Airplane Lab

I. Assumptions

For the purpose of this lab, we assumed that the string connecting the airplane to the ceiling was massless, and that the airplane traveled in a perfectly horizontal circle while on the string.

II. Procedure

1. Mass the airplane using an electronic balance.

2. Measure the length of the string with a meter stick.

3. Measure the period of rotation of the plane with a stopwatch. Start the plane and allow its flight to stabilize before starting the stopwatch. Let the plane complete 10 revolutions and then stop the stopwatch. Divide the time value by 10 to obtain the period.

4. Measure how far the plane is vertically from its attachment point while in flight with a meter stick. Have one person catch the plane while it is in flight, and have another person measure the vertical distance.

5. Repeat for a total of 10 trials.

III. Data

Mass of plane: .240 kg

String length: .980 m

IV. Calculations

Free body diagram:

Sample calcs:

r = sqrt((length)² – (vertical)²) = sqrt((.980 m)² – (.89 m)²) = .41 m

v = 2*pi*r / T = 2*pi*(.41 m) / (1.92 s) = 1.3 m/s

F_x = mv²/r = (.240 kg)(1.3 m/s)²/(.41 m) = 1.1 N

F_y = mg = (.24 kg)(9.8 m/s/s) = 2.4 N

F = sqrt(F_x² + F_y²) = 2.6 N

Average tension: 2.6 N

V. Conclusion

In this lab, we measured the force that the airplane exerted on the string to be 2.6 N; as a result, the string has to have a tensile strength of at least 2.6 N. However, because of unforseen or non-ideal circumstances  (such as the string fraying, children playing a little to roughly with the string, etc.), we recommend that the manufacturer build in a tolerance factor of 10, for a tensile strength of 26 N.