Biomedical Engineering Reference
In-Depth Information
Figure 5.5
Impulse generation curve.
body, the force due to body weight is subtracted or the time axis is moved up to the
corresponding force value. A similar curve can be developed for landing and other
scenarios.
When an impulse acts on a system, the result is a change in the system's total
momentum. The conservation of linear momentum is obeyed only if the impulse
of the resultant force is zero. Hence, momentum will also increase when the mag-
nitude of the impulse is increased. Since this increase may not change the mass, the
result will be a corresponding increase in the magnitude of the velocity. Therefore,
the change in resulting momentum is usually associated with a change in the veloc-
ity. An increase in velocity could be achieved by applying a large force for a short
period of time or a small force for a long period of time. Typically, muscles contract
more forcefully over short periods of time than when they are required to contract
more slowly for long periods of time. Suppose a tennis player is playing tennis and
wants to serve a ball that travels too fast (or an ace) so that the opponent has very
little time to react. The ball should have the largest possible velocity, that is, the
largest possible momentum, when it leaves the tennis racket. Since the ball would
move slowly prior to being hit by the racket, it can be considered to have a negligi-
ble momentum. To change this momentum to a very large momentum toward the
other side of the net, the player has to apply the largest possible impulse on the ball.
Since impulse depends directly on the force applied and the duration of the force,
the player should apply the largest possible force for the longest duration. Swing-
ing the racket harder will hit the ball harder or apply maximum force. If the ball is
hit at twice the force, it will impart at twice the impulse. However, the amount of
force that can be applied depends on the strength of person and body coordination.
Alternatively, the impulse on the ball can be increased by increasing the time that
the racket exerts its force on the ball, a process called following through. If the ball
is hit at twice the duration, the impulse of the ball will also increase twice. Thus,
the greatest impulse is developed or a change in momentum is maximum if the ball
is hit hard and followed through. In general, the linear impulse-momentum relation
states that in the area under the force time (F-t) the curve is equal to the change in
linear momentum, that is,
