** 8. A 500-g block is suspended from a spring. With the block at rest, the spring stretches15 cm. The block is pulled down an additional 10 cm and released.a) What is the spring constant of the spring?b) How many complete oscillations will the system complete in 20 s?c) Find one other combination of mass and spring constant that would produce thesame periodd) By how much would the spring stretch at rest for this new case?

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Asked Nov 18, 2019
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** 8. A 500-g block is suspended from a spring. With the block at rest, the spring stretches
15 cm. The block is pulled down an additional 10 cm and released.
a) What is the spring constant of the spring?
b) How many complete oscillations will the system complete in 20 s?
c) Find one other combination of mass and spring constant that would produce the
same period
d) By how much would the spring stretch at rest for this new case?
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** 8. A 500-g block is suspended from a spring. With the block at rest, the spring stretches 15 cm. The block is pulled down an additional 10 cm and released. a) What is the spring constant of the spring? b) How many complete oscillations will the system complete in 20 s? c) Find one other combination of mass and spring constant that would produce the same period d) By how much would the spring stretch at rest for this new case?

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Expert Answer

Step 1

Given data:

Mass of the block, m = 500 g = 0.5 kg

Stretched in the string, xo = 15 cm = 0.15 m

Step 2

 (a)

The weight of the block would balance the spring force:

= kx.
mg
k =
0.5x9.8
0.15
= 32.66 N/m
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= kx. mg k = 0.5x9.8 0.15 = 32.66 N/m

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Step 3

(b)

Time period:

...
m
T 2T
k
(i)
Plugging in the given values
0.5
T 2x 3.14
32.66
=0.777 s
20
Number of oscillation in 20s
25.74
0.777
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m T 2T k (i) Plugging in the given values 0.5 T 2x 3.14 32.66 =0.777 s 20 Number of oscillation in 20s 25.74 0.777

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