PASCO ME-6844 User Manual

®

Parallel Spring Bracket

ME-6844

Instruction Sheet

012-09843A

Included Equipment Part Number

Suspension Bracket

ME-6844

Parallel Hook Bar

Thumbscrews (2 pieces) 617-016

Additional Equipment Recommended

Series/Parallel Spring Set ME-6842

Equal Length Spring Set ME-8970

Hooked Mass Set SE-8759

Large Table Clamp ME-9472

45 cm Rod ME-8736

Meter Stick SE-8695

800-772-8700 www.pasco.com

Introduction

The Parallel Spring Bracket allows springs to be combined in
series and parallel. Masses can be hung in offset positions to
compensate for springs of different strengths.

The Parallel Spring Bracket is ideal for:

• exploring how spring constants add when springs are
arranged in series or in parallel,

• demonstrating the analogy between combinations of springs
and combinations of capacitors, and

• exploring torque acting on the hook bar by placement of the
mass and springs at different positions.

Parallel Spring Bracket ME-6844

Set-up

1. Assemble the suspension bracket, a
large table clamp and a rod as illus­trated. The table clamp (rather than a
base) and a relatively short rod are
recommended for maximum stabil­ity.

2. Hang any combination of springs
from the suspension bracket.

3. Attach the parallel hook bar to the
bottom of the spring combination.

4. Hook a mass onto the notched slot of
the parallel hook bar. The mass should be large enough to
stretch all springs at least slightly.

5. Move the mass left or right along the notched slot to find the
position that makes the hook bar as close to horizontal as
possible.

6. Check that all springs are stretched. You should be able to
see between the coils of every spring. If one of the springs is
not stretched, increase the hanging mass.

Three Parallel

Three different springs (40 N/m, 20 N/m,
and 10 N/m) from the Series/Parallel
Spring Set are combined in parallel.

Series

Two springs are linked end-to-end to
form a series combination.

Sample Configurations

Single Spring

Though the hook bar is not necessary to
attach a mass to a single spring, it does
provide a convenient point from which to
measure changing displacement.

Two Parallel

Two springs (10 N/m and 40 N/m) from
the Series/Parallel Spring Set (ME-6842)
are combined in parallel. The hanging
mass is placed off center to make the
hook bar level.

Series and parallel

Two short springs from the Series/Paral­lel Spring Set are linked in series. That
combination is in parallel with a single
long spring from the Equal Length Spring
Set (ME-8970). When not stretched, the
long spring is twice the length of each of
the short springs.

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Parallel Spring Bracket ME-6844

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 paral­lel. 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.

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)

∆F

k

-------=

∆x

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

Modified Series

With this combination of springs, string, and pul­leys, 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.

(eq. 2)

k

k1k2k3…+++=

eq




combination

For springs in series, the equivalent spring constant is

1

1

(eq. 3)

1

-------

k

-----

k

eq

1

-----

k

1

----- …+++=

k

2

3




combination

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:

F

mg

s1

r

s2

r

m

parallel

series

F

s2

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Parallel Spring Bracket ME-6844

(eq. 4)

F

Fs1Fs2mg–+0==

net

The axis about which the torques are measured is chosen to be at
the “0 cm” mark. Spring #1 is attached at the axis, therefore its
torque is zero. The net torque is

(eq. 5)

Solving for F

(eq. 6)

τ

netrs2Fs2rm

yields:

s2

mg–0==

r

m

------

F

s2

mg=

r

s2

Combining equations 4 and 6 gives us:

r



m

1

------–

(eq. 7)

F

s1




mg=

r

s2

Period of Oscillation

The period of oscillation of a mass on a spring (or combination of
springs) is

T 2π

The mass, m , should include the hanging mass, the mass of the
hook bar, and 1/3 of the mass of the springs.

m

----=

k

Storage

To keep the bracket and hook bar together when not in use, clamp
the hook bar under the thumbscrews as illustrated.

Technical Support

For assistance with any PASCO product, contact PASCO at:

Address: PASCO scientific

10101 Foothills Blvd.
Roseville, CA 95747-7100

Phone: [phone] (worldwide)

800-772-8700 (U.S.)

Fax: [phone]

Web: www.pasco.com

Email: [e-mail]

To demonstrate this relationship for any combination of springs,
use a stop watch to measure the period of oscillation. Increase the
hanging mass in steps. Make a graph of T
of the best-fit line is 4π

2

/k.

2

versus ∆m. The slope

Sensor-based Measurement

To measure the spring
constant using a rotary
motion sensor (RMS)
and a force sensor, set
up the equipment as
illustrated. Pull the
force sensor to stretch
the spring combination.
Make a graph of force
(measured by the force
sensor) versus linear
position (measured by
the RMS). The slope of
the best-fit line is the
spring constant.

Limited Warranty For a description of the product warranty, see the
PASCO catalog.
Copyright The PASCO scientific 012-09843A

Instruction Sheet

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Parallel Spring Bracket

®

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