27 Force and Circular Motion
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Date: _______________________
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Equipment
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Introduction
According to Newton’s first law, a body in motion will remain in motion with constant velocity if the net force acting on it is zero. Constant velocity means that both the speed and direction do not change. An object moving in a circular path with constant speed does not have a constant velocity because the direction of the velocity is constantly changing. This implies that an object moving at a constant speed in a circular path is accelerating.
According to Newton’s second law, a non-zero net force is needed to cause acceleration. In the case of an object moving in a circular path the acceleration is directed toward the center of the circle. Therefore the net force is also directed toward the center. This net force is often called the centripetal force.
Since the acceleration of an object undergoing uniform circular motion is v2/R, the net force needed to hold a mass in a circular path is F = m (v2/R). In this lab you will investigate how changes in m, v, and R affect the net force F needed to keep the mass in a circular path.
I. Changing Mass
1. Carefully observe as your instructor or lab technician demonstrates the proper use of the Centripetal Force Apparatus. Under no circumstances should you supply the motor with more than 12 volts or 0.40A or you will burn out the motor!
2. Open the file CentripetalForce.
3. Calibrate the force sensor by selecting Experiment/Calibrate. On the pop-up menu, select the force sensor and select Calibrate Now. You will now perform a two-point calibration of the force sensors:
- For the first calibration point, do not apply any force to the sensor, enter 0 N, and hit Keep.
- For the second calibration point, hang a 500 g mass from the sensor. Enter the weight of this mass (4.90 N) and hit Keep.
Note: It is your responsibility to continually check the calibration of the force probe by first removing all mass and seeing if the probe reads 0N and then by hanging 500 grams on the probe and checking to see if it reads 4.9N. If you do not see these values then you either have to re-zero or re-calibrate the probe.
4. Place a 5 g mass on each side of the apparatus at the 70 mm marks. The movable mass must be located by having one partner hold the center of the mass at 70 mm while a second partner moves the force probe up until the string is taut. The force probe must then be secured in this position.
5. The values of m and R can be directly measured from the Centripetal Force Apparatus (CFA). The tangential velocity is found by using a photo-gate timer and a calculation done in LoggerPro. The photo-gate will measure the time (T) for the mass to complete one complete revolution. The tangential velocity is thus:
v = 2πR/T
This formula can be found in Logger Pro under Data/Column Options, and then select Velocity. By default