Objective: To measure the centripetal force required for a mass whirling around ahorizontal circle and compare the result obtained with the theoretical valueF=mwï¿½r.Apparatus: 1 rubber bung, 1 glass tube, screw nuts, 1 nylon string, 1 paper marker, Imetre rule, 1 stop watch, 1 balanceSet-up:Procedure:1. The centripetal force apparatus should be constructed as shown in the above diagram.2. The length of the nylon string that was under investigation was measured (e.g. 0.
3 m) from the centre of the rubber bung to the glass tube and the particular length L was marked with a paper marker.3. The mass of the rubber bung and the screw nuts was weighed with a balance.
4. The glass tube was held vertically and the rubber bung was whirled around in a horizontal circle, the paper mark should be just below the glass tube.5.
The time for 50 revolution was recorded using a stop watch.6. Step 1-5 should be repeated with different length of string.Precaution:1. The paper mark should not be in contact with the glass tube when whirling therubber bung, i.e.
there was no friction between the glass tube and the rubber bung.2. A uniform whirling speed should also be maintained throughout the experiment.3. A certain distance will be kept from your partner when whirling the rubber bung.
4. The time should be counted after the circular motion of the rubber bung becamesteady.5. A reasonable range of length of the string should be selected.
Theories:When the rubber bung is whirling around a circle with a radius r equals to Lsin?, where ? is the angle between the glass tube and the string, the centripetal force F required for circular motion of the rubber bung is provided by the tension T of the string.?F= Tsin?= mwï¿½r= mwï¿½ Lsin??T=mwï¿½L, regardless of the angle ?.Measurement:Mass of rubber bung: 0.
0115 ï¿½0.00005kgMass of screw nuts: 0.0215 ï¿½0.00005kgTension in string T=Mg= 0.
0215×9.8N =0.2107NLength of string L/m0.20.30.40.
5Time for 50 revolution 50t/s33.4238.4843.
5149.51Angular velocity w=2?/t /radsï¿½ï¿½22.214.171.124.
34mwï¿½L/N0.1970.2220.2320.224Mean mwï¿½L= (0.197+0.222+.0232+0.
224)/4=0.218NErrors discussion:The measured value T is smaller than the theoretical value mwï¿½L, this may be due to1. w(measured)>w(true): The time recorded was shorter than the actual value, as thetime recorder might have already stopped the stop watch before the rubber bunghad finished its 50th cycle.2.
L(measured)>L(true):The edge of the glass tube was rough, hence the measuredlength might not be accurate, in such case L might be larger than the actual value.3. m(measured)>m(true): This might be due to the reading error when using thebalance.4. M(measured)<M(true): This might be due to the reading error when obtaining theweight of the screw nuts.Suggestions for a higher accuracy:1. A certain position should be marked when the stop watch started to count and thesame position should be reached when the stop watch was stopped.2.
A glass rod of smooth edge should be used.3. Instead of a balance, an electronic balance might be used.Percentage error:Conclusion:The centripetal force measured in this experiment is slightly smaller than the theoretical value.