Hypothesis
- When an object is released from rest the frictional force (F) is 0 and the resultant force is equal to the weight (W=mg) of the object. When F is less than W the object's velocity increases i.e. there is acceleration. When an object gains velocity a frictional force opposes the weight of the object and this force grows as velocity increases. When F=W the resultant force is 0 and there is no acceleration. The terminal velocity has been reached.
-
A ball bearing with a greater radius than another ball bearing should have a greater terminal velocity because, according to Stoke's law, vt is proportional to r2.
vt = 2r2 (ρ-σ) g Therefore, vt ∝ r2
9η
- Stoke's law can also be used to explain my prediction that the terminal velocity is inversely proportional to the viscosity of the fluid. Simply put:
vt = 2r2 (ρ-σ) g Therefore, vt ∝ 1
9η η
Equipment
- Ball bearings of various sizes
- Measuring cylinder
- Metre stick
- Stop watch
- Oil
- Retort stand and clamps
- Strong magnet
- Thermometer
- Micrometer
Health and Safety
Oil should be handled carefully and any spillages should be cleaned up to keep the environment safe. A glass thermometer can easily shatter and pose a hazard. An object like a metre stick can be dangerous if not used correctly. This will be placed in the middle of the table to ensure it doesn’t pose a hazard. This will be the precaution taken with all of the equipment. Most safety hazards are those outside of the experiment such as chairs and other objects. Such objects will be cleared out of the way to remove any potential risks.
Method
A micrometer should be used to accurately record the diameter of each ball bearing (in m). The ball bearings should be weighed (in kg) and their volumes should be worked out using 4/3πr3 (in m3). This information can be used to work out the density of each ball bearing (in kg m-3) for use with Stoke's law to calculate the terminal velocity of each ball bearing.
Hold a measuring cylinder using a retort stand and clamps. A metre rule should be used to mark every 10cm on the measuring cylinder with a marker pen. Fill up the measuring cylinder with oil, leaving a 5cm gap at the top to stop any spillages. A thermometer should be placed inside the cylinder to be sure that there aren't any major temperature changes and left for a few minutes to ensure that the temperature remains stable throughout the experiment.
To measure the density of the oil it should be weighed (in kg) in the measuring cylinder on a scale but the mass of the measuring cylinder should also be measured separately and taken away to give the mass of the oil itself. To get the density the mass should be divided by the volume, which is simply a case of converting the amount of litres of oil into metres and cubing it.
First some preliminary testing has to be done with the various ball bearings in order to get an idea of the sizes of ball bearings that will reach terminal velocity within the measuring cylinder. To do this the ball bearings should be dropped into the oil and time at regular intervals of 5cm or 10cm until the time readings are constant (i.e. the velocity is constant). If a particular ball bearing doesn't reach terminal velocity it means it won't be used for the experiment.
The ball bearing should be held at rest on the surface of the glycerol and timing with a stopwatch should commence when it is dropped. Once the ball bearing reaches 10cm the time on the stopwatch should be recorded. The ball bearing should be retrieved from the oil by using a magnet to drag it up as it would be impractical to use pour all of the oil out again. The level of oil in the cylinder should be kept constant as some of the oil could come out when the ball bearing is retrieved. This part of the experiment should be repeated three times to eliminate any anomalous results and an average should be taken.
Once the readings of the 10cm distance are complete the experiment should be repeated but the time readings should be taken at the 20cm distance. Again, the average of three readings must be taken and then the experiment should be conducted at regular 10cm intervals. However, timing should not commence when the ball bearing is dropped but between the 10cm and 20cm mark. This will ease the observation of the acceleration by simply comparing the time taken between successive 10cm intervals. Once time readings start to become constant at further intervals it means there is no acceleration and terminal velocity has been reached.
Now the experiment should be repeated with the remaining ball bearings until all the results have been recorded. Once the data has been collected the terminal velocities for each ball bearing will be known and the viscosity of oil can also be measured using Stoke's law.
Fair Testing (Accuracy and precision)
To get an accurate set of results from this experiment it has to be fair. Here are the steps I will take to make the experiment as fair as possible.
