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91
M
OMENTUM
9
Q9.1. Reason:
The velocities and masses vary from object to object, so there is no choice but to compute
p
x
=
mv
x
for each one and then compare.
p
1
x
=
(20 g)(1m/s)
=
20 g
!
m/s
p
2
x
=
(20 g)(2 m/s)
=
40 g
!
m/s
p
3
x
=
(10 g)(2 m/s)
=
20 g
!
m/s
p
4
x
=
(10 g)(1m/s)
=
10 g
!
m/s
p
5
x
=
(200g)(0.1m/s) = 20g
!
m/s
So the answer is
p
2
x
>
p
1
x
=
p
3
x
=
p
5
x
>
p
4
x
.
Assess:
The largest, most massive object did not have the greatest momentum because it was moving slower
than the rest.
Q9.2.
Reason:
We can find the change in momentum of the objects by computing the impulse on them and
using
the
equation
!
p
=
J
.
S
i
n
c
e
t
h
e
y
s
t
a
r
t
a
t
r
e
s
t
w
ith
zero
momentum,
we
can
write
mv
f
=
p
f
=
!
p
=
J
=
F
!
t
.
So the final velocity of either object equals the impulse on the object divided by its
mass. For the first object, this will be
(
v
1
)
f
=
(12 N)(2.0 s) /
m
= (24 N
!
s ) /
m
For the second object, the velocity is given by
(
v
2
)
f
=
(15 N)(3.0 s) /(2
m
) = (22.5 N
!
m
The velocity of the first object is seen to be higher, because no matter what the value of
m
is, the numerator is
greater in the first expression than in the second expression.
Assess:
The second object was subject to a greater force exerted for a greater time. But it ended with less
velocity because it was more massive. All three factors are important in determining the final speed.
Q9.3.
R
e
a
s
on
:
When
the
question
talks
about
forces, times, and momenta, we
immediately
think
of
the
impulsemomentum theorem, which tells us that to change the momentum of an object we must exert a net
external force on it over a time interval:
!
F
avg
!
t
=
!
!
p
.
Because equal forces are exerted over equal times, the impulses are equal and the changes in momentum are
equal. Because both carts start from rest, their changes in momentum are the same as the final momentum for
each, so their final momenta are equal.
Assess:
Notice that we did not need to know the mass of either cart, or even the specific time interval (as long
as it was the same for both carts) to answer the question.
Q9.4. Reason: (a)
The acceleration of the puck with the smaller mass will be four times greater than the
acceleration of the puck with the larger mass. The puck with the larger mass takes longer to travel the distance.
The time it takes an object to move a given distance from rest can be calculated from the kinematic equation
!
x
=
1
2
a
x
(
!
t
)
2
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View Full Document92
Chapter 9
Solving for the time,
!
t
=
2
!
x
a
x
Since the acceleration of the smaller puck is four times that of the larger puck, the time it takes the smaller puck
to travel the distance is half the time it takes the larger puck.
(b)
The force on each puck is the same. Since the smaller puck takes half the time to travel the distance, the
impulse of the smaller puck is half the impulse of the larger puck. From the impulsemomentum theorem, the
change in momentum of the smaller puck is half the change in momentum of the larger puck.
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 Fall '10
 Shawhan
 Mass, Momentum

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