Newton's 2nd Law - Learn

Newton’s 2nd Law

Newton’s 2nd Law states:

When an unbalanced force acts on an object it produces an acceleration that is:

Or stated another way: the acceleration of an object increases as the applied force increases and decreases as the mass of the object increases.

Newton’s 2nd Law can be expressed:

$F=ma$

Where:

$F$ = force in Newtons

$m$ = mass in kilograms

$a$ = acceleration in $\cfrac { { m } }{ s^{ 2 } }$

The unit for force, the Newton is the force required to accelerate a mass of $1kg$ at $1\cfrac { { m } }{ s^{ 2 } }$

Example 1:

A 500kg bike is accelerated at 1.5 $\cfrac { m }{ s^{ 2 } }$ . Calculate the force acting on the bike:

$m=500kg$

$a=1.5\cfrac { m }{ s^{ 2 } }$

$F=?$

Using $F=ma$

$F=500\times 1.5$

$F=750N$

Some questions will require the original equation to be rearranged:

Example 2:

A 2kg ball is accelerated by a force of 15N acting to the right. Calculate the acceleration of the ball:

$F=15N$

$m=2kg$

$a=?$

Using $F=ma$

$15=2a$

$a=\cfrac { 15 }{ 2 }$

$a=7.5\cfrac { m }{ s^{ 2 } }$ to the right

Some questions will use a mass that is not in kg. The mass needs to be converted to kg for the calculation to be in the correct units:

Example 3:

Calculate the force acting on a 200gm toy that accelerates to the left at 2.4 $\cfrac { m }{ s^{ 2 } }$ :

$m=200g=0.2kg$

$a=2.4\cfrac { m }{ s^{ 2 } }$

$F=?$

Using $F=ma$

$F=0.2\times 2.4$

$F=0.48N$ to the left