Terminal velocity of a falling ball.

In this investigation there are many variables that will affect the terminal velocity of ball bearings as it passes through the fluid.

Density of fluid (viscosity)-if an object if falling through a viscous fluid a force of friction is acted upon the object. In order to keep the viscosity of the fluid constant for a fair test the same fluid will be used throughout the whole investigation.

Gravitational field- the ball bearings fall through the oil due to the attraction created by the gravitational field from the Earth (gravity). In this investigation, this can be considered constant at 9.8 ms¯².

Temperature- an increase in temperature decreases the density of a fluid and therefore decreases the friction opposing the motion of the ball bearings. In this investigation the volume of oil is great enough to ensure that fluctuations in temperature during experiments will be very small.

Friction- Friction with the sides of the tube may also play a part if the tube is narrow, the ball is more likely to rub against the tube causing friction. To minimize this, ball bearings will be dropped from the center of the tube so that they will be less likely to collide with the sides of the tube.

Distance- in order to make accurate measurements on the terminal velocity of the ball bearings the distance over which their speed is measured must be kept constant and must be selected so that accurate times can be generated and recorded.

Material- Ball bearings with a smooth shiny surface were selected for this investigation, as these were less likely to have a worn surface that would increase the friction independent of radius.

As the mass of the ball bearings increases so does the weight, which requires more friction to balance the ball bearing's weight hence increasing the terminal velocity. Mathematically the mass of the ball bearing should be directly proportional to the terminal velocity. If the mass and weight of the ball bearing increases it requires twice as much friction to balance the ball bearing's weight, which then increases the velocity. As the ball bearing accelerates the friction acting against the falling ball bearing increases caused by the fluid balances out the forces applied to the ball bearing, and reaches the terminal velocity. Hence my theory is the smaller the ball bearing the quicker the terminal velocity will occur and vice versa.

For our own safety when through out the investigation we must:

. During the experiment goggles will need to be worn, to protect the eyes from the boiling hot oil in case it spills out because of its temperature (bubbling).

2. Equipment should be set up away from the sides and right at the back. As we are working with fluids, the retort stand may fall causing the fluid to come out, leaving the floor slippery hence an injury

3. Long hair must be tied back for the safety of the individuals.

4. Chairs should be tucked under the tables, so nothing will block the escape route.

5. If any spillage is caused it must be cleaned up.

6. If any breakage of equipment happens it must be reported to the supervising teacher and must not be tampered with.

A large vertical plastic tube will be held in mid air using a retort stand, boss and clamp. The tube will also be filled with vegetable oil since that is the fluid I will be using through out the investigation, it will be filled up to an approximation of 5 cm beneath the top of the tube. This is to ensure that the fluid will not spill from the top and the surface of the oil will be high enough to allow the ball bearings to be released from rest. A meter ruler will be used to analyze the length of the tube at 10cm intervals and a thermometer will be placed inside the tube so that the temperature is monitored. A micrometer will be used to accurately measure the diameter of a ball bearing and the readings will be recorded in a suitable results table. The ball bearing will then be held at the surface of the oil and released. The time taken for the ball bearing to travel 10cm will be measured using a stopwatch that then will be recorded in a results table. This will be repeated three times to generate readings at each distance, to allow averages to be taken and the extent of any anomalies to be reduced. (The above passage is illustrated in the diagram below)

Radius

(mm)

First Time

(Sec)

Second Time

(Sec)

Third Time

(Sec)

Average Time

(Sec)

Velocity ms¯²

2

3

4

5

6

This is the results table that I will record all my result in that is measured for the ball bearing and also the average. The experiment will also be repeated several times in order to gain accurate and reliable results, these results will then be interpreted in to graphs to see the affects the ball bearings have over terminal velocity knowing the factors that will affect the investigation.

Trough out this whole investigation, many errors will occur:

The meter ruler is an example of inaccurate readings (the accuracy in to mm)

Distance = 20 cm or 20.0 cm

Error = + or - 0.05cm

0.05 / 20 * 100

% Error = 0.25 %

Diameter = 1 cm = 1.0cm of ball bearing

Area of sphere = 2 / 3*pi r ²

Error = + or - 0.05cm

= 5% error

Hence micrometer accuracy = 1 / 1000 mm

Ball bearing 1 cm - 1.0

Error = 0.0005 cm

% Error = 0.05

Other errors that might occur during the investigation could be experimental errors. These are made when the investigator is recording the time of the fall of the ball bearings, also by the stopwatch where errors can be made at the recording of the starting time and stopping time. Another error can be made when actually measuring the distance of the fall of the ball bearing from the large tube; this could happen if the measurements are not accurately taken from the meter ruler. So therefore the difficulties that can be encounter through out the experiment is. Trying to establish weather the ball bearing has reached terminal velocity before timing is started. Trying to maintain the temperature attained once the oil has been heated or cooled, Human errors when recording the timing, Human errors in general. Trying to hold the ball bearings just above the oil without dropping them in.

Most of these errors can only depend on the individual so it would be assuring to accomplish the experiment twice to discover the errors accomplished by the investigator and such errors as the inaccurate readings will definitely occur but could be reduced by using accurate equipment but the errors will still occur.

The following are the books that I have used in order to accomplish the investigation and obtained useful resources, which can be checked in the following books: -

* A level physics, supplied by the college

* A level advanced physics oxford revision guides