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7.77:
Let
m
18
.
0
1
=
x
,
m
71
.
0
2
=
x
. The spring constants (assumed identical) are then
known in terms of the unknown weight
w
,
w
kx
=
1
4
. The speed of the brother at a given
height
h
above the point of maximum compression is then found from
,
2
1
)
4
(
2
1
2
2
2
mgh
v
g
w
x
k
+
=
or
,
2
2
)
4
(
1
2
2
2
2
2
-
=
-
=
h
x
x
g
gh
x
w
g
k
v
so
s
m
13
.
3
))
m
90
.
0
(
2
)
m
18
.
0
(
)
m
71
.
0
((
)
s
m
80
.
9
(
2
2
=
-
=
v
, or
s
m
1
.
3
to two
figures.
b) Setting
0
=
v
and solving for
h
,
,
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Unformatted text preview: 40 . 1 2 2 1 2 2 2 2 = = = x x mg kx h or 1.4 m to two figures. c) No; the distance 1 x will be different, and the ratio ( 29 2 m 53 . 1 ) m 53 . ( 1 1 2 1 1 2 2 1 x x x x x x + = = + will be different. Note that on a small planet, with lower g , 1 x will be smaller and h will be larger....
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