Newtons Second Law

Sir Isaac Newton (4 January 1643-31 March 1727 ) was an English physicist, mathematician, astronomer, natural philosopher, alchemist and theologian. His accomplishments in different fields have revolutionized the world.

The newton is the SI unit for force. It is equal to the amount of net force required to accelerate a mass of one kilogram at a rate of one meter per second squared i.e. $1 N=1kg\cdot \frac{m}{s^2}$

A force is any influence that causes a free body to undergo a change in speed, a change in direction, or a change in shape. Force can also be described by intuitive concepts such as a push or pull that can cause an object with mass to change its velocity or which can cause a flexible object to deform.

The relationship between force, mass and acceleration of an object

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Introduction

Newton's second law defines the relationship between force, mass, acceleration:

A body of mass $m$ subject to a net force $F$ undergoes an acceleration $a$ that has the same direction as the force and a magnitude that is directly proportional to the force and inversely proportional to the mass, i.e. $F=m \cdot a$ .

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Example 1 [metric]

Problem

A car of mass 800kg is pulling a trailer of mass 200kg along a straight road. The car is connected to the trailer by a tow bar which can be modelled by a light inextensible rod.
The driving force of the car is 2.6kN and the total resistance to motion of the car and trailer is 600N.

Determine the acceleration of the system.

Workings

The total mass is $800 + 200 = 1000 kg$ .

Using Newton's Second Law we have :

$26000 - 600 = 2000 = 1000\times \text{Acceleration}$