# 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*.

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}= 10^{5}g m s^{−2}= 10

^{5}dyne∴ 1 N = 10

^{5}dyneNewton 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 10

^{3}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 |