1
Physics 221
Fall 2008
Homework #7 Solutions
Ch. 8
Due Tues, Oct 14, 2008
7.1 A 0.0100 kg particle is moving horizontally towards the negative
x
axis at a speed of 3.00 m/s and
collides with a vertical stationary wall in the
y

z
plane.
The
x
component of the force
F
x
that the
wall exerts on the particle during the collision is plotted in the figure.
The particle is in contact with
the wall during the time interval between 0.0100 s and 0.0400 s, during which
F
x
= 2.00 N.
(a)
What are the initial momentum and kinetic energy of the particle before the collision?
The initial momentum is
p
1
x
=
mv
1
x
=
(0.0100 kg)(
±
3.00 m/s)
=
±
(0.0300 kg m/s)
.
The initial kinetic energy is
K
1
=
(1/2)
mv
1
x
2
=
(1/2)(0.0100 kg)(
±
3.00 m/s)
2
=
0.0450 J.
(b)
What is the impulse exerted by the wall on the particle?
J
x
=
F
x
dt
±
=
F
x
²
t
=
(2.00 N)(0.0300 s)
=
0.0600 kg m/s
.
(c)
What are the final momentum, velocity, and kinetic energy of the particle after colliding with
the wall?
J
x
=
p
2
x
–
p
1
x
.
Therefore,
p
2
x
=
p
1
x
+
J
x
=
±
(0.0300 kg m/s) + 0.0600 kg m/s
=
0.0300 kg m/s .
The final velocity is
v
2
x
=
p
2
x
/
m
=
(0.0300 kg m/s)/(0.0100 kg)
=
3.00 m/s .
The final kinetic energy is
K
2
=
(1/2)
mv
2
x
2
=
(1/2)(0.0100 kg)(3.00 m/s)
2
=
0.0450 J.
(d) Is the collision elastic or inelastic?
Explain.
From parts (a) and (c), the initial and final total kinetic energies are the same.
Thus by
definition, the collision of the particle with the wall is
elastic
.
F
x
(N)
time (s)
0
1
2
0
0.01
0.02
0.03
0.04
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