Terminal Velocity Experiment 3n2b14

Isabel Wadeson-Lee 12Du

Terminal Velocity Experiment Aim To find the relationship between the mass of a stack of paper muffin cups and the terminal velocity it reaches when it is dropped. paper cups

Equipment Paper muffin cups (you may assume the cups are all identical to each other), stop watch, metre ruler, electronic balance

metre ruler

Task/Method Set up the equipment: 

Select a stack of cups. Make sure they are tightly packed. Open the stack out a bit to increase the surface area presented to the air.



Drop the stack from a height about half a metre more than d. (This ensures it is travelling at its terminal velocity by the time it reaches the top of the metre ruler.)



The terminal velocity is found by measuring the time, t, it takes for the d paper cups to fall through the distance, d, and then using v  . t

d bench top

Make sure you don’t alter the shape of the stack when you remove cup(s) to change the mass. Carry out the experiment and write a report that includes: 

   

Results: Independent variable: mass. Dependent variable: velocity. Controlled variables: surface area and distance. Maximized accuracy by repeating and averaging time and by taking multiple measurements and dividing for the mass of each paper muffin cups.

Time (s) Distanc e (m)

Avera 4 ge

1

2

3

1.723

1.6

1.69

1.65

1.62

1.723

1.13

1.34

1.12

1.28

1.723

0.87

0.93

0.97

0.84

1.723

0.75

0.68

0.81

0.81

1.723

0.56

0.63

0.82

0.84

1.64 1.217 5 0.902 5 0.762 5 0.712 5

Velocity (ms⁻¹) 1.05061 1.415195 1.909141 2.259672 2.418246

Mass V² (kg) (m²s⁻²) 0.000 1.1037 23 81 0.000 2.0027 46 77 0.000 3.6448 69 2 0.000 5.1061 92 18 0.001 5.8479 50 12

Conclusion: Y=mx+c, m=0.0002v²

Discussion: 







g m because if we rearrange that k formula to have m as the subject, m=k/g*v². My findings relate to this because in the conclusion I reached m=0.0002v², which is the same as m=k/g*v² as k/g is the equivalent of the slope of the graph (0.0002). I controlled the surface area of the paper muffin cups by stacking them inside one another when the mass needed to be changed. This was necessary because if the paper muffin cups had different surface areas, there would be different amounts of air resistance, which would affect the velocity. I also controlled the distance from where the paper muffin cups were dropped to ensure they had reached terminal velocity by the time we started timing. For the accuracy improving techniques I used repeating and averaging, and taking multiple measurements and dividing for the mass of each paper muffin cup. I used repeating and averaging because this made the measurement more accurate and closer to the true value, and it also meant that any extreme values did not affect the results. I took multiple measurements and divided by the number of paper muffin cups to get the mass, as it was more accurate because it meant there were more significant figures in the end answer. There was a limit to the range of values I chose for mass, because after 0.00150kg (5 paper muffin cups stacked), the terminal velocity became too great to accurately measure the time it took to travel the distance.

The findings of my investigation relate to physics theory that v 2 