3.3.7 Investigating Terminal Velocity

Aims of the Experiment

The terminal velocity of a ball bearing in a viscous fluid can be determined experimentally using a cylinder filled with a viscous liquid. The aim of this experiment is to calculate the terminal velocity of the mass as it falls through a viscous fluid.

Variables

• Independent variable = Distance between markers (m)
• Dependent variable = Time to travel between markers (s)
• Control variables
  • Use the same viscous fluid
  • Use the same ball bearing

Equipment List

• Resolution of measuring equipment:
  • Metre ruler = 1 mm
  • Stopwatch = 0.01 s

Method

Experimental set up for investigating terminal velocity in a fluid

1. Set up the equipment as shown in the diagram
2. Wrap elastic bands, or draw marks using a marker pen, around the tube of viscous liquid at set intervals measured by the ruler
3. Hold a ball bearing directly above the surface of the liquid, and then release it from rest
4. Record the time it reaches each elastic band or marker line by using the lap feature on the stopwatch
5. Calculate the time taken to travel between consecutive bands and calculate the average speed at each time
6. Repeat the procedure several times over a wide range of readings

• An example table might look like this:

Analysis of Results

• When the ball bearing reaches terminal velocity, the distance it has travelled between each time interval will be the same, and so its velocity can be determined
• Use the equation speed = distance / time to find the average velocity of the ball bearing between each set of bands or markers
• Plot a graph of velocity against time and draw a line of best fit
  • The maximum velocity is where the graph plateaus and has zero gradient
  • This is the terminal velocity

• An example graph of results might look like this:

Evaluating the Experiment

Systematic Errors:

• Use a more viscous fluid to slow the ball more
  • Using a denser fluid makes the object fall slower and therefore makes determining speeds easier

• Use a tube that is as tall as possible
  • This allows the ball bearing to travel at its terminal velocity for longer

• Use larger intervals for the bands
  • This reduces the percentage uncertainty in both the distance and time between the bands

Random Errors:

• Repeat at least four times to reduce the effect of random errors
• Instead of using a stopwatch, attach the ball to some ticker tape
  • This punches holes at a set time interval so the distance between the dots can be used to find the velocities