Weight downwards,
Up thrust and Viscous Force upwards.
Since F= 6 π ч r v, the viscous force is increasing with the speed.
Since F is increasing, at some point the sum of U and F is going to be equal to W.
At this point the resultant force on the sphere is zero, therefore, according to F=MA, a=0, that means the sphere moves at constant speed. This is called the Terminal Velocity.
When the sphere is moving at terminal velocity, W= U+F.
Ч= 2r2 g (d-p)/9vt
D=density of the sphere
P=density of the liquid
The density of the sphere and pulp must be calculated separately using the formula:
Density=Mass /Volume
To find vt, the speed of the sphere must be measured during few intervals to make sure it has reached the terminal velocity.
Then the experiment can be repeated to study the change in viscosity with the concentration of the pulp.
Aim
To find the time taken for a sphere to fall through several viscous liquids and liquids with different concentrations of viscosity.
Diagram/Equipment
Method
I filled up the cylinder container with the viscous liquid, which is wallpaper paste (mixed together beforehand).
I then placed the sphere on the surface of the liquid.
When I let go of the sphere I started the timer.
When the sphere reached the bottom, I stopped the timer.
Using a ruler I measured the distance travelled.
Using Distance / Time I got the speed of the sphere, and the terminal velocity at each 10cm interval.
I then repeated the experiment.
Preliminary
In my preliminary experiment, I tested out different sphere sizes and also the maximum and minimum concentrations of the viscous solutions, so I would know which quantities would be best to use.
The diameter of the sphere I chose was 1.3cm, as it was small enough to travel at a constant rate through the liquid.
The minimum concentration contained 8g of wallpaper paste in 600ml of water, as it was just viscous enough to take a reading. The maximum was 26g of paste, because after that the sphere doesn’t move at all.
Results = First Experiment
17g Paste
Changing Water from 500ml upwards
Results = Second Experiment
600ml Water
Changing Paste from 8g upwards
The graph for the first experiment shows that as Density increases, so does time, though they are not directly proportional because they don’t go up in equal amounts. There is also an anomaly, which could have been caused by human or systematic error.
For the second experiment the graph is quite different. This shows that as Density increases, time actually decreases. So the two quantities are inversely related. There is a constant pattern at first, but then due to human and systematic error there are a few anomalies.
Evaluation/Conclusion
You can see from the first graph that density and time are directly proportional, so as one goes up so does the other. This shows that the relationship between density and time is valid.
For the second graph, the two quantities are inversely related. This is because for that one the liquid is getting more viscous, so slowing down the sphere.
To improve the experiment I could take better precautions to reduce the errors, especially the human errors as they can be prevented more easily.
I could have tried to find out my reaction time and eliminate that from the time to make it more accurate.
Some of the limitations are that you can’t use very big objects, because they won’t fit through the cylinder, and also different shapes, because they have sides of different areas.
