Circular Motion Lab By: Sukhrnani, Mankirat, and Naomi Abstract The purpose of this lab was to determine how the mass of an object and the centripetal radius affects the centripetal force of the object revolving in uniform circular motion. Except for a few minor discrepancies due to procedure errors, the investigation supported the initial hypotheses. Through experimental procedure and the use of scientic principles, the lab results suggested that the force was found to increase when the mass increased, showing a directly proportional relationship. And the force increased as the centripetal radius decreased, showing an inversely 2 ml} proportional relationship. The equation F, = was used to show how mass, radius and force 1" are interconnected. Therefore, the purpose of this lab was successfully achieved and the reliability of the used equation was confirmed. As the investigation continued new questions arose concerning the effect that the period and the frequency have on the centripetal force. Introduction The centripetal force is present in our lives every day and all around us, from keeping satellites and our moon in orbit, to making sharp turns on banked highways. The centripetal force is the sum of all forces, or components of forces that keeps an object in a circular path. In mechanics, The velocity is usually moving along with the acceleration, however in circular motion, the Acceleration is always perpendicular to the velocity. In circular motion, the velocity is aligned with the tangent, and the acceleration always points towards the centre of the circular path. The purpose of this lab is to investigate how the centripetal force is affected by two variables; the size of the radius, and mass. Hypothesis: 1. If the mass is increased, then the centripetal force increases proportionally. 2. If the radius is increased, then the centripetal force will decrease in an inversely proportional manner This hypothesis makes sense using logic. As the mass increases, since the velocity of the car is not in the same direction as the acceleration, the centripetal force (in this case tension and kinetic friction) required to keep the car in the circular path increases. As the radius increases, the centripetal acceleration required to keep the car in the circular path decreases. The logic behind this is that when the radius increases, the car travels a lesser proportion of the circle then if the radius was smaller. For example, if 2 cars are in a circular path, and one car makes it 180 degrees around the path while the other car has made a full revolution. The car that went 180 degrees around the path has only travelled across 50% of the circle while the other car has travelled 100% of the circle regardless of the distance covered. A larger acceleration can be achieved in two ways, either a larger change in velocity, or the velocity changing in a shorter amount of time. So since the car with the larger radius path has travelled a lesser proportion of the circle, its change in direction (change in velocity) is not as great. This lesser change in velocity results with a smaller acceleration. This hypothesis will be tested using a contraption where both the mass and the radius will be altered while leaving all other variables of the experiment the same. This experiment is conducted using a self propelled car attached to a string. The string will be attached to a retort stand which is connected using a Force sensor which is necessary to depict the centripetal force being exerted in the system. Various lengths of strings are attached to the car to see how radius affects the centripetal force. Masses of different magnitudes will also be placed on the car while keeping the radius the same to see the effect that mass has on the centripetal force. Methods Materials Retort stand - 5 masses of different weights 5 strings of different lengths A toy car - Spring scale Paper clips (2) - Force sensor Sparkvue soware (available as an extension or app) - Metre Ruler Procedure 1. Collect all the necessary materials mentioned above (toy car, masses, retort stand, etc). 2. First, set up the retort stand and insure the base is secured tightly to the metal rod. 3. Then, get a working toy car and place the desired amount of mass/s in the car (change the mass in intervals of 20 starting from 20 when investigating mass, do not use any mass when investigating radius) in a way where they will not fall during movement (mass can be measured with spring scale if needed). 4. Next, choose the desired beginning string length (keep the length at 0.79m when investigating mass and change the size in intervals of about 1m when investigating radius), attach paper clips to both ends by tying a knot with the string around the clip. 5. Attach one end of the paperclip to the toy car and the other end to the force censor. 6. There are three holes in the force censor, slide the censor in the retort stand through one of the holes (the middle hole is preferred). 7. Before starting the car, set up the Sparkvue software which can be downloaded on a smartphone or as a chrome extension. 8. When the car is on the ground, start it using the \" on -off\" switch on its side. 9. At the same time, get another group member to start a new graph on Sparkvue. 10. Insure Sparkvue is working correctly and measuring the force of the moving car 11. Allow the car to go through one whole period, then stop the Sparkvue graph as well as the car. 12. Use the select tool on Sparkvue and select the graph, use this tool to find the \"mean\" force. 13. Finally, write the discovered force in the data table. 14. Repeat steps 8-13 ve times for each variable to achieve the most accurate results. Variables Likely impact upon the How will the variable be investigation changedfmeasuredlcontrolle (1? Independent Variables 1. Radius vs Centripetal 1. Radius vs Centripetal l. Radius vs Centripetal Force Force Force When the The size of the - The radius is radius is at its string will be the lowest value changed in independent (m) , the intervals of 1 variable centripetal m. 2. Mass vs Centripetal force (N) will 2. Mass vs Centripetal Force be at its Force - The mass is highest value - The mass will the - When the be measured independent variable Dependent Variables The centripetal force is the dependent force (N) in every experiment. WM 1. Radius vs Centripetal Force - The mass will be 0 2. Mass vs Centripetal Force - The radius of radius(m)is at its highest value, the centripetal force(N) will be at its lowest value 2. Mass vs Centripetal Force When the mass is at its lowest weight (20g in this lab), the centripetal force will be at its lowest value When the mass is at its highest weight (100g in this lab), the centripetal force will be at its highest value. The centripetal force will vary for every trial in every experiment based on what is being measured. For example, when