Purpose The purpose of this lab is to investigate circular motion and centripetal acceleration. Uniform Circular Motion Newton's second law states that an object in motion will remain in motion in a straight line unless acted upon by a net force. This means that an object moving in a circle must have a force acting it to keep it moving in a circle. Uniform circular motion occurs when objects travel in a circular path at a constant speed, while the direction of their velocity changes. This change in velocity means acceleration, called centripetal acceleration when it occurs in uniform circular motion. The word centripetal means center-seeking, and centripetal acceleration always points towards the center of the circular path traveled by the object. The center point of the circular path is the location of the rotational axis, perpendicular to the plane of rotation. The centripetal acceleration always points towards the center of the circular path while remaining perpendicular to the tangential velocity, the velocity of the object as it moves in the circular path in uniform circular motion. The tangential velocity is always tangent to the circular path at each point in the object's motion. See Figure 1. The directions of the tangential velocity and centripetal acceleration change over time, but their magnitudes remain constant. tangential velocity tangential velocity centripetal acceleration centripetal acceleration Time 1 Time 2 Figure 1 Diagram of an object in uniform circular motion at two successive points in time. Centripetal acceleration is determined by the speed, v of the object undergoing uniform circular motion and the radius, r, of the circular path. The equation for centripetal acceleration is: acWhere: a, = centripetal acceleration (m/sz) v = tangential velocity, or speed (m/s) r = radius of circular path (m) Newton's second law states that an applied force causes acceleration, Thus, the centripetal force experienced by an object in uniform circular motion can be found with Newton's second law of motion, F : ma: F 711172 = ma = c c r Where: F; = centripetal force (N) (1,7 = centripetal acceleration (rn/si) v = tangential velocity, or speed (m/s) r = radius of circular path (m) T e centripetal force points in the same direction as the centripetal acceleration, towards the rotational axis, and causes the velocity to change directions without changing the magnitude The centripetal force keeps an object in uniform circular motion The centripetal force is equal to some regular force, such as gravity, friction, or the normal force. T18 circumference, C, is the linear distance an object has traveled after one full revolution, The equation for circumference is: C = 2117 The speed of an object undergoing uniform circular motion can be determined using the circumference (the distance traveled during one revolution) and the period, T (the time required to complete one revolution) Using the equation for velocity, this results in the equation: _ distance _21:T_ C 17 time _ T _ T Where: V = tangential velocity, or speed (m/s) r = radius of circular path (m) T = Period (5) C = circumference (m) Tension An object can be kept in uniform circular motion using a swinging string, The tension of the string provides the centripetal force needed to keep the object on its circular path. Tension is a force transmitted through a string (or similar material) that allows a force to act over a distance In the upcoming procedures, the weight of the hanging masses will provide the tension of the string in the centripetal force apparatus. '7. FE = msvz/r FC = Tension = Fg ng=mhg Figure 2 A centripetal force apparatus Figure 2 above shows an illustration of the Centripetal force apparatus you will use in this lab. The apparatus uses a swinging object attache Q33 a string with hanging masses on the other end, The tension in the string is caused by the hanging mass and provides the centripetal force needed to keep the moving object in uniform circular motion. The tension (and therefore the centripetal force) can be calculated using the force due to gravity (weight) of the hanging mass and the equation: Tension =Ev =mg = FE Where 5;: the gravitation force (N) : weight of the hanging mass M = hanging mass (kg) g = 9.81 "1/52, the acceleration due to gravity 55: the centripetal force (N) The Step by Step procedures for this lab are on the remaining pages below. Gather the following materials Student Supplied HOL Supplied Assistant\" Centripetal force apparatus *** Digital stopwatch\" Pair of safetngggles Dark marker Digital scale, precision Tape measure, 3 m * The data collection portion of this lab is very difcult to do without an assistant. \"Either a physical stopwatch or computer/phone app may be used as long as it records to 0.01 seconds. *** assembly directions are at the end of the lab Procedure I Using a Classical Circular Force Simulation Part 1: Varying Hanging Mass 1. Open the Classical Circular Force simulation provided by The Physics Aviary 2, Read the directions on the simulation home page and press the \"Begin" button. 