Question 2
Editorial safety note: Work with teacher supervision, use only the supplied liquid, avoid splashes, and keep small metal balls away from mouths. All measurement cells remain blank until measured.
EXPERIMENT II Falling ball inside the liquid
Introduction
When a metal ball is dropped into a liquid, a viscous force will drag it. Naturally, this force is not constant but depends on the ball’s speed. The greater the speed, the greater the viscous force. In this experiment, a ball will be released just above the liquid surface, and after a while its speed will become constant called “terminal speed”. By intuition, one would expect that this terminal speed must be greater for a bigger ball because it is heavier. In this experiment, one wants to know exactly whether the terminal speed is proportional to (i) surface area of the ball ($4\pi r^2$) or (ii) the volume of the ball ($4\pi r^3/3$). To prove the proportionality, we need to plot a graph between two quantities on x-axis and y-axis respectively. When the plot of data has a linear tendency, i.e. fitted nicely with a linear line, one can say that they are proportional to one another.
Equipment and accessories 1 plastic bottle with unknown liquid 18 metal balls (6 sizes, 3 balls each) 1 stopwatch 1 magnet 2 rubber bands 1 ruler 2 graph papers Tissue paper
Experimental procedure
1. Wrap the plastic bottle with 2 rubber bands and set their position as the start and finish lines. Keep the start line about 60-70 mm below the liquid surface and the finish line as low as possible. Measure the distance between them with 1 mm precision.
2. Drop the ball less than 10 mm above the liquid surface and measure the time of falling between the start and finish lines. Leave the balls in liquid. Record your observation in the table.
3. Repeat this one more time and for all other provided ball sizes.
4. Calculate the terminal speed with two digit decimal in mm/s unit.
5. Plot your data on graph paper so that one can make conclusion whether the terminal speed is proportional to the surface area or the volume of the ball.
6. Answer questions 1–3 in your answer sheet.
Distance between the liquid surface and the start rubber band is … mm.
Distance between two rubber bands is … mm.
| No. | Surface area A (mm²) | Volume V (mm³) | Time trial 1 (s) | Time trial 2 (s) | Average time (s) | Terminal velocity (mm/s) |
| --- | --- | --- | --- | --- | --- | --- |
| 1 | 12.6 | 4.2 | … | … | … | … |
| 2 | 17.8 | 7.1 | … | … | … | … |
| 3 | 28.3 | 14.1 | … | … | … | … |
| 4 | 31.7 | 16.8 | … | … | … | … |
| 5 | 50.3 | 33.5 | … | … | … | … |
| 6 | 71.2 | 56.5 | … | … | … | … |
Plot your data on graph paper so that one can make conclusion whether the terminal speed is proportional to the surface area or the volume of the ball.
Question 1. Is the terminal speed proportional to the surface area or the volume of the ball? How do you make that conclusion? (1 point)
Question 2. From the information provided in the introduction, explain clearly why does the speed finally become constant? (2 points)
Question 3. If a student mistakenly set the start rubber band at the liquid surface, the speed will be too large or too small? Explain it. (2 points)
EXPERIMENT II Falling ball inside the liquid
Introduction
When a metal ball is dropped into a liquid, a viscous force will drag it. Naturally, this force is not constant but depends on the ball’s speed. The greater the speed, the greater the viscous force. In this experiment, a ball will be released just above the liquid surface, and after a while its speed will become constant called “terminal speed”. By intuition, one would expect that this terminal speed must be greater for a bigger ball because it is heavier. In this experiment, one wants to know exactly whether the terminal speed is proportional to (i) surface area of the ball ($4\pi r^2$) or (ii) the volume of the ball ($4\pi r^3/3$). To prove the proportionality, we need to plot a graph between two quantities on x-axis and y-axis respectively. When the plot of data has a linear tendency, i.e. fitted nicely with a linear line, one can say that they are proportional to one another.
Equipment and accessories 1 plastic bottle with unknown liquid 18 metal balls (6 sizes, 3 balls each) 1 stopwatch 1 magnet 2 rubber bands 1 ruler 2 graph papers Tissue paper
Experimental procedure
1. Wrap the plastic bottle with 2 rubber bands and set their position as the start and finish lines. Keep the start line about 60-70 mm below the liquid surface and the finish line as low as possible. Measure the distance between them with 1 mm precision.
2. Drop the ball less than 10 mm above the liquid surface and measure the time of falling between the start and finish lines. Leave the balls in liquid. Record your observation in the table.
3. Repeat this one more time and for all other provided ball sizes.
4. Calculate the terminal speed with two digit decimal in mm/s unit.
5. Plot your data on graph paper so that one can make conclusion whether the terminal speed is proportional to the surface area or the volume of the ball.
6. Answer questions 1–3 in your answer sheet.
Distance between the liquid surface and the start rubber band is … mm.
Distance between two rubber bands is … mm.
| No. | Surface area A (mm²) | Volume V (mm³) | Time trial 1 (s) | Time trial 2 (s) | Average time (s) | Terminal velocity (mm/s) |
| --- | --- | --- | --- | --- | --- | --- |
| 1 | 12.6 | 4.2 | … | … | … | … |
| 2 | 17.8 | 7.1 | … | … | … | … |
| 3 | 28.3 | 14.1 | … | … | … | … |
| 4 | 31.7 | 16.8 | … | … | … | … |
| 5 | 50.3 | 33.5 | … | … | … | … |
| 6 | 71.2 | 56.5 | … | … | … | … |
Plot your data on graph paper so that one can make conclusion whether the terminal speed is proportional to the surface area or the volume of the ball.
Question 1. Is the terminal speed proportional to the surface area or the volume of the ball? How do you make that conclusion? (1 point)
Question 2. From the information provided in the introduction, explain clearly why does the speed finally become constant? (2 points)
Question 3. If a student mistakenly set the start rubber band at the liquid surface, the speed will be too large or too small? Explain it. (2 points)