Experiment 103 UNIFORM CIRCULAR MOTION LAST NAME, F.N. M.I.: ________________________________________ Student No. __________________ Program/Year: ______________ PHY104L/Section: ____________ Group No. __________________ _____________________ Date of Performance: _________________________________________ Date of Submission: __________________________________________ GRADING RUBRICS Grade Components POINTS Data Tables and Graphs 20 Sample Computations 5 Guide Questions 10 Analysis 10 Conclusion 10 Presentation 5 Group Report Grade 40 TOTAL 100 SCORE _________________________________________ Instructor/Professor 20 EXPERIMENT NO. 103 UNIFORM CIRCULAR MOTION INTRODUCTION Centripetal force is a force that tends to deflect an object moving in a straight path and compels it to move in a circular path. Centripetal force is just a label to represent the unbalanced force experienced by the body every time it moves in a circular fashion. Newton’s Second Law of Motion is used to measure the magnitude of the centripetal force. In this experiment, you shall investigate the relationship between centripetal force and factors such as frequency and radius of circular motion. This activity is limited to horizontal circular motion only. OBJECTIVES: 1. To determine the relationship between centripetal force and frequency of revolution. 2. To determine the relationship between centripetal force and radius of revolution. APPARATUS: 1 set 1 pc 1 set rotating platform clamp-on pulley Standard weights 1 pc 1 pc mass hanger Stopwatch EQUIPMENT CARE AND SAFETY PRECAUTION • Take extra care when handling the clamp-on supper pulley to avoid damages. THEORY From Newton’s Second Law of Motion, Fnet = ma Equation 1 In the case of bodies moving in a circular motion, Fnet is the centripetal force, and the acceleration is called the centripetal acceleration ac . Newton’s 2nd Law can be written as Fc = mac Equation 2 The magnitude of the centripetal acceleration is given by the expression, Dv v 2 ac = = Dt r Equation 3 where v is the tangential velocity of the body and r is the radius of revolution. 21 As Dt approaches zero, the instantaneous acceleration is Dv dv v 2 = = Dt ®0 Dt dt r ac = lim Equation 4 Thus, the centripetal force in terms of tangential velocity is expressed as, Fc = mv 2 r Equation 5 Frequency f is the number of revolutions a body makes per unit time. It is expressed in rev/s, s-1, or hertz Hz. Period T is the time it takes for a body to make one complete revolution. Period is the inverse of frequency. T= 1 f f = or 1 T Equation 6 The magnitude of the tangential velocity is equal to the circumference of the circular path divided by the period of revolution. v= 2p r = 2p rf T Equation 7 Centripetal force may be written as m ( 2p rf ) Fc = r 2 Fc = 4mp 2 f 2 r Equation 8 22 PROCEDURE Part A. Determining Centripetal Force (constant mass and variable radius of rotation) 1. Weigh the rotating body using digital weighing scale and record its mass in Table 1. 2. Hang a mass over the clamp-on pulley. The weight of the total hanging mass is the centripetal force. 3. Initially set the radius to 16 cm. You can loosen up the thumb screw on the side post and slide it to the desired radius. Tighten the thumb screw to secure its position. 4. Adjust the spring bracket up or down to make sure that the string connecting the rotating body is in a vertical orientation. 5. Move the bracket with the orange indicator up or down located on the center post. Mark the position of the orange indicator using the bracket. This will be the reference point. 6. Remove the hanging mass. 7. Gently rotate the apparatus. The orange indicator must be centered in the indicator bracket to keep the rotating object at its desired radius. 8. Use a stopwatch to record the time to complete 10 revolutions. Divide the time by 10 to get the period of revolution. Determine the frequency. 9. Compute the centripetal force using equation 8. 10. Do 5 trials using a different radius each trial. rotating body mass hanging mass Figure 1. Uniform Circular Motion Apparatus 23 PART B. Determining the Centripetal Force (with constant radius and variable mass) 1. For this part of the experiment, there is no need to slide the side post to different positions. Move the side post to the desired radius. 2. Weigh the rotating body using digital weighing scale and record its mass. 3. Hang a mass over the clamp-on pulley. The weight of the total hanging mass is the centripetal force. 