Lab 7: Uniform Circular Motion

Transcription

1 Lab 7: Uniform Circular Motion Professor Dr. K. H. Chu INTRODUCTION: When an object moves in a circular path, there exists a force called the centripetal force, directed toward the center of the circle, that acts to keep the object moving in a circle. The acceleration due to this force is called the centripetal acceleration and, like the force, it is radial in direction. The centripetal force can be due any type of force: electric, magnetic, friction, the restoring force on a string. In this experiment the tension in a string will act as the centripetal force on an object. THEORY: When a body moves with a constant speed in a circular path, it is said to move with uniform circular motion. Although the speed of the object is constant, the direction of the motion is continually changing. Thus the velocity is continually changing and the object experiences a net acceleration. Since only the direction and not the magnitude of the velocity changes, the acceleration must be directed perpendicular to the velocity resulting in an acceleration in the radial direction. 1

2 The magnitude of the centripetal acceleration is given by (1) where v is the speed of the object and r is the radius of the circle in which it moves. The centripetal force that produces this acceleration is determined from Newton s 2 nd law of motion: where m is the mass of the object. The centripetal force can be written in terms of the angular speed using the relationship v = r. (2) In most cases this angular speed is expressed as 2 times the number of revolutions per second, n: So the force becomes (3) For an object at the end of a string moving with uniform circular motion, the tension of the string is the centripetal; force. However, if the force due to gravity pulls the object downward the string is no longer horizontal. In this case only the radial component of the tension will produce a centripetal acceleration. 2

3 As seen from the above figure, the magnitude of T r is given by And since T r = F r ( ) (4) Using this result in equation (3) gives ( ) (5) If the tension in the string is generated by a mass M hanging from its end, then T = Mg and equation (5) becomes ( ) (6) 3

4 PROCEDURE: Apparatus: Rubber Stopper and String 10 long ¾ PVC Pipe Alligator Clip Meter Stick Timer Set of Hooked Masses Digital Balance Vernier Caliper A light rubber stopper is attached to the end of a string that passes through a PVC pipe. A hooked mass is suspended from a loop at the opposite end and the length of string that is allowed to pass through the tube is controlled by attaching an alligator clip to the string above the holder. Measure and record the mass of the rubber stopper Hang 150 g at the end of the string. The rubber ball will be pulled against the top of the pipe by the weigh at the end of the string. Hold the pipe vertically, at arm length and above your head. Whirl the rubber stopper in a circular, horizontal path. As the speed of rotation of the all increases, the radius of the circular path increases and the hanging mass at the end of the string rises. The tension in the string (supplied by the mass suspended from it end) provided the centripetal force necessary to keep the stopper moving in a circular path. Practice swinging the stopper until it moves in a horizontal circle with a constant speed and the mass is just supported by the string. To stop the motion, bring the rotating stopper toward the pipe by grasping the mass and pulling it downward until the stopper rests again the end of the tube. Set the pipe on the table and pull about 50 cm of string through the pipe. Securely attach the alligator clip to the string about 1 cm below the end of the pipe, making certain that the clip cannot slip along the string. Measure the radius of the circular path in which the rubber stopper will move. 4

5 Secure a mass M, of 150 g to the end of the string. Swing the stopper in a horizontal circle; adjusting the speed of rotation until the alligator clip remains stationary 1 cm below the pipe (the clip should not touch the pipe). When the speed is constant, one lab partner should measure the time required for the stopper to swing through N = 20 revolutions. Record the time. Measure again; the two values recorded should not differ by more than 2 seconds. Keep the same radius. Repeat above procedure for changing the hanging mass of 200 g, 250 g, 300 g, and 350 g. ANALYSIS: Using Microsoft Excel Tabulating and graphing M/L versus n 2. Find the mass of the rubber stopper from the slope of the plot. Estimate the percentage difference the measuring mass and experimental mass of the rubber stopper Using the measuring mass of the rubber stopper, find the gravity from the slope of the plot Estimate the percentage error of the theoretical g (9.81 m/s 2 ) and experimental g. Write a brief conclusion and mention the sources might contribute the errors. 5