kuruvila (lk5992) – HW 14 – opyrchal – (11113)
1
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001
10.0 points
A spring stretches 3
.
3 cm when a 14 g object
is hung from it. The object is replaced with a
block of mass 34 g which oscillates in simple
harmonic motion.
The acceleration of gravity is 9
.
8 m
/
s
2
.
Calculate the period of motion.
Correct answer: 0
.
568197 s.
Explanation:
Let :
x
= 3
.
3 cm = 0
.
033 m
,
m
1
= 14 g = 0
.
014 kg
,
and
m
2
= 34 g = 0
.
034 kg
.
The force on the spring is
F
=
k x
k
=
F
x
=
m
1
g
x
.
When the 34 g is placed into simple harmonic
motion,
T
= 2
π
radicalbigg
m
2
k
= 2
π
radicalbigg
m
2
x
m
1
g
= 2
π
radicalBigg
(0
.
034 kg) (0
.
033 m)
(0
.
014 kg) (9
.
8 m
/
s
2
)
=
0
.
568197 s
.
002 (part 1 of 3) 10.0 points
A block of unknown mass is attached to a
spring of spring constant 6
.
8 N
/
m and under
goes simple harmonic motion with an ampli
tude of 9
.
2 cm.
When the mass is halfway
between its equilibrium position and the end
point, its speed is measured to be 23
.
5 cm
/
s.
Calculate the mass of the block.
Correct answer: 0
.
781646 kg.
Explanation:
Let :
k
= 6
.
8 N
/
m
,
A
= 9
.
2 cm
,
and
v
= 23
.
5 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 (6
.
8 N
/
m) (0
.
092 m)
2
4 (0
.
235 m
/
s)
2
=
0
.
781646 kg
.
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 Fall '08
 moro
 Simple Harmonic Motion, Periodic function, 1 min, 0.235 m/s

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