# Newton’s Second Law of Motion

**Definition:**

“If a net force acts on a body the body accelerates. The direction of acceleration is the same as the direction of net force. The magnitude of acceleration is in inversely proportional to the mass of the body.”

**Mathematical:**

[latex s=2]a\propto F[/latex]

[latex s=2]a\propto \frac{1}{m}[/latex]

Combining

[latex s=1]F = K ma[/latex]

where **k=1 **

[latex s=1]F = ma —— (A)[/latex]

**Explanation:**

Lets us consider two bodies of masses **m1** and **m2** such that **m1** **= m2** when use apply the forces **F1** and **F2** on them respectively. The acceleration a1 and a2 are produced. If **F1 > F2**, the **a1 > a2**. It means that greater the force greater will be acceleration produced. i.e.

[latex s=1]a\propto F —— (i)[/latex]

If the same force is applied on two different masses i.e. m1 = m2 then we will deserve that

[latex s=1]a\propto \frac{1}{m} —— (ii)[/latex]

Combining (i) and (ii) we get

[latex s=2]F = K ma[/latex]

when** K = 1**

[latex s=1]a = \frac{F}{m}[/latex]

[latex s=1]F = ma —— (A)[/latex]

Equation (A) represents the Newton 2nd Law. If we write in the form.

[latex s=1]a = \frac{F}{m}[/latex]

We can easily say and see that the acceleration of a body is in magnitude directly proportional to the resultant force and its direction parallel to this force. We also see that the acceleration for a given force is inversely proportion to the mass of a body. Note that the first Law of motion appears to be contained in the 2nd Law as a special case, for it if F= 0 then a= 0.

**Unit of Forces: **

The SI unit of force is Newton. One Newton is the amount of net force that give and acceleration of one meter per second squared to a body of mass one kilogram.

[latex s=1]1N = 1Kh. 1m/s^2[/latex]

Dimension of force are

[latex s=1][F] = [M] [L / T^2 ][/latex]

[latex s=1][F] = [ML T^-2 ][/latex]

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