4. Adjust the spring bracket up or down to make sure that the string connecting the rotating body is in a vertical orientation. 5. Move the bracket with the orange indicator up or down located on the center post. Mark the position of the orange indicator using the bracket. This will be the reference point. 6. Remove the hanging mass. 7. Gently rotate the apparatus. The orange indicator must be centered in the indicator bracket to keep the rotating object at its desired radius. 8. Use a stopwatch to record the time to complete 10 revolutions. Divide the time by 10 to get the period of revolution. Determine the frequency. 9. Compute the centripetal force using Equation 8. 10. Do 3 trials using a different mass each trial. Part C. Determination of mass of rotating body (with variable force) 1. Weigh the rotating body using digital weighing scale and record its mass. 2. Hang a mass over the clamp-on pulley. The weight of the total hanging mass is the centripetal force. 3. Set the radius. You can loosen up the thumb screw on the side post and slide it to the desired radius. Tighten the thumb screw to secure it position. Keep the radius constant. 4. Adjust the spring bracket up or down to make sure that the string connecting the rotating body is in a vertical orientation. 5. Move the bracket with the orange indicator up or down located on the center post. Mark the position of the orange indicator using the bracket. This will be the reference point. 6. Remove the hanging mass. 7. Gently rotate the apparatus. The orange indicator must be centered in the indicator bracket to keep the rotating object at its desired radius. 8. Use a stopwatch to record the time to complete 10 revolutions. Divide the time by 10 to get the period of revolution. Determine the frequency. 9. Compute the centripetal force using equation 8. 10. Do 3 trials using a different hanging mass each trial. 24 GUIDE QUESTIONS 1. When the radius and mass are held constant, how will the centripetal force vary when the frequency is increased? (3 points) ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ 2. Why is it important to keep the rotating platform horizontal? (3 points) ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ 3. If the body is moving in a vertical circle instead, how does it affect the centripetal force? (2 points) ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ 4. Give at least two sources of error in this experiment. (2 points) ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ 25 DATA SHEET NAME PROGRAM/YEAR STUDENT No. PHY104L/SECTION Group No. Date: Seat No. TABLE 1. Determining Centripetal Force (constant mass, variable radius) total hanging mass = _______________ g mass of rotating body m = _______________ g centripetal force (accepted value): Fc = _______________ dynes TRIAL radius, r period, T frequency, f centripetal force, Fc (experimental value) 1 cm s Hz dynes 2 cm s Hz dynes 3 cm s Hz dynes 4 cm s Hz dynes 5 cm s Hz dynes Average Centripetal Force dynes Percent Difference % APPROVED BY: INSTRUCTOR 26 DATE TABLE 2. Determining Centripetal Force (constant radius, variable mass of rotating body) total hanging mass = _______________ g radius r = _______________ cm centripetal force (accepted value): Fc = _______________ dynes TRIAL period, T mass of rotating body, m frequency, f centripetal force, Fc (experimental value) 1 g s Hz dynes 2 g s Hz dynes 3 g s Hz dynes Average Centripetal Force dynes Percent Difference % TABLE 3. Determining the Mass of the Rotating Body (constant radius, variable force) mass of rotating body (accepted value): radius r = _______________ cm TRIAL centripetal force, Fc m = _______________ g period, T frequency, f mass of rotating body, m (experimental value) 1 dynes s Hz g 2 dynes s Hz g 3 dynes s Hz g Average Mass g Percent Difference % 27 SAMPLE COMPUTATIONS: Part A: Centripetal Force (Trial 1 only), and Percentage Difference Part B: Centripetal Force (Trial 1 only), and Percentage Difference Part C: Mass of Body (Trial 1 only), and Percentage Difference 28 ANALYSIS: ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ______________________________ CONCLUSION: ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ______________________________ 29
0
You can add this document to your study collection(s)
Sign in Available only to authorized usersYou can add this document to your saved list
Sign in Available only to authorized users(For complaints, use another form )