Aim of experiment: To find out how the period of oscillation of a pendulum differ when it is placed in liquids of different viscosities.
Hypothesis:
As stated in my summary of research, particularly with reference to Stoke’s Great Law of Drag:
Where
r = the radius of a sphere in cm
d1 = the density of the sphere in g/cm3
d2 = the density of the fluid in g/cm3
g = the local gravitational acceleration in cm/S2
c = the Viscosity of the fluid in Poise
v = the terminal velocity in cm/S
I can derive that the more viscous the fluid, the smaller the terminal velocity. Thus, I can form an hypothesis for my experiment (how does viscosity affect the movement of a pendulum in terms of speed?): The higher the viscosity of the liquid, the slower the pendulum will travel, therefore, the longer the time taken for one oscillation.
Materials Needed:
- 1 litre of water (viscosity 1)
- 1 litre of honey water (viscosity 10)
- 1 litre of honey water (viscosity 20)
- 1 litre of honey water (viscosity 30)
- 1 pendulum
- 1 measuring beaker (1 litre)
- 1 stopwatch
- 1 plastic container
Experiment Set-up:
Experiment Procedure:
1. Using the measuring beaker, pour 1 litre of water into the container.
2. Allow the water to reach the temperature of the air-conditioned room (20ºC).
3. Use the thermometer to check the temperature.
4. Position the chopsticks above the beaker such that the pendulum (string included) is fully submerged.
5. Raise the pendulum till it is just touching the surface of the water.
6. Release the pendulum and start the stopwatch at the same time.
7. Stop the stopwatch after 5 oscillations.
8. Repeat the experiment 4 times more for more accurate results.
9. Repeat steps 1-8 with honey water (10, 20, 30 cSt) instead of water.
Independent Variable: Viscosity of liquids the pendulum moves through.
Constant Variables:
1. Amount of mixture poured into beaker (1 litre).
2. Length of string of pendulum. (10cm)
3. Weight of pendulum. (25g)
4. Temperature of liquids tested. (20ºC)
5. Height to which pendulum is raised to before release. (Parallel to ground)
Dependent Variable: Time taken for the pendulum to complete one oscillation.
Results:
Water (20ºC) | Viscosity/cSt | Time taken to complete 5 oscillations/s | Period of oscillation/s |
1 | 4.09 | ||
4.04 | |||
4.07 | |||
4.09 | |||
4.03 | |||
Average time taken to complete 5 oscillations/s | 4.07 | 0.814 | |
Honey water (20ºC) | 10 | 4.35 | |
77% water | 4.25 | ||
23% honey | 4.3 | ||
4.26 | |||
4.39 | |||
Average time taken to complete 5 oscillations/s | 4.31 | 0.862 | |
Honey water (20ºC) | 20 | 4.82 | |
51% water | 4.86 | ||
49% honey | 4.89 | ||
4.72 | |||
4.81 | |||
Average time taken to complete 5 oscillations/s | 4.82 | 0.964 | |
Honey water (20ºC) | 30 | 5.21 | |
26% water | 5.32 | ||
74% honey | 5.24 | ||
5.18 | |||
5.22 | |||
5.234 | 1.0468 |
Data Analysis:
The pendulum that moved through the most viscous honey water that had a viscosity of 30cSt (26% water and 74% honey), took the longest time to complete 5 oscillations, 5.234s, resulting in the largest period of oscillation of 1.0468. The pendulum that moved through water that had a viscosity of 1cSt (least viscous), took the shortest time to complete 5 oscillations, 4.07s, resulting in the shortest period of oscillation of 0.814. The pendulum in the honey water of viscosity 10cSt had a period of oscillation of 0.862s, while the pendulum in the honey water of viscosity 20cSt had a period of oscillation of 0.964. The period of oscillations increase as the viscosity of the liquid increases. However, the period of oscillation of the pendulums in varying viscosities of liquids do not increase proportionally. For example, the pendulum in the honey water of 10cSt does not have a period of oscillation that is ten times as long as that of the pendulum in water. Likewise, the period of oscillation of the pendulum in honey water of 30cSt, does not triple that of the pendulum in honey water 10cSt.
Conclusion:
The more viscous the liquid, the longer the period of oscillation. Also, the viscosity of the liquid does not affect the period of oscillation proportionally. This conclusion is valid only with the following assumptions:
1. The pendulum was raised to the same height before release, and there was no external force acting on it.
2. Human error of starting and stopping the stopwatch was minimal.
3. The amount of liquid poured into the container was the same.
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