Experiment 2: Surface Area and Terminal Velocity Introduction After establishing

Question

Experiment 2: Surface Area and Terminal Velocity

Introduction After establishing the concept of terminal velocity in Experiment 1, students can use this experiment to investigate the relationship between the surface area of the sail and terminal velocity.

Analysis

Graph of terminal velocity vs. sail surface area. Sails with different surface areas to establish the relationship between terminal velocities and sail surface area.

Average terminal velocity for each of the sails

Sail

Av. Terminal Velocity

1-small

2-medium

3-large

1.84 m/s

1.6 m/s

1.32 m/s

1. What does the graph suggest about the relationship between terminal velocity and sail surface area?

2. Explain why this relationship does or does not follow physical intuition.

Sail

Av. Terminal Velocity

1-small

2-medium

3-large

1.84 m/s

1.6 m/s

1.32 m/s

ean: 1.32 0.8 1.0 1.2 14 Linear mt b m 0.308 t 0.054 0.757 t 0.13 r 0.944 1.6 1.8 Linear mt b m 0.00181 t 0.037 b 1.32 t 0.088 r 0.020 2.0 2.2 Time (s) Linear mt b m 0.0109 t 0.0 b 1.82 t 0.0 1.000 Run #8 H Run #9 Run #13 24 2.6

Explanation / Answer

For small sail.
v = 0.0109t + 1.82
mean = 1.84 m/s
r = 1

FOr medium sail
v = 0.308t + 0.757
mean = 1.32 m/s
r = 0.944

For large sail
v = 0.00181t + 1.32
mean = 1.6 m/s
r = 0.02

1. From the graph, we realise that
a. surface area of the sail and r squared errors in linear approximation of the results are inversly related, so larger the surface are , lesser the r squared errors in the lineaqr approximation of the results

b. the rate of change of the spped with time does not depend on the suface area of the sail
c. the mean velocity however shows an interesting trend. Higher the surface area of the sail, lower is the mean velocity of the sail
2. This relations does not follow intuition as higher surface area sails would force more push from the air and hence should gain speed faster, but the higher surface area of the sail would also result in higher drag force which is probably the reason why the mean speed of the sail decreases as the surface area is increased

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