

In order to introduce the definition of impulse, at the
beginning of this unit, the net force and the acceleration are regarded as
constant. The definition of impulse is developed while considering as starting
point Newton's second law of
motion,
, where
is the net external force acting on the object
and the mass, m, and acceleration,
,of the object, along with the
definition of acceleration,
where
is the change in velocity and
is the time taken. In this
case, because the acceleration
is constant; thus, equal to its average. Combining these two expressions the
following relation is obtained,
The last expression is the foundation for the definition of
Impulse, . From this definition
it is concluded that in order to know the effect of a net force acting on an
object, it is not only necessary to precise the value of the force but it is
also necessary to recognize the time that this force acts on the object. Further
understanding of this definition is obtained studying the graphical
representation of the impulse from the graph of the force versus the time.

In the graph at the left, the area under the curve of the force
versus the time correspond to the impulse,
. This
definition can be extended to situations where the acceleration and/or
force are variant. Thus,
Impulse is the area under
the curve of the force versus the time.

The units of impulse are
.

Calculate the impulse associated to the force represented on the
graph at the left. 

a)

360 kg m/s 


b)

240 kg m/s 

c)

80 kg m/s 
N

d)

380 kg m/s 

e)

None of the above. 

Calculate the impulse associated to the force represented on the
graph at the left. 

a)

420 kg m/s 

N 
b)

245 kg m/s 

c)

105 kg m/s 

d)

140 kg m/s 

e)

None of the above. 



In most cases,
the forces applied over objects are not constant or they do not have a
simple variation with the time such like the case of the force applied
by a golf club to a golf ball.
A variant force can also be the force applied by a soccer player when kicks the ball,
a kicker of a football team when kicks the football, a hitter hitting a baseball
with a bat, or a tennis player hitting the ball. In all these cases, the force
can vary dramatically over a very short period of time. The following
graphical representation illustrate the form in which the force can vary, as a
function of the time, in these cases. 



The applet on the left shows a sequence of drawing
illustrating the processes of matching the area of the actual peak
representing the impulse to the area of the above defined average force. 
