Introduction:
We will build a beam composed of a
meter-stick, platforms, pivot and fans as a
two dimensional model or analog of the SOFIA
balanced telescope. The model will be used
in the classroom to define torque and to
measure the torque which can be created by a
spinning fan for this experiment, but it
will also provide the basic system for all
the experiments related to the physics and
engineering of the SOFIA telescope. The
actual telescope has wind forces on it from
the open cavity as the aircraft is flying,
and they create a torque on it which must be
counteracted by a special electromagnetic
torque motor, but the torque involved is
orders of magnitude larger than what we can
create with a fan on the end of a 50 cm arm.
In the classroom we are relying on our
ability to minimize the force of external
wind to allow controlling the beam with only
the weak forces of the small fans used to
cool electronics such as your desktop
computers.
The primary reason we balance the beam
(and the telescope) is to minimize the
force of gravity of it and thus allow
moving it with small torque. The same
engineering technique is used to minimize
the forces needed when massive structures
must be moved in controlled ways, such as
a lift bridge. However, in the case of the
telescope, balancing also allows precision
control, without the need to react to the
dynamic linear forces associated with a
flying aircraft.
Once the beam is built we will use it to
weigh objects and measure the torque
associated with a mass, using the
definition of torque and a known mass.
Then we will measure the torque of the
fans by counteracting it using the same
known masses and measured distances.
Objectives:
1. To build a balancing system for
experiments.
2. To develop an understanding of
torque.
3. To measure the torque created
by the fans on the beam system.
Procedure to
build the beam:
1. Component list:
 | One rigid meter-stick |
| One balance stand and
pivot bracket for a
meter-stick |
| Two 5-inch electronics
cooling fans (called ‘muffin’
fans), brushless, |
| 12 volts D.C.,
approximately 0.6 amperes. |
| About six plastic tie-raps
(to mount fans to the
meter-stick) |
| Two pieces of 1/8 inch
(3-4 mm) fiber board, about 3
x 7 inches (7.5 x 17.8 cm) |
| Four pieces of molding
stock, 1/2 or 5/8 inch square
x 7 inches long |
| One box of paper clips |
| Assorted fishing weights:
(four each of 1, 2, & 4
oz., plus a bag of 1/8 oz.) |
| Masking tape & Latex
glue |
| One centimeter ruler |
| Approximately 4 feet of 22
guage insulated solid wire. |
| Handy Board and desktop PC
or Mac |
2. Construction:
- Assemble meter-stick with
pivot and balance stand;
verify that with the pivot
located at the 50 cm point the
stick balances itself.
- Add muffin fans to each
end of the stick using
plastic tie raps so that
they are centered with the
stick oriented to provide
minimal air blockage and
both fans facing down to
push air perpendicular to
the stick. Before adding the
second fan balance one fan
against a few hanging
weights from a hook made out
of paper clips. Record in a
lab book how much weight was
required and at what
distance from the pivot. Add
the second fan and adjust
one of the fans until the
meter-stick and fans
balances at 50 cm. The
following diagram shows the
stick and fans looking down
from the top:
- Make two platforms from
the fiberboard and molding
stock pieces with the slot
between molding pieces just
wide enough to fit the
meter-stick. Glue the pieces
together. One platform is
shown upside-down for clarity:
- Assemble the platforms on
top of the meter-stick near
the fans, but not blocking the
air flow; be sure the
platforms can side on the
stick for balance adjustments.
Procedure
to experiment with torque
1. Torque is defined as
rotational force at a
distance or force times
distance. In metric units it
would be Newton-meters = 100
Newton-cm or N-cm. Since our
fishing weights are in
English force units, lets
convert:
4 oz. =
1/4 lb, 1 lb = 4.45 N,
thus 4 oz. = 1.11 N
1 oz. ~= 0.28 N
To demonstrate the
balance of torque notice
that you can hang 0.28 N
at 20 cm on each side of
the pivot and the beam
will balance. Now put 0.56
N at 10 cm on one side and
0.28 N at 20 cm on the
other. The beam still
balances, showing that
0.56 N-cm of torque or any
other quantity of torque
can be provided many ways.
2. We can also use
torque to measure an
unknown weight. Take one
platform off the beam and
adjust the distance of
0.28 N until the beam is
balanced. Record the
distance to the weight
(dw) and the distance to
the center of the platform
(dp). Since we know the
torques are equal when the
beam is balanced:
0.28 x
dw = platform_weight x dp,
thus platform_weight =
0.28 x dw/dp
Likewise we can
calculate the weight of a
fan from the previosly
recorded balancing weight
(W1) and distance (dw1):
Fan_weight
= W1 x dw1/df,
Where df is the distance
to the center of the fan
(~ 42 cm)
Record this value in
your lab book so it can be
used in the Moment of
Inertia experiment.
3. Now we are ready to
measure fan torque: Mount
the Handy Board on a
platform and secure it
with masking tape; balance
it by hanging about 3 N on
the opposite side. . A
short program called ‘torque.c’
has been written to use
the Handy Board to apply
power to the fans and
adjust the power level on
one fan. Download the
torque.c program into the
Handy Board. Plug the
tinned leads from one fan
into the motor ports #0.
For the first set of
measurements, adjust fan
#0 using the knob on the
board for 30%, 50%, 70%,
85% and 100% power, and
for each power level hang
a weight at the distance
required to rebalance the
beam, recording the torque
for each case. For the
second set of
measurements, fan #1 has
its wiring extended about
two feet with the solid
wire, and plugged into
port #1. It is powered up
at the 50 % level. Once
again set the fan #0 power
to various levels,
rebalance the beam and
record the torque measured
for each case. Notice that
both positive and negative
torque can be provided
using the two fans.
-----------------------------------
/*torque.c
tlg 10/99
This
program allows the Handy
Board to provide power to
the fans to complete
the
torque measuring
experiment.
Port '0' has power
set by the knob, and port
'1'
is
set to 50% power. */
void
main ()
{
motor(1,50);
while
(1)
{
printf("fan(0)=
%d \n", knob()/2);
sleep
(0.3);
motor(0,
knob()/2);
}
}
