Ball bearing

Drag the orange bands to reposition them. Read each position off the ruler to find the distance.

Results

Ball Measured d / mm Distance / cm Time 1 / s Time 2 / s Time 3 / s

Enter your raw measurements. Do not calculate averages, velocities, or viscosity here — that is your off-screen analysis.

Guided Investigation

Work through these prompts in order. All calculations are done on paper or in your notebook — the simulation gives you the raw measurements only. The analysis is yours.

1

Collecting the data

For each ball A through E, release the ball and time how long it takes to travel between the two rubber bands. Repeat each drop at least three times without moving the bands. Record the ball letter, the band-to-band distance read from the ruler, and all three times in the results table.

2

Reading the micrometer

Select each ball in turn and read its diameter from the micrometer in the apparatus panel. First read how many whole millimetres are exposed on the sleeve, then check whether the half-millimetre mark is also showing. Finally, read the thimble scale — each small division represents 0.01 mm. Add these three parts to get the full diameter, and record it in the "Measured d / mm" column of the table.

3

Choosing your independent variable

You are varying the size of the ball between runs. The diameter you measured is a convenient starting point, but what related quantity is physically more meaningful as your independent variable? Calculate this quantity for each ball and record it in your notebook — you will need it for your graph.

4

Finding terminal velocity

For each drop, use the distance and the time to calculate the average speed over the timed section. These balls reach their terminal velocity almost immediately after entering the liquid, so this average speed is a reliable estimate. Calculate a mean terminal velocity for each ball from your three repeated drops.

5

Choosing what to plot

You want to test whether terminal velocity is proportional to the square of your independent variable. Decide what to plot on each axis so that, if the relationship holds, the graph will be a straight line through the origin. Plot the five data points and draw a line of best fit.

6

Testing the relationship

Examine your line of best fit. Does it pass through, or very close to, the origin? What does your answer tell you about how terminal velocity depends on ball size? If the line clearly does not pass through the origin, suggest one reason that could explain it.

7

Reasoning from the gradient

Your line of best fit has a gradient with a specific numerical value and a unit determined by your axis labels. The gradient depends on the gravitational field strength, the two densities listed in the apparatus panel, and one further physical property of the liquid that you have not been given directly. Use your gradient to calculate a value for that property and state it with its correct unit.

8

Evaluating your result

Compare your experimental value to a published figure for the liquid shown in the apparatus panel at 20 °C. State whether your value is higher or lower and by roughly what percentage. Does the direction of the discrepancy suggest a systematic effect in your experiment? Propose one likely cause.

9

Sources of uncertainty

Consider each point below and write a brief note for each:

  • Reaction time. Your stopwatch was started and stopped by hand. Is this a random or a systematic error? How does repeating each drop three times help reduce its effect, and what are the limits of that approach?
  • Band placement. Both rubber bands are positioned below the liquid surface. Why is it important that the upper band is well below the entry point? What would happen to your measured time if the upper band were placed close to the surface?
  • Ruler reading. Estimate the uncertainty in reading a band position from the ruler. How does this propagate into the calculated velocity, and why does using a longer distance between the bands reduce the percentage uncertainty?
  • Wall effects. The measuring cylinder has a fixed internal diameter. For which ball — A or E — would you expect the proximity of the walls to have the greater influence on the result, and in which direction would it shift your velocity measurement?
  • Temperature. Viscosity is sensitive to temperature. If the liquid warmed slightly during the session, would the balls appear to fall faster or slower as the experiment progressed? Which of your repeated drops for a given ball would you trust most, and why?