Toy+Airplane+Lab


 * Lab Title: TOY AIRPLANE LAB!!**




 * Primary Authors: Troy F!**


 * Contributing Authors: Lindsay L! and YOUNGAAAA**


 * Abstract:** The goal of the toy airplane lab is to find the acceleration of the toy airplane flying around a pole, which are connected to each other by a string. Two methods were used to calculate this acceleration. One using the equation to find acceleration, and the other by a free body diagram. Using the first method, we obtained an acceleration of 7.5 m/s/s. Using the second method, we obtained an acceleration of 11.75 m/s/s. (The results should have posted a similar number, but due to a measurement error in the second method, they did not.)


 * Introduction:** The purpose of this lab was to find the acceleration of the toy airplane when traveling in a circle. Since the airplane is traveling in a circle, it has centripetal acceleration, which is the rate of change of the tangent velocity. Also, because the airplane is traveling in a circle, the acceleration is always pointed inwards.


 * Methods:**
 * Method One!** Method one is to find the acceleration using the acceleration equation, which is a = v^2/r (a = acceleration, v = velocity and r = radius). To obtain the velocity, we needed to find how far the plane traveled in a certain amount of time. We measured the radius as the plane was flying around the pole. Along with that we measured the time it took for the plane to make a revolution. For a more accurate answer we timed how long it took the plane to do multiple revolutions then divided the time by the number of revolutions. One the radius is calculated, we found the circumference (perimeter) of the circle using the equation C = 2*pi*r. Now we have found the distance it travels for one revolution, and using that distance and dividing it by the time it take the airplane to travel one revolution, we found the velocity of the plane (at an instant, because the velocity is always changing). Finally, take your numbers and plug them into your equation to find acceleration and calculate!


 * Method Two!** Method two uses a free body diagram to calculate the acceleration. First we found the force of gravity acting on the airplane using a force meter that was attached to the sting. Then we found the angle between the radius and string using cosine, because the cosine of the angle = the radius / the length of the string. Next, we found the components of the tension in the string. The vertical component is equal to the force of gravity, because they cancel out, thus making the horizontal component the net force. From prior lessons in class, we figured out that the net force = mass * acceleration. Now we need to find the mass, and the mass is just the force of gravity divided by acceleration due to gravity, which is 9.8. This gets us our mass. Now with simple algebra we can calculate our acceleration.

Radius = 23 cm = .23 m Went 7 Revolutions in 7.7 seconds, thus making it go 1.1 seconds/ revolution Circumference = 2 * pi * r = 2 * pi * .23 = 1.445 m Velocity = Cicumference / time = 1.445 / 1.1 = 1.314 m/s Acceleration = (velocity)^2 / radius = (1.314)^2 / .23 = 7.5 m/s/s
 * Results:**
 * Method One!**


 * Acceleration = 7.5 m/s/s**

r=0.23m 1.1sec./revolution ||  ** Circumference **  ||  ** Velocity **  ||  ** Acceleration **  || ** Work(calculation) ** ||   c=2· π · r c=2 · π ·0.23 c=1.445m ||  v=circumference/time v=1.445/1.1 v=1.314m/s ||  a= v2/r a=(1.314)2/0.23 ** a=7.5m/s/s ** ||
 * **Given**:

Free body diagram!
 * Method Two!**



Fgravity = 1.35 N Radius = 23 cm = .23 m Length of String = 30 cm = .3 m (Error was most likely here.) Cos Ø = .23/.30 Ø = 39.94 degrees Fgravity = vertical component of Ftension Fnet = horizontal component of Ftension Fnet = Fgravity / Tan Ø = 1.35 / tan 39.94 = 1.61 N Mass = Fgravity / acceleration due to gravity = 1.35 / 9.8 = .137 kg Fnet = mass * acceleration Acceleration = Fnet / mass = 1.61 / .137 = 11.75 m/s/s


 * Acceleration = 11.75 m/s/s**

Fg=1.35N r=0.23m length of string=0.3m Fg=Ft ｙ Fnet=m ·a= Ft ｘ  ||  **Angle Ø **  ||  **Fnet **  ||  **Mass **  ||  **Acceleration **  || ** (calculation) ** ||  Cos Ø= adj/hypoténuse Cos Ø = .23/.30 Ø = 39.94 °  ||   Fnet=Fg/tan  Ø <span style="color: black; display: block; font-family: 'Arial','sans-serif'; text-align: center;">Fnet=1.35/tan(39.94) <span style="color: black; display: block; font-family: 'Arial','sans-serif'; text-align: center;">Fnet=1.61N ||  m=Fg/g m=1.35/9.8 m=0.137kg ||  a=Fnet/m a=1.61/0.137 ** a=11.75m/s/s ** ||
 * **Given**:
 * ** Work **

<span style="color: black; font-family: 'Calibri','sans-serif'; font-size: 10pt;">We were able to find that the acceleration for the toy airplane was 7.5m/s/s in method 1 and 11.7m/s/s in method 2. We figured that there was error in method 2 like measurement of the length of the string that held the toy airplane.


 * Conclusion:** Determining a pilot's acceleration is important in real life because their acceleration may put them at risk for 'gray-outs' or 'black-outs'. We found our two values, 7.5 m/s/s and 11.75 m/s/s, by either determining the velocity and solving based on the given radius and period, or measuring the angle and using our knowledge of mass, angles, and gravity to determine the force and then solve for acceleration. The two methods should have yielded the same result, but calculation errors changed our results. The significance of this lab was the introduction to movement and forces in a circle.