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# Spring Force

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```Spring Force
Compression and Extension
пЃќ
It takes force to press a
spring together.
пЃќ
It takes force to extend a
spring.
пЃќ
More compression requires
stronger force.
пЃќ
More extension requires
stronger force.
Spring Constant
пЃќ
The distance a spring moves
is proportional to the force
applied.
F п‚µ x
пЃќ
The ratio of the force to the
distance is the spring
constant (k).
k пЂЅ F /x
F
x
HookeвЂ™s Law
пЃќ
пЃќ
пЃќ
The force from the spring
attempts to restore the
original length.
This is sometimes called
HookeвЂ™s law.
The distance x is the
displacement from the
natural length, L.
L
L+ x
L-x
F пЂЅ пЂ­ kx
Spring Constant
пЃќ
YoungвЂ™s modulus is a from a
linear relation like HookeвЂ™s
law.
вЂў YoungвЂ™s modulus describes
a type of material.
вЂў The spring constant
describes an object.
пЃќ
Y and k are related.
Y пЂЅ
пЃі
пЃҐ
F пЂЅ(
пЂЅ
YA
F /A
пЃ„L / L
пЂЅ
FL
AпЃ„L
)пЃ„ L пЂЅ kпЃ„ L
L
F
пЃ„L
Position-dependent Force
F
пЃќ
The spring force increases in
magnitude with increasing
displacement.
пЃќ
The slope of the line is the
spring constant.
stiff spring
soft spring
пЃ„x
Scales
пЃќ
One common use for a
spring is to measure weight.
пЃќ
The displacement of the
spring measures the mass.
Fs = -k(-y)
F g пЂЅ Fs
-y
mg пЂЅ пЂ­ k ( пЂ­ y )
m пЂЅ (k / g ) y
Fg = -mg
Stiff Springs
пЃќ
пЃќ
Two spring scales measure
the same mass, 200 g. One
stretches 8.0 cm and the
other stretches 1.0 cm.
What are the spring
constants for the two
springs?
пѓ�
The spring force balances
the force from gravity: F = 0
= (-mg) + (-kx).
пѓ�
Solve for k = mg/ (вЂ“x).
пѓ� x is negative.
пѓ�
Substitute values:
пѓ�
(0.20 kg)(9.8 m/s2)/(0.080 m)
= 25 N/m.
(0.20 kg)(9.8 m/s2)/(0.010 m)
= 2.0 x 102 N/m.
пѓ�
Restoring Force in Motion
пЃќ
When springs are in motion
they oscillate.
пЃќ
The motion has a period, T.
пЃќ
Is it like the period of circular
motion?
next
```
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