AP Physics Investigation of Circular Motion

Flying in Circles

AP Physics Investigation of Circular Motion

Discussion

The purpose of this laboratory activity is to examine the centripetal force acting on a toy airplane (or other object) suspended from the ceiling and moving in uniform circular motion in what is called a “conical pendulum”.

Procedure

1.Unhook the flying object from the support string and use a balance to determine its mass.

Mass = ______g = ______kg

2.Place the flying object back on the support string and check that the pivot is secured to the ceiling. When you are ready, turn on the switch and give the object a gentle push to get it started in a circular path. The goal is to launch the pig tangent to the circle of flight. It is better to launch it too easy than too hard. If the object does not fly in a stable circle in 10 seconds or so, carefully grab it and try launching it again. If necessary, allow a few minutes for the object to achieve equilibrium (a stable flight path of constant radius).

3.Determine theradius, r, and angle the string makes with the vertical, θ, as accurately as you can. Discuss with your lab group how you will do this. Remember that the radius of the circle in which it flies is NOT the length of the string. Within reason, you may use whatever basic equipment is available. There are several methods that may work and would be more practical than using a protractor. Once you have devised a method for determining r and θ, check MvP for “clearance” before attempting. In the space below, describe your method and include a neat, clearly-labeled sketch that shows how you determined r and θ. Neatly show your data, calculations, and determined values for r and θ.

r = ______θ = ______°

4.Determine the period of flight by timing a significant number (at least 10) of revolutions. Record your data and calculate the period:

# revolutions = ______Total Time = ______Period: ______

5.Using your radius obtained in step 3, calculate the circumference and speed of the plane below. Show your work!

C = ______mspeed = ______m/s

6.In the space below, draw and clearly label a free-body diagram showing the two forces on your flying object (weight and string tension, T). You may ignore air resistance and the “engine force” because they balance out at equilibrium. Use a dotted line to show the horizontal (Tx) and vertical (Ty) components of the tension in the string.

7.Does the object accelerate in the vertical direction? ______

8.What does this tell you about the magnitude of the vertical component of the tension (Ty) and the weight? ______

9.Calculate Ty. Show your work below.

Ty = ______N

10.Does the object accelerate in the horizontal (radial) direction? ______

11.Knowing that the centripetalforce for any object in uniform circular motion is the net force in the radial direction, what does this tell you about the magnitude of the horizontal component of the tension (Tx) and Fc? ______

12.Using θ (found in step 3) and Ty(found in step 9), calculate Tx showing all work in the space below. Include a diagram for clarity.

Tx = ______N

13.Now, using the mass, radius, and speed of the object (determined in step 5) calculate the theoretical value for the centripetal force on the flying object using the expression below. (show all work)

Fc = ______N

14.Since the horizontal component of the tension (Tx) is what provided the centripetal force, your answers to steps 12 and 13 should be similar. Compare these values using Percent Difference. (show all work)

Percent Difference = ______%

15.In the space below, briefly discuss why the “engine force” and air resistance did not enter into the calculations.