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?