yoon (jy4326) – HW11 – markert – (58840)
1
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001
(part 1 of 3) 10.0 points
A block of unknown mass is attached to a
spring of spring constant 5
.
3 N
/
m and under
goes simple harmonic motion with an ampli
tude of 15 cm.
When the mass is halfway
between its equilibrium position and the end
point, its speed is measured to be 20
.
8 cm
/
s.
Calculate the mass of the block.
Correct answer: 2
.
06725 kg.
Explanation:
Let :
k
= 5
.
3 N
/
m
,
A
= 15 cm
,
and
v
= 20
.
8 cm
/
s
.
If the maximum displacement (amplitude) is
A
, the halfway displacement is
A
2
. By energy
conservation,
K
i
+
U
i
=
F
f
+
U
f
0 +
1
2
k A
2
=
1
2
m v
2
+
1
2
k
parenleftbigg
A
2
parenrightbigg
2
k A
2
=
m v
2
+
1
4
k A
2
m
=
3
k A
2
4
v
2
=
3 (5
.
3 N
/
m) (0
.
15 m)
2
4 (0
.
208 m
/
s)
2
=
2
.
06725 kg
.
002
(part 2 of 3) 10.0 points
Find the period of the motion.
Correct answer: 3
.
92409 s.
Explanation:
ω
=
radicalbigg
k
m
=
radicalBigg
5
.
3 N
/
m
2
.
06725 kg
= 1
.
60118 rad
/
s
,
so the period is
T
=
2
π
ω
=
2
π
1
.
60118 rad
/
s
=
3
.
92409 s
.
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 Fall '09
 BOCKNACK
 Organic chemistry, Energy, Kinetic Energy, Potential Energy, Correct Answer, Yoon

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