Uniform Circular Motion Lab Objective: To study the forces involved in the motion of a body moving with constant speed in a circular path. Introduction : Circular motion refers to the movement of object with its velocity and tangential acceleration always perpendicular to the centripetal force. There are various types of circular motion, both include circular motion with constant speed, which is Uniform Circular Motion (For example, Horizontal plane, Conical Pendulum, Motorcycle and car in circular path road, Movement of Satellites, Constant magnetic field circular motion, and gravitational attraction), and Nonuniform circular motion, which the speed varies, including swinging rope in vertical line under gravity, and roller coaster movement. In this lab, we will study about the feature of uniform circular motion. When a particle moves in a circle with constant speed, the motion is called uniform circular motion. In uniform circular motion, there will be only centripetal acceleration that always perpendicular to velocity. In this experiment, we will explore the feature of circular motion in horizontal plane circular motion, with the relation of radius and the hook mass, to calculate centripetal force as well as the change of centripetal due to change of tension of rope from the change of hook mass. Also, we will use the Newton first law of motion and second law of motion to predict the trajectory of the metal ball after the string that holds metal objects breaks. Materials: 1. 2. 3. 4. 5. 6. 7. 8. Rope Glass tube Upper Clip Two Weight Hanger with mass 50 grams and 100 grams. Stop watch String Metal ball with mass 50 grams. Goggles. Procedure : 1. 2. 3. 4. 5. Measure the mass of the tiny metal disk. Pass the string through the tube and attach the disk on the top of tube. Hang a hook mass of 50g on the other end of the string Hold the tube vertical and swing the disk in a circular path in horizontal plane. Adjust the speed of rotation of the disk and the radius so that the hooked mass is just supported by the string 6. Start the motion with the tube at arm’s length and above the head. 7. Count and record the number of revolution in 30 seconds. 8. Grasp the string at the bottom of the tube to mark the position of the string while the disk is moving. Measure the distance from the top of the tube to the center of the disk. 9. Change the radius of rotation. Use smaller value and larger one. 10. Repeat steps 3-9 using hooked mass of 100g. Data and Results： Material Number of revolutio n Time Velocity Centripetal Centripeta Acceleration l Force Weight Hooked mass % diff, between Fc & Mg 50 gram metal object 28 30 s 175.93 cm/s 1031.71 cm/s2 51585.5 Dynes 49000 dynes 5.14% 20 30 s 251.32 cm/s 1052.69 cm/s2 52634.5 Dynes 49000 dynes 7.15 % 41 30 s 257.61 cm/s 2212.09 cm/s2 110604.5 Dynes 98000 dynes 12.08 % 30 30 s 376.99 cm/s 2368.69 cm/s2 118434.5 Dynes 98000 dynes 18.88 % 30 cm radius 50 gram hooked mass 50 gram metal object 60 cm radius 50 gram hooked mass 50 gram metal object 30 cm radius 100 gram hooked mass 50 gram metal object 60 cm radius 100 gram hooked mass 50 gram metal object 26 30 s 163.36 cm/s 889.55 cm/s2 44477.5 Dynes 49000 dynes 9.67 % 39 30 s 245.04 cm/s 2001.49 cm/s2 98000 dynes 2.09 % 30 cm radius 50 gram hooked mass 50 gram metal object 100074.5 Dynes 30 cm radius 100 gram hooked mass Analysis of Results: According to the result of the experiment, we conclude that radius has an effect on velocity, centripetal acceleration, and centripetal force; where radius is directly proportional to velocity, and inversely proportional to centripetal acceleration, and centripetal force, Therefore, if radius of the circle increases, velocity of the metal ball will also increase, and centripetal acceleration will decrease. Apart from the previous point, mass of the metal ball is directly proportional to centripetal force; that means if mass increases, Fc will also increase. Next, mass of hook is directly proportional to the tension of rope as well as centripetal force. In the experiment, the metal is moving in horizontal circular motion while the hook remains stationary. Since it is same rope, the tension in the end of string is equal to the tension in all position of rope. According to Newton’s second law of motion, the tension in the end of rope is equal to mass of the hook multiply by gravity. Since gravity is constant value, it means that tension is directly proportional the mass of the hook. That means if hook mass is increased, tension in rope will also increase all well. Since tension of rope is the factor that affects centripetal force, if mass of hook and tension are increased, centripetal force will also increase. Since circular movement in experiment falls into horizontal line circular motion, we can conclude that there are three forces from the outsider view and four forces from object’s view or reference of object that act on metal ball. The first force is tension, which exerts from the object to the origin of rope. The second force is Centripetal force which acts from metal object to the center. Since it is uniform circular motion with constant speed, its value is constant. The third force is gravity, which will always act pass through center of gravity, which is the point that all force passes through metal ball. The fourth force is Centrifugal force. This force isn’t count in regular physics calculation because physics calculation is always from view of outsider. It is only in the reference of the ball, not the viewer. This force can only be feel by the metal ball itself. So, if you were the ball, you would feel that you are acted by this force out of the trajectory of circle. Since you are still in rest, we can conclude that the magnitude of centrifugal force is equal to tension in rope and centripetal force, however its direction is opposite of both forces. Due to Newton 2nd law, in the view of object that has acceleration, this force is needed. Its acts at CM of the balls. This force shouldn’t include in regular free body diagram. Lastly, if the string that holds the whirling metal objects in circular path breaks, there will be no force other than gravity acts to it. Which means tension equals zero. Since an object isn’t be in circular path anymore, there will be no centripetal force and centrifugal force. There is only gravity acts on it. According to Newton 1st law, since sigma force equals zero, the objects want to maintain its motion as straight line, it will continue move in straight line “for a while (very short period of time).” However, since the object is moving under gravity which is constant acceleration, it will continue moving as projectile/parabolic path after straight line with initial velocity tangent to original circle. The calculation can be used as simple projectile motion. However, since projectile motion calculation in high school doesn’t calculate the effect of air drag which acts against gravity, it doesn’t really accurate if it is used in real life. Conclusion: From the result of experiment, we can conclude that there is only component of centripetal acceleration which acts in uniform circular motion, there is no component of acceleration parallel (tangent) to the path; otherwise, the speed would change. The major factors that affect the component of circular motion are radius, which is directly proportional to velocity and inversely proportional to centripetal acceleration and centripetal force. Also, mass of hook can cause major change in the motion, because it is directly proportional to tension of rope as well as centripetal force. Since its speed, centripetal acceleration, and centripetal force are constant all the way, we can conclude that this experiment really shows the features of uniform circular motion. Recommendation: For further experiment, we recommend to swing the rope more quickly and try to make the trajectory become in horizontal line, not conical pendulum line. Since the conical pendulum circular motion has angle between rope and laboratorian hand, we would need to use the help of trigonometry to calculate thing like tension, which is the major factor that will change centripetal force. Also, people’s eye are lack of accuracy to watch the revolution of the metal ball to get the exact value. Instead of swinging 30 second, I recommend to test in only 10 to 15 second, but increase the experiment time to 10 round. After 10 round of experiment, we can plus all result and ten divided by ten. Also, we could use “root-meansquare” method to create more accurate result. This will lessen the error from the experiment. Work log: Members Works Krissaanapong Nimanussornkul Calculate the result Write the introduction Record the result Write the Analysis of Results Write conclusion Tanwarat Kuariyakul Do the experiment Write the work log Write materials Raweroad Opornsawat Do the experiment Write Data and Results Write Procedure