Central Forces – LO3
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Transcript of Central Forces – 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.
Hanging mass
Satellite mass
TheoryTherefore: Fc = msrω2
Fc = Wh = mhg
mhg = msrω2
As ω = 2πT
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 rotationWh = Weight of hanging mass
Apparatus
Hanging mass
Satellite mass
Gear
Griffin Air Bearing
Stopwatch
Voltmeter
Hanging Mass
PulleySatellite Mass
Gear/Motor Assembly
Air Blower
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
Mass(kg)
t1
(s)
t2
(s)
t3
(s)
t4
(s)
t5
(s)
t6
(s)
tMEAN
(s)
T(s)
1/T2
(s-2)
Time for ten rotations
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.
Error bars should be included, using the values from the uncertainties table.
T2
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?
There may be friction in the pulley system meaning all of the weight was not necessarily converted to centripetal force.
Is the radius constant or was it changing slightly? How could this be overcome?
Anything else?