Transcript 10 Central Forces (Activity 3A – LO3)

Central Forces – LO3
Experiment – Central Force and
Angular Velocity
Aim
To show the relationship between
central force and angular velocity.
Theory
In this experiment, the turntable rotates. There
must therefore be a centripetal force. This
centripetal force will be provided by the hanging
mass.
Satellite mass
Hanging mass
Theory
Therefore:
Fc = msrω2
Fc = Wh = mhg
mhg = msrω2
As ω = 2π
T
mhg = msr4π2
T2
g, ms, r and π are all constant. Therefore:
mh α 1
T2
Confirming this relationship will prove the relationship
between central force and angular velocity.
Fc = Centripetal Force
g = Acceleration due to gravity
mh = Hanging Mass
ms = Satellite Mass
ω = Angular Velocity
r = Radius of satellite mass’ rotation
T = Period of rotation
Wh = Weight of hanging mass
Apparatus
Gear
Griffin Air
Bearing
Satellite mass
Hanging mass
Satellite Mass
Pulley
Voltmeter
Gear/Motor
Assembly
Air Blower
Stopwatch
Hanging Mass
Method
The apparatus was set up as shown, with a 10g mass hung
from the pulley.
The motor, voltmeter and air blower were all switched on.
With the satellite mass at its minimum radius, the gear was
set to move the turntable.
The voltage was slowly increased, causing the turntable to
rotate more quickly. When the hanging mass moved slightly
upwards, the timer was started and the time for 10
rotations was recorded.
Method
This process was repeated a further five times.
The mass was then increased in 10g steps, with the
process being repeated six times for each mass.
A graph of hanging mass, mh, against 1 was drawn.
T2
Results
Time for ten rotations
Mass
(kg)
t1
(s)
t2
(s)
t3
(s)
t4
(s)
t5
(s)
t6
(s)
tMEAN
(s)
T
(s)
1/T2
(s-2)
Uncertainties
A table of uncertainties should be completed
as shown on the next slide.
A full set of example calculations (both
absolute and percentage) must also be given
but only for one set of results (e.g. for 10g).
Note – the mass is subject to a manufacturer’s
calibration uncertainty of ± 1%.
Uncertainties
Mass
(kg)
±1%
Random
Unc.
t (s)
% Random
Unc.
tMEAN (%)
Calib.
Unc.
tMEAN (s)
% Calib.
Unc.
tMEAN
(%)
Reading
Unc.
tMEAN (s)
% Reading
Unc.
tMEAN (%)
Combined
Unc.
T (%)
Combined
Unc.
1/T2
(%)
Absolute
Unc.
1/T2
(s-2)
Graph
A graph of hanging mass, mh, against 1 should be
plotted.
T2
Error bars should be included, using the values
from the uncertainties table.
Conclusion
The graph of mass against 1/T2 is a straight line
passing (almost) through the origin. This confirms
the relationship between centripetal force and
angular velocity.
Evaluation
Why does the graph not pass through the origin?
Is the radius constant or was it changing slightly?
How could this be overcome?
There may be friction in the pulley system meaning
all of the weight was not necessarily converted to
centripetal force.
Anything else?