Centripetal Force on a Model Plane
Purpose
Investigate the forces acting on a plane as it moves with uniform circular motion. Determine the centripetal force using two different methods.
Equipment
One model plane, string/wire, a meter stick
Procedure
Weigh the plane, then hook it up to the ceiling using the wire, measure the length between the ceiling and the plane. Start the plane and measure the radius of the circle it flies in, and measure the time it takes to make one revolution. After that use the information gathered to determine centripetal force using two different 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
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
Data Analysis
Method 1 Method 2
use Sin(ø) = r/L Use F= m *(4 *pi² *r)/(T²)
ø=Sinˉˡ(.72/.765) F= .1324*4*pi²*.72/1.1764²
ø=70.25° (this theta is the angle that is made F= 2.719
by the imaginary vertical line, that is
perpendicular to the ceiling and
connects to the plane, and the string)
so, TCos(ø)=Ty and TSin(ø)=Tx
Given that there is no vertical acceleration we know Ty=Mg
use substitution
TCos(ø)=mg
T=(mg)/Cos(ø)
use substitution
((mg)/Cos(ø))*(Sin(ø))=Tx
Tx=((.1324*9.81)/(Cos(70.25°)))*(Sin(70.25°))
Tx= 3.617= centripetal force
use Sin(ø) = r/L Use F= m *(4 *pi² *r)/(T²)
ø=Sinˉˡ(.72/.765) F= .1324*4*pi²*.72/1.1764²
ø=70.25° (this theta is the angle that is made F= 2.719
by the imaginary vertical line, that is
perpendicular to the ceiling and
connects to the plane, and the string)
so, TCos(ø)=Ty and TSin(ø)=Tx
Given that there is no vertical acceleration we know Ty=Mg
use substitution
TCos(ø)=mg
T=(mg)/Cos(ø)
use substitution
((mg)/Cos(ø))*(Sin(ø))=Tx
Tx=((.1324*9.81)/(Cos(70.25°)))*(Sin(70.25°))
Tx= 3.617= centripetal force
Percent Error
(2.719-3.617/2.719 ) *100% = 33.02%error
Conclusion
We failed to produce accurate results, mainly due to our inability to work with the model plane. It fell down twice, and when we fixed it so that it would stay up, it messed with its circular motion (It did not have constant speed and did not fly in a circle).