Newton’s 2nd Law


Newton’s 2nd Law states:

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

  • Directly proportional to the force, and
  • Indirectly proportional to the mass of the object

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

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