changing masses, the force will depend on how heavy the mass is. By controlling the appropriate/specic variables for every experiment, it will ensure that those instruments do not affect the result for the instrument that is being investigated. For example, keeping the radius 0.79m with a spring scale for accurate readings The mass will be changed by intervals of 20g starting from 20g (20,40,60,80,1 00) The centripetal force will be measured using a force sensor. There is a pairing software called \"Sparkvue\" that will be used to nd numerical values of the force. There are graph and table options which provide accurate results. Also, the car will complete one full period. . Radius vs Centripetal Force There will be no mass/s in the car Velocity of Sm/s . Mass vs Centripetal curvature will when investigating mass vs Force remain as centripetal force will not Radius of 0.79m for interrupt the accuracy of the curvature will every trial experiment. remain 0.79m for every trial Velocity of 5m/s Results: Through the results found during the conduction of this lab, our two independent variables were either proportional or inversely proportional to the centripetal force in our apparatus. WHAT EFFECT DOES MASS (g) IN THE SYSTEM HAVE ON THE CENTRIPETAL FORCE (N) AS THE SYSTEM EXPERIENCES CIRCULAR MOTION? As the mass increases, then there is an increase in centripetal force. Constants Radius: 0.79m Velocity: 5m/s Mass(g) Centripetal Force (N) 20 0.256 40 0.391 60 0.561 80 0.716 100 0.801Centripetal Force (N) vs. Mass(g) . Centripetal Force (N) Trendline for Centripetal Force (N) 1.00 - _ E g 9 g i '-_'- 0.50 g _ n. 6 .5 C c _ 8 0.25 g 0.00 20 40 so an 100 Mass(g) The X-axis in this graph represents the mass (g) and the yaxis represents the centripetal force (N). As seen in the graph, the relationship between the variables is positive and mostly linear (error bars represent possible uncertainties). This can further be proven by the trendline which is also in a positive linear path. As the size of the mass increases, the size of the centripetal force also increases, their relationship is also directly proportional. WHAT EFFECT DOES THE RADIUS (111) IN THE SYSTEM HAVE ON THE CENTRIPETAL FORCE (N) AS THE SYSTEM EXPERIENCES CIRCULAR MOTION? As the radius increases, then the centripetal force decreases. Constants; - Mass: 0g Velocity: SID/s Centripetal Force (N) 62.5 40.65 31.95 25 F(N) vs. Radius(m) Q F(N) Trendline for F(N) 80 a. r 2 4o 0 I ' i g 20 i 0 2 3 4 5 6 Radius(m) The X-axis in this graph represents the radius (m) and the yaXis represents the centripetal force (N). As seen in the graph, it is not always linear (the error bars represent the possible uncertainty of the data) but there is a negative relationship between the variables. This relationship can also be seen by the trendline which is a polynomial line in the negative direction. As the size of the radius increases, the size of the centripetal force decreases, their values are inversely proportional. Discussion The results om the lab investigation led to the following conclusions as well as validating the hypotheses: 1. If the mass is increased then the centripetal force increases proportionally. 2. If the radius increases then the centripetal force decreases in an inversely proportional manner. Newton's second law states that the force acting on a moving object is the product of the mass and acceleration (F=ma). This principle can also be used in circular motion to find the centripetal force (in this case the force of tension). The equation to find centripetal force is F, = 2 2 my where m is the mass (g) and \"T is the centripetal acceleration (HI/5'2). The car has no 3 vertical acceleration because there is no net force acting on it in that direction, therefore the equation for centripetal force cannot be used. However, there is a net force acting in the horizontal direction and this is the centripetal acceleration. It always faces the centre of a circle and this is what causes objects to move in a circle. So this equation can be used for the horizontal axis. When the equation from Newton's second law and the results from the investigation are applied to the hypotheses, it is evident that they make logical sense. The first hypothesis states that if the mass is increased then the centripetal force increases proportionally. The graph supports this claim because the smallest mass of 20g had the smallest centripetal force of 0.256N and the force keeps on increasing up to the largest mass of 100g grams which had the largest centripetal force of 0.801N. In the equation, the centripetal force is directly proportional to the mass, meaning that if the centripetal force increases, then so does the mass and vice versa. The second hypothesis states that if the radius increases, then the centripetal force decreases in an inversely proportional manner. This is evident in the graph because it shows that the smallest radius of 2m has the largest centripetal force of 62 .SN and the largest radius of 6m has the smallest centripetal force of 2 l .2N. The values in between the smallest and largest radius are decreasing as well. In the equation, the centripetal force is inversely proportional to the radius meaning that as the radius increases, the centripetal force decreases and vice versa. Future Applications Now that the relationship between the radius and the mass with the centripetal force has been established, the apparatus can be reset with a constant mass and radius to nd the relationship between other variables and the centripetal force. One of the variables to investigate is the period. This is the time (s) it takes for the car to travel one full revolution. Using the equation Fc 41:21' 41:21' . : m T2 , where m is the mass and T2 is the centripetal acceleration, one can observe how the period affects the centripetal force. Another variable to investigate is the frequency. This is the number of revolutions per second and it is measured in hertz (Hz). The equation used here is F6 = m (41:21:19, where m is the mass and 45:21:!\" is the centripetal acceleration. This can be used to find how the frequency alfects the centripetal force. m a Inaccurate recording and reading of the centripetal force- . Inaccurate measurement of the radius- since a metre was used to measure the length of the string, these measurements could be slightly 011" by 0.1-0.01m o The straightness or limpness of the string after it is attached to the car could affect the force readings I Placement of car at an angle could cause it to travel in a slanted manner I Interferences on the path (such as the indents on the oor) causing minor changes in the force readings. 0 Applied force to the toy car when switching it on Works Cited 1.Forces and Newton's laws of Motion | Physics Library. (n.d.). Retrieved May 16, 2022, from https://www.khanacademy.org/science/physics/forces-newtons-laws