70 5. IMPULSE, MOMENTUM, AND IMPACT OF PARTICLES
5.3.3 CONSTRAINED OBLIQUE CENTRAL IMPACT
In the foregoing sections, the two particles are assumed to be moving freely before and after im-
pact. In this section it is assumed that one or both of the colliding particles is or are constrained.
Specifically, consider the case illustrated in Figure 5.6 in which block A is constrained to move
horizontally on the smooth surface and ball B is free to move in the plane of the figure. For
simplicity, it is assumed that no friction between block A and the horizontal surface, and no
friction between block A and ball B. It should be noted that the impulses acted on the system
consist of those of the internal forces
*
F and
*
F directed along the line of impact (that is, the
n-axis), and the impulse of the external force
*
F
e
acted on by the horizontal surface on block A
and directed along the vertical.
Smooth Surface
(No friction between block A and smooth surface)
Smooth Surface
(No friction between block A and smooth surface)
t
t
y
y
x
n
n
F
⃑
e
Δt
–F
⃑
Δt
A
B
A
t
y
n
A
B
θ
θ
θ
m
A
⃑
A
m
A
⃑'
A
m
B
⃑'
B
m
B
υ⃑
B
+ =
F
⃑
Δt
Figure 5.6: Constrained oblique central impact of a block and a ball.
e unknown velocities of block A and ball B immediately after impact are the magnitude
of the velocity
*
v
0
A
(its direction is known to be along the horizontal surface), the magnitude and
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