Hood, Charles – Homework 14 – Due: Dec 14 2006, 11:00 pm – Inst: Jan Opyrchal
1
This
printout
should
have
8
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 2) 10 points
A 36
.
9 kg girl is standing on a 235 kg plank.
The plank, originally at rest, is free to slide on
a frozen lake, which is a flat, frictionless sup
porting surface. The girl begins to walk along
the plank at a constant speed of 1
.
72 m
/
s to
the right relative to the plank.
What is her velocity relative to the ice sur
face?
Correct answer: 1
.
48658 m
/
s.
Explanation:
v
g
= velocity of girl relative to ice
v
p
= velocity of plank relative to ice
v
gp
= relative velocity of girl.
Let :
m
g
= 36
.
9 kg
,
m
p
= 235 kg
,
and
v
gp
= 1
.
72 m
/
s
.
By conservation of momentum
0 =
m
g
v
g
+
m
p
v
p
,
v
p
=

m
g
v
g
m
p
The relative velocity is
v
gp
=
v
g

v
p
(1)
=
v
g


m
g
v
g
m
p
¶
=
v
g
m
p
+
m
g
v
g
m
p
=
v
g
(
m
p
+
m
g
)
m
p
.
Thus
v
g
=
m
p
v
gp
m
g
+
m
p
=
(235 kg) (1
.
72 m
/
s)
235 kg + 36
.
9 kg
=
1
.
48658 m
/
s
.
002
(part 2 of 2) 10 points
What is the velocity of the plank relative to
the ice surface?
Correct answer:

0
.
233424 m
/
s.
Explanation:
Using Eq. (1),
v
p
=
v
g

v
gp
= 1
.
48658 m
/
s

1
.
72 m
/
s
=

0
.
233424 m
/
s
,
directed opposite to the girl’s direction.
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 Fall '08
 KEN
 Momentum, Work, Correct Answer, kg, Hood

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