7.2. Impulse http://www.ck12.org
7.2 Impulse
Objectives
Students will learn the meaning of impulse force and how to calculate both impulse and impulse force in various
situations.
Vocabulary
- impulse
Introduction
Earlier, we solved a problem dealing with change in momentum. We emphasized that momentum is a vector quantity
and that care must therefore be taken in dealing with the direction of velocity. Now, we will again discuss a change
in momentum, but we will investigate it from the point of view of Newton’s Second Law (N2L). The connection
between the change in momentum and N2L will help to explain some everyday occurrences involving collisions, for
example, why it is a good idea to bend your knees when landing on the ground, why it is a good idea to bring your
arm back as you catch a fast ball, or why it hurts more to land on concrete than on a mattress bed.
We can explain the reasons for these statements by defining a quantity called animpulse.
Newton’s Second Law Revisited
Recall that N2L can be stated as∑F=Fnet=ma. We will rewrite this equation dropping the “net” subscript. We
will also assume thatFrepresents the average net force (we will see why in a moment) and express the acceleration
asa=∆∆vt=(vf∆−tvi), giving us:
F=m
(vf−vi)
∆t=
mvf−mvi
∆t→F∆t=mvf−mvi=∆p→F∆t=∆pWe callF∆t=∆pthe impulse-momentum equation. The left-hand side is referred to as the impulse and the right-
hand side is referred to as the change in momentum. The equation suggests that we needn’t only use the unitkgs∗mto
express momentum since the change in momentum is equivalent toF∆t, expressed in the unitN−s.
In typical collisions there is a rapid buildup of force between the objects colliding and a rapid diminishing of the
force as they either come to rest or separate from each other. In either case the force is not constant and the time of
interaction is brief.Figure7.8 shows a baseball as it compresses and expands as it’s being hit by a bat.Figure7.8
shows a graph of the force on the baseball as function of time during the interaction with the bat. The times for such
interactions are measured in milliseconds and the force is in kilo-newtons.
Illustrative Example 7.2.1
If a ball thrown by Aroldis Chapman remains in contact with a baseball bat for 0.70 milliseconds:
(a) What is the impulse the ball experiences?