3, Conrm the radius is set at 200 cm and the moving mass is set at 25 g. Note: Do not touch the masking tape below the holder. This will change the radius and will not allow you to return to a radius of 200 cm. If this happens, refresh the simulation. 4. Calculate the circumference of the moving mass's circular path in meters using the equation: Note: Use the conversion factor 1 m = 100 cm. Note Note Note Note : Use the conversion factor 1 m = 100 cm. 5. 6. Record the circumference in Data Table 1. Record the mass of the hanging washers in kg for Trial 1 in Data Table 1. : The mass of each washer is 10 g. Use the conversion factor 1 kg = 1000 g. 7. Press the \"Start\" button and count 10 revolutions before pressing the \"Pause" button. : The \"Reset\" button will save your settings. If your timing for the trial is off, press \"Reset\" and try again 8. 9. 10. Record the time in Data Table 1 for Trial 1 Calculate the time T for one revolution by dividing your measured time by 10 and record the result in Data Table 1. Calculate the magnitude of the rubber stopper's velocity for each trial using the equation: 17 = an/T = C/T : The circumference (C) was measured in step 4. 111 12. 13, 14, 15, 16, 17, 18, 19 Record the velocity in Data Table 1. Calculate the centripetal force experienced by the moving mass: Fa = mmvinsz/T Record the centripetal force in Data Table 1. Calculate the expected centripetal force by nding the gravitational force of the hanging mass 5] = Fatheory = mhangingg Record the expected centripetal force in Data Table 1. Calculate the percent error between the expected centripetal force and the measured centripetal force: |F F 9 cl 0 pg xioM Percent error = Record the percent error in Data Table 1. Press the Reset button and add more washers by clicking once on the set of washers hanging on the string Repeat steps 6-18 three times, for a total of 4 trials with different hanging masses Part 2: Varying Rotating Mass 20. Conrm the radius of 200 cm and the moving mass of 25 g. 21. Click on the washers until you have between 10 and 15 washers 22. Record the mass ofhanging washers in kg in Data Table 2. 23. Calculate the circumference of the moving mass's circular path using the equation given in step 4 and record in Data Table 2. 24. Record the rotating (moving) mass in kilograms in Data Table 2 for Trial 1, 25. Press the \"Start\" button and count 10 revolutions before pressing the \"pause\" button and record the time in Data Table 2 for Trial 1, 26. Calculate the time T for one revolution by dividing your measured time by 10 for each trial and record the results in Data Table 2. 27. Calculate the velocity of the rotating mass using the time T and the circumference using the equation give in in step 10. Record in Data Table 2. 28. Calculate the centripetal force experience by the moving mass using the equation given in step 12. Record in Data Table 2 29. Calculate the expected centripetal force by nding the gravitational force of the hanging mass using the equation given in step 14. Record in Data Table 2. 30. Calculate the percent error using the equation given in step 16. Record in Data Table 2. 31. Press the \"Reset\" button and increase the rotating mass by clicking once on the up arrow below the red \"Moving Mass\" text. 32. Repeat steps 25~31 three times for a total of 4 trials with different rotating masses. Part 3: Varying Radius 33. Rettun the rotating mass to 25 g by clicking the red down arrow and leave the amount of hanging washers unchanged. 34. Record the mass of the rotating mass and hanging mass in Data Table 3. 35. Click one on the masking tape located directly below the holder. 36. Record the radius to the 0.01 m in Data Table 3 by measuring to the center of the rotating mass. 37. Press the \"start\" button and count 10 revolutions, Press the \"pause\" button aer 10 revolutions and record the time in Data Table 3 for Trial 1. 38. Calculate the time T for one revolution by dividing your measured time by 10 for each trial and record the results in Data Table 3 39. Calculate the velocity of the rotating mass using the time T and the circumference using the equation given in step 10. Record in Data Table 3, 40. Calculate the centripetal force experience by the moving mass using the equation given in step 12. Record in Data Table 3. 41. Calculate the percent error using the equation given in step 16. Record in Data Table 3. 42. Calculate the percent error using the equation given in step 16. Record in Data Table 3. 43. Press the \"Reset\" button and increase the radius by clicking twice on the masking tape below the holder. 44. Repeat steps 3643 three times for a total of 4 trials with different radii, Procedure I: Simulation Data Table 1 Rotating Mass (kg): Radius (m): Circumference (m): Trial Hanging Mass Time Time Velocity FC (N) Fg (N) % Error (kg 10 rev (s) 1 rev (s) 2 3 -A Data Table 2 Hanging Mass (kg): Radius (m): Circumference (m): Time Time Trial Rotating Mass Velocity FC (N) Fg (N) % Error kg) 10 rev (s) 1 rev (s) 2 3 Data Table 3 Rotating Mass (kg): Hanging Mass (kg): Time Time Trial Radius (m) Circumference (m) Velocity 10 rev (s) 1 rev (s) 1/ 2 3 4 FC (N) Fg (N) % Error