Variables
- Viscosity of liquid: The viscosity is kept constant in this experiment by using the same oil. This is because viscosity is the reason why a ball bearing experiences friction. A change in viscosity will lead to a change in friction, which will result in inconsistent results.
- Temperature of the liquid: The viscosity of a fluid and the friction opposing the movement of the ball bearings decreases as the temperature increases.
- Size/radius of ball bearings
- Distance travelled by ball bearing in oil (measured at regular 10cm intervals)
- Friction: The sides of the measuring cylinder can cause friction so the ball bearing is dropped from as close to the centre as possible.
-
Gravitational field: This is constant at 9.8ms-2. The ball bearings move through the fluid due to the attraction of the Earth's gravitational field.
- Material: Ball bearings of the same material have been selected to keep the conditions fair. This is because the texture of the material can change the friction upon the ball bearing.
Sources of Error
-
Measurement of distance: Each measurement is has an absolute error of ±0.5mm as each measurement is given to the nearest mm.
-
Measurement of radius: Each measurement is has an absolute error of ±0.005mm as each measurement is given to the nearest 0.01mm.
- Measurement of time: Human error as well as reaction times can make a large contribution to any errors in the experiment. Readings from digital stopwatches are accurate to the nearest 0.01s but human error means this reading is unlikely to be accurate.
-
Temperature of the liquid: This will be monitored with a thermometer to ensure that it stays as constant as is possible. It's impossible to keep it at an exact value due to the environment the experiment is being conducted in but a large change in temperature will not be tolerated. Each measurement is has an absolute error of ±0.05oC as each measurement is given to the nearest 0.1oC.
- Parallax error: Mistakes can be made when making measurements or when choosing the moment start/stop the stopwatch as a ball bearing arrives at a certain point due to the eyes not being directly in front of the marker. This can cause errors, especially if the ball bearing is moving quickly.
- Random error: These are associated with nearly all measurements and can never be completely eliminated.
- Take three sets of readings and then take the average of those readings. I will do this to eliminate any anomalous results. If I only take one reading it could be an anomalous result but I won’t know this unless I have more sets of results to compare my data with. Multiple readings ensure that anomalous results are spotted and eliminated.
- The only equipment changed during the experiment will be the ball bearings. This also satisfies the condition of a fair testing environment. As I mentioned in the method, some oil could come out of the measuring cylinder when the ball bearing is removed with the magnet. Air bubbles could also be formed if the ball bearing is dropped above the surface of the liquid. The level of oil will be kept constant at up to 5cm below the measuring cylinder throughout the experiment.
An estimate of the percentage error in the calculation of viscosity
This has been calculated by estimating possible values for the variables during the experiment and using known or estimated values of the absolute error in each measurement.
Percentage Error = Absolute Error x 100
Value of Quantity
Percentage error in r: 0.005m/0.01m x 100 = 5%
Percentage error in ρ: (5x10-5) kg/0.1kg x 100 = 0.05%
Percentage error in σ: 0.05kg/1kg x 100 = 5%
Percentage error in distance: 0.05cm/50cm x 100 = 0.1%
Time: Absolute error of 0.1 seconds plus reaction times in starting and stopping the stopwatch, estimated to be 0.5 seconds.
Percentage Error in time = 0.1+0.5s/10s x 100 = 6%
Percentage Error in Vt = 0.1 + 6 = 6.1%
= [Distance] + [time]
Percentage Error in η = 2 x (5+5) + (0.05+5) + (9 x 6.1)
[2r2] + [(ρ-σ)] + [9Vt]
= 79.95%
A lot of assumptions have been made when calculating the total percentage error, such as the estimated values for each variable when calculating the percentage error, so the large result cannot necessarily be accepted but can be used as a guide when the actual results are recorded.
However, it is clear that a large proportion of the percentage error in η is made up of the percentage error in Vt. The percentage error in Vt is large due to the large error in time, which is due to the reaction times in starting and stopping the stopwatch.
HANNAN SHAH
