Purpose: The purpose of the lab was to explore and understand the forces that act upon a model airplane that flies in a uniform circle. To do this we must find the centripetal force through two methods. (method 1 uses Sin(ø) = r/L and method 2 uses F= m *(4 *pi² *r)/(T²))
Equipment: Model plane, string or wire fastening device (to keep motion uniform), and a meter stick.
Procedures:
- First, one must mass the model airplane.
- Next, one should fasten the aircraft to the ceiling using the string or wire. (check to make sure it is a strong hold)
- Then one needs to measure the distance between the ceiling fastener and the center of lift on the airplane. (where the wire or string connects to the tailing edge of the wings or fuselage)
- To continue, begin the motion of aircraft. Allow the motion to stabilize into a uniform circular pattern and then measure the radius of the airplane's circular path.
- Next, record the time that it takes the aircraft to make one full revolution.
- Finally, one shall calculate the centripetal force using both methods.
Data:
- Length of string = 76.5 cm or .765m
- Radius of circle of flight= 72cm or .72m
- Mass of model plane = .1324kg
- Period (the time it takes to make one full revolution) of plane = 1.1764seconds
Analysis:
Method 1
- In this case, theta is the angle between the vertical line (the string before the aircraft was in motion) and the angle of the string during flight.
- ø=Sinˉˡ(.72/.765)
- ø=70.25°
- TCos(ø)=Ty TSin(ø)=Tx
- Ty=Mg because of the lack of acceleration on the y-axis
- TCos(ø)=mg so T=(mg)/Cos(ø)
- ((mg)/Cos(ø))*(Sin(ø))=Tx
- Tx=((.1324*9.81)/(Cos(70.25°)))*(Sin(70.25°))
- Tx= 3.617
- F= m *(4 *pi² *r)/(T²)
- F= (.1324)*(4)*(pi²)*(.72/1.1764²)
- F= 2.719
Error Calculation:
- (2.719-3.617/2.719 ) *100% = 33.02%error
Conclusion:
Our experiment was highly flawed, proven by the 33.02% error. The likely cause of our flaw was the extensive troubles that we encountered in the operations of the experiment. The string and fastener became dislodged twice, forcing us to adjust the way we fastened the string to the ceiling. The adjustment caused a slight inconsistency in the aircraft's velocity, which in turn caused a non-uniform circular flight path. On another note, we were able to reach a mathematical solution using the two alternate calculation methods.
Our experiment was highly flawed, proven by the 33.02% error. The likely cause of our flaw was the extensive troubles that we encountered in the operations of the experiment. The string and fastener became dislodged twice, forcing us to adjust the way we fastened the string to the ceiling. The adjustment caused a slight inconsistency in the aircraft's velocity, which in turn caused a non-uniform circular flight path. On another note, we were able to reach a mathematical solution using the two alternate calculation methods.