Impulse
A cue at rest struck by the player achieves a velocity
in a relatively short span of time. When the collision or impact occurs the ball is
deformed and large internal stresses are created. These stresses tend to restore the ball
to its original shape and it is the combined effect of these stresses which cause the ball
to jerk forward. These special motions are called impulsive motions and are caused by forces
which are delivered in very short span of time, or impulse.
Mathematically speaking, an impulse is equivalent to:
From the above equation, we see that impulse is the total force from t=0 to t=t, or
the change in the linear momentum.
When two bodies collide, as in the diagram, each body will experience an impulsive reaction due
to the impact of the other, I and -I in the figure. We assume that the impulsive
reactions act along the normals to the surfaces at the point of impact (if friction must be
taken into account there will, in addition, be an impulsive tangential reaction on the bodies).
For each of the bodies the balance of impulse and jump of linear momentum still hold, whilst
for the system as a whole, since no external impulse acts, the impulsive reactions must be equal
and opposite. This concept is important for the following section, Conservation of Linear Momentum.
Sample Problem
Thee cue ball initially at rest, was hit and its final momentum after being struck was 50 m/s. If
the cue was struck for t seconds, and the striking follows the equation
F=3t2+t-1, what is t? (nearest to hundredth second)
