Solutions Prelim I Spring 2007
1.
speeding up, slowing down, slowing down, speeding up
2.
(A)
3.
(B)
4.
(B)
5.
(C)
6.
(E)
7.
(C)
8.
(A)
9.(a)
down, up, zero
9.(b)
down, up, up
1. (a)
v
A
=
v
A
ˆ
i
=
v
0
x
ˆ
i
is also the initial velocity of the bale. The time
T
that it takes to
fall to the ground is given by
H
=
1
2
gT
2
.
T
=
2
H
g
. While the bale falls, it travels
the distance
D
=
v
0
x
T
to the right.
v
A
=
v
0
x
=
D
T
=
D
g
2
H
(b)
v
fx
=
v
0
x
=
v
A
=
D
g
2
H
v
fy
=

gT
=

2
gH
2. (a)
Springs in parallel: same extension
x
, add the forces
F
A
and
F
B
for each
x
. Because
they must have the same extension, neither spring stretches, i.e.
x
= 0 until
F >
4 N.
F
(0
.
5cm) = 6 N+2 N = 8 N.
F
(1
.
0cm) = 8 N+4 N = 12 N.
F
(2
.
0cm) = 12 N+8 N =
20 N.
(b)
Springs in series: same force
F
, add extensions
x
A
and
x
B
. For
F
= 0
, x
A
+
x
B
= 0.
Spring A does not stretch until
F >
4 N.
F
= 2 N
,
x
A
+
x
B
= 0 + 0
.
5 cm = 0
.
5 cm
F
= 4 N
,
x
A
+
x
B
= 0 + 1
.
0 cm = 1
.
0 cm
F
= 6 N
,
x
A
+
x
B
= 0
.
5 cm + 1
.
5 cm = 2
.
0 cm
Series
x(cm)
F(N)
0
8
14
16
20
18
12
10
6
4
2
0
2.0
1.5
1.0
0.5
Parallel
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3. (a)
Air speed
v
PA
refers to motion of the plane relative to air,
v
PA
. Wind speed
v
W
refers
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 Spring '07
 LECLAIR,A
 mechanics, Friction, maximum friction force, Air speed vP

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