# Objective:

The purpose of this lab is to investigate the relationship between the speed of an object in uniform circular motion (UCM) and the centripetal force (FC) on it. This direct correlation will be calculated by determining our values for how long it may take for any given weight to undergo 20 cycles. Using this information, we will be able to conclude how velocity relates to centripetal force.

# Hypothesis:

We hypothesize that the more weight we add to the contraption, the faster the cycles will become as it will create more force and therefore, increase its acceleration. As the acceleration increases, so will the velocity and since all these variables are increasing at a uniform rate, the force of tension will increase as well. Whereas when the weight is decreased on the mechanism, these values (acceleration, net force, velocity etc.) will decrease as well. An Additional hypothesis presented can be the amount of force needed to make the weight spin. As the weight increases, the amount of force needed to keep it spinning will decrease with the weight but it will need more force to start spinning it. However, as the weight decreases, it will take more force to keep it spinning at uniform motion, however less force to begin spinning it . The reason for this hypothesis is the knowledge that the greater the mass, the more momentum it will generate but since it’s in uniform circular motion, the momentum will only just act upon itself exponentially increasing its speed. Whereas when you spin the lighter weight, it will generate much less momentum resulting in less speed output.

# Procedure:

- Place a small number of weights or washers (be sure that all of the washers you use are the same size.) on the bottom clip of the apparatus. This part of the apparatus hangs straight down, and the weight of the washers supplies the centripetal force.
**Lab Notes:**The net mass we added to the bottom of the clip in each trial may be found in Table 1. - Practice whirling the stopper (or ball) until you can keep the top clip a short distance below the bottom of the glass tube while the stopper whirls. If the clip touches the bottom of the glass tube, the weights are no longer supplying the centripetal force! If the clip rises or falls appreciably as the stopper whirls, the radius of the circle changes.
**Lab Notes:**We measured our radius before the experiment to be 0.42m - Use a stopwatch to measure the time taken for a reasonable number of revolutions. Record your data.
**Lab Notes:**We recorded the time it took for the weight to have 20 revolutions three times, to ensure we have accurate data to plot - Change the number of washers on the bottom clip (centripetal force) and repeat steps 2 and 3. Repeat for several different weights. Record the data.
**Lab Notes:**All of the masses that we used throughout our experiment may be found in Table 1. We added on 2 washers in each trial and measured with a scale that gave us 2 decimal places - If you have time, you might try to determine the relationship between mass and centripetal force. In order to do this, you need to keep both the radius of the circle and the speed constant while you vary the mass and centripetal force. You can design your own data table for this. You could also investigate the relationship between the radius and centripetal force.

# Graphical Correlations:

Figure 1: The Relationship Between Speed (v) and ΣF when The Radius of The Apparatus is 0.42m

Figure 2: The Relationship Between Speed squared (v2) and ΣF when The Radius of The Apparatus is 0.42m

# Safety Precautions:

In this lab, we ensured to take various safety precautions to ensure that we can obtain our data accurately but safely as well. Some of the safety precautions that were taken:

**Clean Environment:**By ensuring our trials were performed in a clean area, this prevented any collisions that may interfere with the apparatus, especially glass**Handling Weights:**While handling weights, we ensured to use proper technique to not drop any weights which may cause personal injury**Proper Whirling Technique:**By practising our whirling, we ensured that there would be no sudden movement which may lead to accidents**Clear Communication:**By carefully outlining our tasks, our group was able to conduct the trials without any confusion or potential risk**Electrical Safety:**While using electronic devices such as our cellphones, we ensured to insulate ourselves with rubber gloves to prevent any electric shocks**Familiarise With Emergency Procedures:**Before conducting our experiments, we knew where to locate the nearest first aid kit in case it was required in such a situation.**Informed And Mature Actions:**While conducting our experiment, we made sure to conduct ourselves in a respectful and careful manner so the lab can run smoothly and in uniform.**Understanding The Experiment:**Before conducting the experiment, we analyzed and made sure we understood what the experiment asked us to do to ensure a organized lab.**Work Cautiously:**While we were completing the lab, we made sure to stay focused on the task to minimize accidents and injuries.

# Conclusion:

By conducting our experiment with an apparatus with a radius of 0.42m, we have been able to achieve our objective and visualise the relation between ΣF with v, and v2 through various graphs. By conducting trials with our apparatus, we have noticed that ΣF is directly proportional to the square of speed and speed is directly proportional to the square root of ΣF. In Figure 1, we analysed and plotted the relation between speed (v) and net force (ΣF) which was best fit by a quadratic function (y = -3.1508×2 + 7.0464x + 1.2789). Given the nature of quadratics, we observed that as net force increases, speed does as well but at a lower rate. This is explained mathematically with the equation ΣF = FC which also equals mv2/r. Once isolating for v, one can understand that the relationship between speed and net force is not directly proportional but still influenced by the magnitude of the net force. Moving onto Figure 2, we plotted the relation between speed squared (v2) and net force. Here, we noticed that it would best fit a linear function (y = 23.067x + 1.808) which can also be proved mathematically. In this case, we isolated for v2 in the ΣF = mv2/r equation where we realised that v2 and ΣF are directly proportional to each other. This explains why Figure 2 is best modelled with a linear function, since as we increase the ΣF, the v2 will increase proportionately as well. Therefore, our conclusions after the lab have aligned with our original hypothesis, where the square of speed increases proportionately to the net force and weight of the rings on the string. As we begin to spin the weighted rings, the first round took less force to get it spinning in uniform circular motion however needed more force to keep it spinning. The speed output was affected by the little momentum the rings generated overall creating a much less net force output after calculations. Furthermore, as more weighted rings were added to the string, the force needed to start the spinning motion increased yet, the force needed to keep it in uniform circular motion decreased additionally making the net force output increase as well. This occurred for the entire

lab as we continuously added more weight. This lab not only confirms the approximations given in our hypothesis but it confirms real life occurrences as well provided in Newton’s second law of motion. In the formula provided by Issac Newton F = ma, we see that the force needed to accelerate an object is related to its mass and as the mass increases, it will take more force to reach a certain fixed acceleration than it would for a lighter object. But as both objects accelerate, the heavier object will result with a greater velocity and greater momentum than the lighter object. Moreover, we see affirmation in of our findings in our chart as the velocity increases as the weight increases as well with the force consequently leading to less time needed to complete 20 laps. Thus meaning the outcome of this lab experiment has matched with our hypothesis.