

Test Your Skills Now!
Take a Quiz now
Reviewer Name