Lab #6: Centripetal Force on a Model Plane
Purpose:
The purpose of this lab is to investigate the forces that act upon a small battery powered model airplane hanging from a ceiling that cause it to undergo approximately uniform circular motion, and to, therefore, better understand the nature of circular motion and the measurement of circular motion in the lab.
Equipment:
- One Battery-Powered Model Airplane
- One Moderately Long Cord
- One Measuring Strip
- One Stopwatch
- One Triple Beam Balance
- One Flip Camera
Procedure:
First, find the mass of the battery-powered model airplane using the triple beam balance. Then, measure the length of the moderately long cord using the measuring strip. Next, attach the model airplane to the cord, and attach the other end of the cord to a poing high off of the ground, preferably away from any obstructions. Secure the measuring tape from the same point that the cord and model airplane are attached to, so that zero is at the attachment point, and the numbered side of the measuring tape faces downward. Then, activate the model airplane and mode it so that it begins to move in an approximately circular motion. Let the model airplane move in this fashion for 5-10 revolutions so that the motion can become more regular. Next, position the Flip Camera underneath the measuring strip and the flight path, positioning the lens upwards. Film a revolution from this angle to find the radius of the circular motion of the model airplane. Then, suing the same position and camera, film ten revolutions of the model airplane's path and time each revolution. Then, find the mean of the ten times. Finally, calculate the rotational velocity, the angle the cord makes from the vertical when the model airplane was in flight, the tangential velocity, the circular acceleration, the tension in the cord, and the centripetal force (using two different methods).
Collected Data:
Mass of Model Airplane | .1326 kg |
---|---|
Length of Cord | .976 m |
Radius of Flight Path | .69 m |
Mean Time per Revolution | 1.51 s |
Data Analysis:
The calculation of the rotational velocity is as follows:
2*pi/t= omega
Where t is the mean time per revolution and omega is the rotational velocity in rad/s.
The angle the cord makes with the vertical during the model airplane's flight is as follows:
arcsin(r/L) = theta
Where r is the radius, L is the length of the cord, and theta is the angle the cord makes with the vertical when the model airplane is in flight.
The tangential velocity is calculated as follows:
omega*r = v of T
Where v of T is the tangential velocity.
The calculation of the circular acceleration is as follows:
(v of T)^2/r = a of C
Where a of C is the circular acceleration.
One way of calculation for the of the centripetal is as follows:
T of y = m*g
T of x = centripetal force
tan(theta) = T of x/T of y
(T of y)*tan(theta) = T of x = centripetal force
Where T of y is the tension in the cord in the vertical, T of x is the tension in the cord in the horizontal direction, m is the mass of the model airplane, and g is the acceleration due to gravity.
Another way of calculation for the centripetal force is as follows:
Centripetal force = a of C*m
2*pi/t= omega
Where t is the mean time per revolution and omega is the rotational velocity in rad/s.
The angle the cord makes with the vertical during the model airplane's flight is as follows:
arcsin(r/L) = theta
Where r is the radius, L is the length of the cord, and theta is the angle the cord makes with the vertical when the model airplane is in flight.
The tangential velocity is calculated as follows:
omega*r = v of T
Where v of T is the tangential velocity.
The calculation of the circular acceleration is as follows:
(v of T)^2/r = a of C
Where a of C is the circular acceleration.
One way of calculation for the of the centripetal is as follows:
T of y = m*g
T of x = centripetal force
tan(theta) = T of x/T of y
(T of y)*tan(theta) = T of x = centripetal force
Where T of y is the tension in the cord in the vertical, T of x is the tension in the cord in the horizontal direction, m is the mass of the model airplane, and g is the acceleration due to gravity.
Another way of calculation for the centripetal force is as follows:
Centripetal force = a of C*m
Conclusion:
In conclusion, the centripetal force applied to the model airplane while in flight was calculated by two methods: one by finding the horizontal component of the tension in the cord while the model airplane was in flight, the other way was by measuring the period and the radius of the flight path of the model airplane, finding the circular acceleration, and multiplying it by the mass of the model airplane. The centripetal force as calculated by the first procedure equals approximately 1.35 N, and the centripetal force as calculated by the second procedure equals approximately 1.58 N. There is an approximate 15.6% difference between the two methods' results. Errors that may have affected the outcomes of this lab include how the cord contracted in size during the model airplane's flight due twisting, affecting the measurement of the radius and period (making it smaller than it should have been); this error could be reduced by measuring the radius and period as early as possible, so that the twisting would have less effect. Another error would be the accuracy of the measurement of the period, as there may have been human error in its measurement (thought this can be reduced with additional measurements of the period). Finally, the human error in the measurement of the mass of the model airplane should be taken into account, as the model airplane's mass was measured using a mechanical device (the triple-beam balance), which may lack precision in the measurement of the model airplane's mass.