Centripetal Force Lab Report

Lab Report: Centripetal Force Objective: The objective of the experiment is to observe a mass 𝑚as it undergoes centripetal motion and to understand what forces aside from centripetal force is acting upon the mass 𝑚.. Methods: According to Newton's First Law, in order for an object to to undergo uniform circular motion 𝐹𝑐 a net force 𝐹𝑛𝑒𝑡 must be directed at the center of the circle at all times; without 𝐹𝑛𝑒𝑡 the object would not be in circular motion but rather fly off tangent at a linear velocity. The force of an object in circular motion is called Centripetal Force𝐹𝑐. The equation for centripetal force is 𝐹 𝑐 = 𝑚 𝑎𝑐 Acceleration in the equation is represented by 𝑎𝑐and is called centripetal acceleration. This can be solved for by 𝑎𝑐 = 2 𝑣 𝑟 As the mass completes a circle around, at a certain radius 𝑅, the covered distance is represented by 2π𝑅 . If the mass is moving with a constant linear speed 𝑣 , then the equation to solve for 𝑣 is 𝑣 = 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑇𝑖𝑚𝑒 = 2π𝑅 𝑇 Where the 𝑇represents for the period in seconds. The period is the time it takes for the mass to complete one revolution. By being able to measure the period it takes for the mass to complete a revolution along with the radius of the circle, the speed 𝑣can be calculated. Procedure: The apparatus used to perform the experiment, is a length of nylon cord that is run through a PVC pipe. Attached to the top of the cord will be a small mass 𝑚1 , of about 10g to 20g; this mass will remain a constant for the entire experiment. In the middle of the cord, underneath the pipe, an adjustable reference clip will be placed on the cord that will serve as a reference point for when the mass is in circular motion. Finally at the bottom of the cord, a mass𝑚2 will be attached to perform the experiment. 𝑚2 will be interchanged during the experiment with each new procedure. To perform the experiment, the reference clip was placed at an appropriate distance above 𝑚2 . The reference point will be moved either lower or higher as the the weight of 𝑚2 is increased. To begin enacting centripetal force, the person conducting the experiment will hold the apparatus by the PVC pipe and will begin spinning the cord and the mass 𝑚1 attached to it. To determine if there is a constant speed, the person will either spin the apparatus faster or slower by paying close attention to the reference clip. One the reference clip has stopped moving up or down and is in the same position for an extended period of time, the system has then reached a constant speed 𝑣. While the system is in constant speed, the Period 𝑇will be measured. To measure 𝑇, a person will need to begin a timer, paying attention to where the revolution started when the timer began. Once 10 revolutions had passed, the timer was stopped and the time was recorded. Once 𝑇had been measured. The radius 𝑅 of the circle was measured by holding the cord at its position on top of the PVC pipe, being careful not to lose this position. The measured 𝑅was recorded These steps were repeated for a total of five trials. With each trial the mass 𝑚2 was changed to an increasing mass. The values for 𝑇and 𝑅were measured and recorded. The following equation was used to calculate motion for the mass 𝑚1 , 𝐹𝑛𝑒𝑡 = 𝐹𝑐 𝑇 = 𝑚1𝑣 2 𝑅 (Equ. 1) The equation to solve for the motion of mass 𝑚2 is 𝐹𝑛𝑒𝑡 = 0 𝑦 𝑇 − 𝑚2 𝑔 = 0 𝑇 = 𝑚2𝑔 (Equ. 2) To eliminate 𝑇, equation 1 and equation 2 were set equal to each other. 𝑚2𝑔𝑅 𝑣 = 𝑚1 (Eq. 3) Equation 3 was used to calculate for the theoretical values of 𝑣.The calculations are shown in Table 1. Raw Data: m1 (kg) m2 (kg) t (sec) T = t/10 (sec) For 10 rev For 1 rev R vexp= (m/s) vtheor (Eq. 3) % Error (Eq. 4) 0.0141 0.05 6.17 0.617 0.675 6.87 4.84 41.9% 0.0141 0.1 7.26 0.726 0.737 6.13 7.16 14.4% 0.0141 0.2 5.4 0.540 0.671 7.8 9.65 19.1% 0.0141 0.3 3.56 0.356 0.652 11.5 11.7 1.71% Table 1. Recorded and calculated values Analysis: There were two main possible sources of error that may have occurred while conducting the experiment. While performing the experiment and enacting circular motion onto the system, one source of error was that the system was not in constant circular motion. Throughout the execution of the experiment, any slight change in the speed would directly affect the measured 𝑇 value and the calculations. The second possible source of error is directly affected by the first, being that of not accurately calculating the period 𝑇. Not only is this value affected by the speed but also by the timing. Having to manually time the 10 revolutions, was not only affected by the velocity variability but by not accurately measuring when each revolution started and ended. During the procedure, estimating where one revolution ended and the next started was not 100% accurate and the inaccuracy would be directly proportional to our percent error values. These values remained relatively low with four out of the five being lower than 20%, including one percent error of 1.71% that hinted at a near perfect system. The one outlier occurred in the first trial with a percent error of 41.9% . The motion observed in the experiment was the uniform circular motion of mass 𝑚1 . This system occurs on the horizontal plane, and because weight force occurs on the vertical axis it is ignored in the system for circular motion. Conclusion: They system completed and observed was based on enacting circular motion on mass 𝑚1 , in which centripetal force was the main focus. Through the experiment the main sources of error were regarding the measurement of period and obtaining a constant velocity when enacting circular motion on the system. With the low values in percent error, aside from the one outlier, they demonstrated that the system and its experimental values were close to the theoretical values and their ideal system.