
Mechanics
Newton’s Laws of Motion
Law 1:
A body will continue in a state of rest or uniform motion unless acted on by an
external force.
This is often called the law of inertia.
Law 2:
The net (or resultant) force acting on a body is equal to the
product of its mass and its acceleration.

Force = mass × acceleration 

F = ma 
Law 3:
If body A exerts a force on body B, then body B exerts an
equal but opposite force on body A. 
The symbol
means "the sum of" so, if we have two forces
and ,
acting on a body, then
means .
So, remember,
represents a vector addition.
For example:

The sum of these two forces is found by vector addition. 
If the two forces act along the
same line then the arithmetic becomes a little easier.

In this case,
is equal to
+10 – 4 = 6 N (to the right) 
Using Newton’s Second Law of Motion
An object of mass m = 20kg rests on a horizontal surface. Calculate the
magnitude of the force exerted by the surface on the object in the following situations.
a) Stationary or moving with
constant velocity

F
= ma
also,
F
= R + mg
but, in this case a = 0
therefore, R + mg = 0
and so R =  mg
R = 196 N 
b) Accelerating upwards at 2 ms^{2}

F
= ma
also, F
= R + mg
therefore,
R + mg = ma
and so R = m(a – g)
R = 236 N 
c) Accelerating downwards at 9·8 ms^{2}

F
= ma
also,
F
= R + mg
therefore,
R + mg = ma
and so R = m(a – g)
R = 0
So, in this case, the body would appear to be
weightless. 

