Gozick, Brandon – Homework 12 – Due: Oct 20 2006, 8:00 pm – Inst: D Weathers
1
This
printout
should
have
10
questions.
Multiplechoice questions may continue on
the next column or page – find all choices
before answering.
The due time is Central
time.
001
(part 1 of 1) 10 points
A 1
.
44 kg particle has a velocity of
v
x
=
1
.
23 m
/
s and
v
y
=

4
.
91 m
/
s.
Find the magnitude of its total momen
tum.
Correct answer: 7
.
28888 kg
·
m
/
s.
Explanation:
Let :
m
= 1
.
44 kg
,
v
x
= 1
.
23 m
/
s
,
and
v
y
=

4
.
91 m
/
s
.
Given the velocity vector, the magnitude of
the velocity vector is
v
=
q
v
2
x
+
v
2
y
The momentum is defined by
p
=
m v
=
m
q
v
2
x
+
v
2
y
= (1
.
44 kg)
q
(1
.
23 m
/
s)
2
+ (

4
.
91 m
/
s)
2
= 7
.
28888 kg
·
m
/
s
.
Alternatively, the momentum vector is de
fined by
p
x
=
mv
x
and
p
y
=
mv
y
, so
p
=
q
p
2
x
+
p
2
y
=
q
(
m v
x
)
2
+ (
m v
y
)
2
=
m
q
v
2
x
+
v
2
y
=
m v
=
7
.
28888 kg
·
m
/
s
.
keywords:
002
(part 1 of 1) 10 points
A uranium nucleus
238
U may stay in one piece
for billions of years, but sooner or later it de
cays into an
α
particle of mass 6
.
64
×
10

27
kg
and
234
Th nucleus of mass 3
.
88
×
10

25
kg,
and the decay process itself is extremely fast
(it takes about 10

20
s). Suppose the uranium
nucleus was at rest just before the decay.
If the
α
particle is emitted at a speed of
2
.
1
×
10
7
m
/
s, what would be the recoil speed
of the thorium nucleus?
Correct answer: 359381 m
/
s.
Explanation:
Let :
v
α
= 2
.
1
×
10
7
m
/
s
,
M
α
= 6
.
64
×
10

27
kg
,
and
M
Th
= 3
.
88
×
10

25
kg
.
Use momentum conservation: Before the de
cay, the Uranium nucleus had zero momentum
(it was at rest), and hence the net momentum
vector of the decay products should total to
zero:
~
P
tot
=
M
α
~v
α
+
M
Th
~v
Th
= 0
.
This means that the Thorium nucleus recoils
in the direction exactly opposite to that of the
α
particle with speed
k
~v
Th
k
=
k
~v
α
k
M
α
M
Th
=
(2
.
1
×
10
7
m
/
s) (6
.
64
×
10

27
kg)
3
.
88
×
10

25
kg
=
359381 m
/
s
.
keywords:
003
(part 1 of 1) 10 points
A gadget of mass 19
.
55 kg floats in space
without motion.
Because of some internal
malfunction, the gadget violently breaks up
into 3 fragments flying away from each other.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 Weathers
 mechanics, Kinetic Energy, Mass, Momentum, Work, Velocity, kg, m/s

Click to edit the document details