sitting at rest. The collision is 1-dimensional.
(a) If the collision is perfectly elastic, what is
the final speed of the puck that was initially at
rest?
√
(b) If the collision is perfectly inelastic, what
is the final speed of the two pucks after the
collision?
√
(c) If the collision is perfectly inelastic, what
fraction of the total energy was lost during the
collision?
√
(d) If one-fourth of the initial kinetic energy was
lost during the collision, what is the final speed
of the puck that was initially at rest?
√
8-m7
A bullet of mass
m
strikes a block of
mass
M
which is hanging by a string of length
L
from the ceiling.
It is observed that, after
the sticky collision, the maximum angle that the
string makes with the vertical is
θ
. This setup is
called a ballistic pendulum, and it can be used
to measure the speed of the bullet.
(a) What vertical height does the block reach?
√
(b) What was the speed of the block just after
the collision?
√
(c) What was the speed of the bullet just before
it struck the block?
√
8-m8
A car of mass
M
and a truck of mass
2
M
collide head-on with equal speeds
v
, and the
collision is perfectly inelastic.
(a) What is the magnitude of the change in mo-
mentum of the car?
√
(b) What is the magnitude of the change in mo-
mentum of the truck?
√
(c) What is the final speed of the two vehicles?
√
(d) What fraction of the initial kinetic energy
was lost as a result of the collision?
√
8-m9
A 5
.
00 kg firework is launched straight
up into the air.
When it reaches its maximum
height of
H
= 140 m, it explodes into two frag-
ments that fly off in horizontal directions. The
explosion is very quick, and only lasts 15 ms.
One of the two fragments (fragment A, with mass
M
A
= 2
.
00 kg) lands 290 meters away from the
initial launch position.
(a) Find the speed of fragment A just after the
explosion.
√
(b) By using conservation of momentum and
your answer from part a, find the speed of the
other fragment (call this fragment B) just after
the explosion.
√
(c) Calculate the magnitude of the momentum
transferred to fragment A due to the explosion.
√
(d) Calculate the magnitude of the momentum
transferred to fragment A due to the force of

PROBLEMS
101
gravity.
√
(e) How far away from the initial launch position
does fragment B land?
Hint: the center of mass
of the two fragments lands at the location where
the firework was initially launched.
√
8-m10
An object of mass
m
, moving at veloc-
ity
u
, undergoes a one-dimensional elastic colli-
sion with a mass
km
that is initially at rest. Let
the positive direction be in the direction of the
initial motion, so that
u >
0.
(a) What is the
final velocity of mass
m
?
√
(b) What is the final velocity of the mass
km
?
√
?
8-m11
Two blocks, each of mass
M
, are con-
nected by a thread and moving with speed
v
0
.

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