Chapter 9
Page 1
CHAPTER 9 - Linear Momentum and Collisions
1.
We find the force on the expelled gases from
F
=
∆
p
/
∆
t
= (
∆
m
/
∆
t
)
v
= (1200 kg/s)(50,000 m/s) = 6.0
×
10
7
N.
An equal, but opposite, force will be exerted on the rocket:
6.0
×
10
7
N, up
.
2.
For the momentum
p
= 4.8
t
2
i
– 8.0
j
– 8.9
t
k
, we find the force from
F
= d
p
/dt =
9.6
t
i
– 8.9
k
, in SI units
.
3.
(
a
)
p
=
mv
= (0.030 kg)(12 m/s) =
0.36 kg
·
m/s
.
(
b
)
The force, opposite the direction of the velocity, changes the momentum:
F
=
∆
p
/
∆
t
;
– 2.0
×
10
–2
N = (
p
2
– 0.36 kg
·
m/s)/(12 s), which gives
p
2
=
0.12 kg
·
m/s
.
4.
The change in momentum is
∆
p
=
p
2
–
p
1
=
mv
j
–
mv
i
= (0.145 kg)(30 m/s)
j
– (0.145 kg)(30 m/s)
i
=
– (4.35 kg
·
m/s)
i
+ (4.35 kg
·
m/s)
j
.
5.
The force changes the momentum:
F
= (26 N)
i
– (12 N/s
2
)
t
2
j
= d
p
/d
t
.
Because
F
is a variable force, we integrate to find the momentum change:
d
p
=
F
d
t
;
∆
p
=
(26N)
i
– (12N/s
2
)
t
2
j
dt
1.0s
2.0s
= (26N)
t
i
– (4.0N/s
2
)
t
3
j
1.0s
2.0s
=
(26N
?
s)
i
– (28 N
?
s)
j
.
6.
If
M
is the initial mass of the rocket and
m
2
is the mass of the
expelled gases, the final mass of the rocket is
m
1
=
M
–
m
2
.
Because the gas is expelled perpendicular to the rocket in the
rocket’s frame, it will still have the initial forward velocity,
so the velocity of the rocket in the original direction will not
change.
We find the
y
-component of the rocket’s velocity after
firing from
v
1
⊥
=
v
0
tan
= (120 m/s) tan 23.0° = 50.9 m/s.
Using the coordinate system shown, for momentum
conservation in the
y
-direction we have
0 + 0 =
m
1
v
1
⊥
–
m
2
v
2
⊥
,
or
(
M
–
m
2
)
v
1
⊥
=
m
2
v
2
⊥
;
(4200 kg –
m
2
)(50.9 m/s) =
m
2
(2200 m/s), which gives
m
2
=
95 kg
.
7.
(
a
)
We choose downward as positive.
For the fall we have
y
=
y
0
+
v
0
t
1
+
!
at
1
2
;
h
= 0 + 0 +
!
gt
1
2
, which gives
t
1
= (2
h
/
g
)
1/2
.
To reach the same height on the rebound, the upward motion must be a reversal of the downward
v
0
Before
v
2
v
1
After
x
y
gas

This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*