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Key Concept: Impact is a special case of linear and
angular impulse and momentum where the time duration of the impulse, Δt, is very small.
Examples include a bat striking a ball, a car’s bumper striking a
post, and a cue stick striking a billiard ball. During impact you need only include the
“impulsive force”. Finite
forces such as weight, friction, and external loads do not contribute
to the impulse. Note: The impulsive force, ∫F dt, acts along the “line of impact” as shown in the
figure below.
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Δt
∫
F dt j =
( m vbx2 ˗ m vbx1 ) i + ( m vby2 ˗ m vby1 ) j (impulse momentum for B)
0
Δt
∫ ˗ F dt j
= ( m vAx2 ˗ m vAx1 ) i + ( m vAy2 ˗
m vAy1 ) j (impulse momentum for A)
0
where A and B denote particles of mass m, the
subscripts 1 and 2 refer to prior to and after
impact
respectively, and vAx, vAy, vBx,
and vBy denote components of velocity
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NOTE: “impulsive force” results in change in
linear momentum (vector equation)
Coefficient of
restitution, e e is a material property i.e. putty, steel, etc 0 ≤ e
≤ 1
Definition
e = ˗
(magnitude of relative velocity
along line of impact after impact) /
(magnitude of relative
velocity along line of impact before impact)
NOTE: expression for e applies
at the impact point along line of impact
Click here for examples.
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