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517
Chapter 8
Systems of Particles and Conservation of
Momentum
Conceptual Problems
1
•
Determine the Concept
A doughnut. The definition of the center of mass of an object
does not require that there be any matter at its location. Any hollow sphere (such as a
basketball) or an empty container with any geometry are additional examples of three
dimensional objects that have no mass at their center of mass.
*2
•
Determine the Concept
The center of mass is midway between the two balls and is in
freefall along with them (all forces can be thought to be concentrated at the center of
mass.)
The center of mass will initially rise, then fall.
Because the initial velocity of the center of mass is half of the initial velocity of the ball
thrown upwards, the mass thrown upwards will rise for twice the time that the center of
mass rises.
Also, the center of mass will rise until the velocities of the two balls are equal
but opposite.
correct.
is
)
(
b
3
•
Determine the Concept
The acceleration of the center of mass of a system of particles is
described by
,
cm
i
ext
i,
ext
net,
a
F
F
r
r
r
M
=
=
∑
where
M
is the total mass of the system.
Express the acceleration of the
center of mass of the two pucks:
2
1
1
ext
net,
cm
m
m
F
M
F
a
+
=
=
and
correct.
is
)
(
b
4
•
Determine the Concept
The acceleration of the center of mass of a system of particles
is described by
,
cm
i
ext
i,
ext
net,
a
F
F
r
r
r
M
=
=
∑
where
M
is the total mass of the system.
Express the acceleration of the
center of mass of the two pucks:
2
1
1
ext
net,
cm
m
m
F
M
F
a
+
=
=
because the spring force is an internal
force.
correct.
is
)
(
b
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518
*5
•
Determine the Concept
No.
Consider a 1kg block with a speed of 1 m/s and a 2 kg
block with a speed of 0.707 m/s.
The blocks have equal kinetic energies but momenta of
magnitude 1 kg·m /s and 1.414 kg·m/s, respectively.
6
•
(
a
) True. The momentum of an object is the product of its mass and velocity. Therefore,
if we are considering just the magnitudes of the momenta, the momentum of a heavy
object is greater than that of a light object moving at the same speed.
(
b
) True. Consider the collision of two objects of equal mass traveling in opposite
directions with the same speed. Assume that they collide inelastically. The mechanical
energy of the system is not conserved (it is transformed into other forms of energy), but
the momentum of the system is the same after the collision as before the collision, i.e.,
zero. Therefore, for any inelastic collision, the momentum of a system may be conserved
even when mechanical energy is not.
(
c
) True. This is a restatement of the expression for the total momentum of a system of
particles.
7
•
Determine the Concept
To the extent that the system in which the rifle is being fired is
an isolated system, i.e., the net external force is zero, momentum is conserved during its
firing.
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This note was uploaded on 08/18/2010 for the course IMT 12253 taught by Professor Mikael during the Spring '10 term at École Normale Supérieure.
 Spring '10
 Mikael

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