PASCO ME-6844 Parallel Spring Bracket - Manual (Page 3)

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P a r a l l e l S p r i n g B r a c k e t M E - 6 8 4 4
3
Parallel Springs of Different Length
A long spring
from the Equal
Length Spring Set
and a short spring
from the
Series/Parallel
Spring Set are
combined in paral-
lel. Both springs have
the same spring constant
(40 N/m). The initial mass
is placed off-center to make
the hook bar level; however
addition mass is added to the
center to stretch both springs
equally.
When the system oscillates, the hook
bar rocks. However, if the mass is hung
from the center (so that the hook bar is not
level) it oscillates without rocking.
A similar effect can be achieved using two identical springs with
one vertically offset using string.
Modified Series
With this combination of springs, string, and pul-
leys, the balance point of the hanging mass is
always at the center of the hook bar regardless of
the spring constants or lengths.
Measurements and Calculations
Spring Constant
Use the following method to measure the spring constant of a
spring or combination of springs.
1. With the initial mass hanging from the hook bar (so that all
springs are slightly stretched), measure the distance from the
floor to the bottom of the hook bar.
2. Add some mass (typically about 500 g) to the hanging mass.
3. Measure the distance from the floor to the bottom of the
hook bar again.
4. Calculate the change in force (the weight of the additional
mass),
∆F.
5. Calculate the change in position of the hook bar,
∆x.
6. Calculate the resultant spring constant using
(eq. 1)
The above equation lacks the negative sign usually found in
expressions of Hooke’s Law because F in this case is the applied
force rather than the force exerted by the springs.
For better precision, increase the hanging mass incrementally and
make a graph of
∆F versus ∆x. The slope of the best-fit line is k.
Addition of Spring Constants
The combination of springs is analogous to the combination of
capacitors. The equivalent spring constant of two or more springs
in parallel is
(eq. 2)
For springs in series, the equivalent spring constant is
(eq. 3)
Force and Torque
The objects
attached to the
hook bar (springs
and hanging
mass) each exerts
a torque and a
force on it. When
the system is
static, the net
torque and net
force are both
zero.
When the hook
bar has two
springs and one
mass attached to
it, it is possible to
determine the
three separate
forces:
k
∆F
∆x
------- =
k
eq
k
1
k
2
k
3
… + + + =
parallel
combination
 
 
1
k
eq
-------
1
k
1
-----
1
k
2
-----
1
k
3
-----
…
+ + + =
series
combination
 
 
mg
F
s1
F
s2
r
s2
r
m