Circular Motion The wind goes towards the south, and turns towards the north; it turns about continually, and the wind returns again to its circuits. Ecclesiastes 1:6 Introduction Most have been on a Ferris wheel and have experienced circular motion. Today, we will construct a device to simulate a Ferris wheel and which will be subjected to centripetal acceleration. From this, we will study some of the concepts relating to circular motion. When an object moves along a curved path it has a velocity that is at a tangent to the path, at all points on the path. When the object moves at constant speed, it experiences acceleration even though the speed stays the same. Remember, velocity has both speed and direction. Circular motion requires a force directed toward the center of the circle and is called the centripetal force. If the centripetal force is removed, the object will continue to follow the tangential path it was on due to inertia. The equation for centripetal force is: F = mv2 Learning Objectives: Determine the relationship between radius and time period Study the relationship between mass, speed and radius in the forces required for circular motion Materials Required: From Physics Kit Student Supplied Safety Glasses Ruler 5 Washers (Each weighs an average 6.42 g) Marker PVC Pipe Stopclock (seconds) String r Safety Wear eye protection at all times. Circulating objects may disengage and cause significant harm. Perform experiments away from other persons and from fragile objects, preferably outside. Do not swing the objects too fast or when others are in the area Part 1: Relationship of Radius and Time Period Preparation Weigh washers: The average mass of a washer is given in the Materials Table above Use this and place the mass of 1 and 4 washers in the appropriate places in Table B If you wish, you can obtain your own average for one washer using your Spring Scale: o Weigh all the washers at one time on your Spring Scale and cup device o Obtain an average number per washer and use this for the rest of the class 2015 Catholic Initiatives in Math and Science, LLC All Rights Reserved 1
Prepare the device: Measure out 1 meter of string and thread through the PVC pipe Tie one end to a single metal washer Tie the other end to four metal washers as a group From the single washer, measure and mark a distance 0.20 m, 0.30 m and 0.40 m The device should look like the figure to the right. Make sure you and your assistant are wearing goggles Procedure *You will need an assistant to keep time 1. Hold the PVC tube vertically away from your body, with the single washer facing up 2. Take practice swings: Carefully swing PVC tube to rotate the single washer The washer should be rotating in a circular motion Make sure the washer is rotating horizontal to the ground In this way, the radius will be the distance between washer and top of PVC pipe Make a few practice swings while increasing and then decreasing the speed Notice: As you increase speed, more of the fishing line appears That is, the radius increases Notice: As you decrease speed, the radius decreases Notice: When the speed remains the same, the forces are equal due to the tensile forces (t) through the string See figure to the right 3. Test with a radius (r) of 0.20 meters: Adjust the speed until you see the 0.20-meter mark appear at the top edge of the PVC tube At this speed, the radius of rotation is 0.20 meters Once the proper speed has been obtained, have your partner use the stopwatch to record the time it takes to make 20 revolutions Record in Table A the time for 20 revolutions at 0.2-meter radius 2015 Catholic Initiatives in Math and Science, LLC All Rights Reserved 2
4. Test with a radius of 0.30 meters: Adjust the speed until you see the 0.30-meter mark appear At this speed, the radius of rotation is 0.30 meter With the stopwatch, measure the time it takes to make 20 revolutions Record in Table A the time for 20 revolutions at 0.30 radius 5. Test with a radius of 0.40 meters: Adjust the speed until you see the 0.40-meter mark appear At this speed, the radius of rotation is 0.40 meter With the stopwatch, measure the time it takes to make 20 revolutions Record in Table A the time for 20 revolutions at 0.40 radius 6. Perform Data Analyses and Conclusions 2015 Catholic Initiatives in Math and Science, LLC All Rights Reserved 3
Lab Report for NAME: TABLE A Relationship of Radius and Time Period Mass of 1 washer = kg Time for 20 Radius (r) Rotations (meter) (sec) 0.20 m 0.30 m 0.40 m Force (N) Mass of 4 washers = kg Period (T) (sec) Speed (v) (m/sec) Speed 2 (v 2 ) (m 2 v 2 ) Data Analyses and Conclusions 1. Calculate the Force in Newtons and record in Table A. Remember, when the speed is constant, the forces are equal due to the tensile force in the string. F1 = F2 = mg (See Figure) 2. Calculate the period of revolution (T) for each trial. Record these values in Table A. Show a representative calculation below. T = time (s) # of revolutions 3. Calculate the speed, v, for each trial and record in Table A. Then calculate v 2. Include sample calculations. v = 2πr T 4. Plot a graph of radius (y-axis) versus v 2 (x-axis). Examine your plot. Based on the plot, what is the relationship between the speed and the radius of the circular path? 2015 Catholic Initiatives in Math and Science, LLC All Rights Reserved 4
5. As the radius increased, what was the effect on the period of rotation (T)? 6. Expected Values: a. Calculate the Expected Value for the velocity needed at the 0.2 m radius and at the 0.4 m radius: F = mv2 r. Show your work. b. Calculate Percent Error: %Error = Experimental Value Expected Value Expected Value x 100% c. What could explain any discrepancies between the expected values and your experimental values? 7. If the string broke while you were swinging at a constant speed, what would have happened to the washers? Explain the forces behind why this would have occurred? 2015 Catholic Initiatives in Math and Science, LLC All Rights Reserved 5