Arbor Scientific
Pendulum sensor
Pendulum Sensor
(Product No PC-3155)
Range ±20° rotation
Resolution 0.01°
Introduction
Locking screw
Shaft
Clamp end
The Smart Q Pendulum Sensor has been
designed specifically to suit investigations
into pendulum theory. It incorporates a very
low friction potentiometer encased in a metal
body that is tapered at one end to enable a
firm fix in a ring stand clamp. The shaft has
a 2mm hole drilled through and is fitted with
a locking screw thus allowing attachments to
be securely held. The sensor incorporates an
LED indication of the zero position.
The Smart Q Pendulum Sensor is
equipped with a micro controller that
greatly improves the accuracy, precision
and consistency of the reading. The sensor
is supplied calibrated and the stored
calibration (in deg) is automatically loaded
when the Pendulum sensor is connected.
Connecting
The EasySense unit will detect that the Pendulum sensor is connected.
1. Connect the end of the cable to the Input socket on the EasySense unit (with the
locating arrow facing upwards).
2. Set the pendulum to zero i.e. so that when the pendulum is in its rest position, it
corresponds to the zero point on the graph.
For pendulum investigations this is achieved by:
1. Clamp the end of the pendulum sensor in a ring stand with the cable hanging
downwards.
2. Thread a length of straight wire through the hole in the shaft and tighten the
locking screw (a length of approximately one meter is generally suitable and
will give a periodic time of approximately 2 seconds).
3. Position the ring stand so that the pendulum wire hangs freely over the
surface edge (a weight at the end of the wire will help to keep it in position).
4. With the pendulum hanging still and freely at rest, loosen the clamp and
rotate the body of the sensor until the red LED illuminates. At this point the
zero of the pendulum is the same as on the graph. Clamp the sensor firmly in
position.
Note: It is possible for the shaft to be 180° out of phase. If so, unscrew the pendulum wire,
rotate the shaft by 180° and reattach.
Investigations
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The Period of a Pendulum – adjusting the amplitude
Period and Length – adjusting the length of the pendulum rod
Damped Oscillations – using stiff card of different sizes to cause air resistance
Simple Harmonic Motion
Monitoring plant growth
For these investigations the pendulum sensor is used with a
Rise of bread dough
lever arm attached to the shaft. As the lever moves, it
rotates the sensor
Rates of reaction
Pendulum Investigations
Pendulum Sensor
θ
Stiff Wire
l
Mass
In mechanics, a simple pendulum is defined
as a small heavy body suspended by a light
inextensible string.
One complete to and fro movement of the
pendulum is called an oscillation. The time
taken for one complete oscillation is called
the periodic time. The length of the
pendulum (l) is defined as the distance from
the point of suspension to the center of
gravity of the mass. As the pendulum swings
to and fro, the maximum displacement of the
mass from rest position is called the
amplitude.
Galileo first showed that the period of oscillation of a pendulum is independent of its amplitude.
The period of oscillation is given by the formula: T = 2π l
g
As π and g are constants, this means that T is proportional to l1/2.
l = length in m and g = acceleration due to gravity in m/s2.
As the period of oscillation is independent of both mass and also amplitude, it is possible by
measuring the period of oscillation to determine a value for g.
Displacement Graphs
With this sensor it is possible to investigate the effect of amplitude, length and mass
on its periodic time. Using the analysis tools within Sensing Science Laboratory, a
graph of displacement can be differentiated to produce plots of velocity and
acceleration.
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Connect the Pendulum sensor to the EasySense unit and clamp in a ring stand.
Attach a straight wire, (approximately one meter in length) with a mass at the end.
Set the pendulum to zero.
Open the Graph application. Select the New Recording Wizard, the method as
Real time and the Timespan required (a time of 10 or 20 seconds is
recommended). Next.
Select the Start Condition to start the logging at a fixed reference point, e.g.
Trigger when the Pendulum sensor Rises above a value of 0.00. Finish.
Swing the pendulum and then click on the START button so a trace of the
pendulum is obtained
To repeat the trace with different conditions e.g. amplitude, select Overlay from
the Display Wizard in the Display menu, select Input 1 & click on the enable
box.
The parameters for this investigation can be saved as a Setup file (using Save Setup
from Setup in the File Menu). A worksheet, to accompany this setup file, could be
created so that the complete investigation would be opened via the Workroom
program.
Using the Displacement against time data
To calculate the Angular Velocity:
Decide the data set to be used. To hide the other
pendulum traces un-tick their show/hide box.
Select the Function Wizard from the Tools menu.
Select the function as a dx/dt, with x as the selected
pendulum displacement trace e.g. [1] Pendulum. Type
‘Velocity’ in the name box.
Click on Apply and the Velocity trace will appear on
the graph. If the line appears off the axis, alter the
constant value (a) to a more suitable number e.g. 0.5
and click on Apply again. When you are satisfied with
the line, click on OK to load.
Show/hide box
To plot a Displacement against
Velocity graph:
Select the Display Wizard from
the Display menu. Select to Plot
as point and the X axis as Sensor.
Finish.
If necessary alter the display ( by
clicking to the left of the axis) so
that Pendulum is on the Y axis and
the Velocity is on the X axis.
To calculate the Acceleration:
Select the Function Wizard from the Tools menu – select the function as a dx/dt, select
x as the Velocity trace. Type ‘Acceleration’ in the name box. Click on Apply and the
Acceleration trace will appear on the graph. If the line appears off the axis, alter the
constant value (a) to a more suitable number e.g. 0.5, click on Apply. When you are
satisfied with the line, click on OK.
To plot an Acceleration against
Time graph:
Select the Display Wizard from
the Display menu. Select to Plot
as a line and select the X axis as
Time. Finish.
Hide the Velocity trace so just
pendulum displacement and
acceleration are displayed.
To plot an Acceleration against
Displacement graph:
Select the Display Wizard from the
Display menu. Select to Plot as a
line and the X axis as Sensor.
Finish.
Select Pendulum as the X axis and
Acceleration as the Y axis.
Warranty
All sensors are warranted to be free from defects in materials and workmanship for a period
of 12 months from the date of purchase, provided they have been used in accordance with
any instructions, under normal laboratory conditions. This warranty does not apply if the
sensor has been damaged by accident, or misuse.