Controlling Variables:Our controlling variables are the mass of the stopper being swung, and the radius of the string that is spinning the stopper. We can control this by using the same stopper for each trial. This would ensure that the mass of the stopper is the same each time, as it is the same stopper. To get the same radius of the string, we can mark the string at a set radius, and hold it at that point for each trial. This would ensure the radius of the string is the same each time.
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Developed Method for Collection for Data:To find the acceleration and the velocity, we needed to measure the net forces acting upon the stopper when we swung it at different speeds. To measure the inward force of tension acting upon the object, a force sensor was attached to the bottom of the string. While we swung the stopper, the force was measured and plotted into Logger Pro. We then took the average of the graph as the value of our net force. To measure the speed of the object, we measured the rotations per second. We used a metronome to determine how fast we spun the stopper, and measured how long it took to swing it 20 rotations. We also simply measured the mass of the stopper. We now had time, rotations, mass, and net force, allowing us to calculate the speed and acceleration.
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Procedure:We attached the force sensor to the bottom of the string. We set the metronome to varying beats per minute of 75, 90, 100, 120, and 130. We then held the string at a radius of 50 cm, and swung the stopper to match the beat of the metronome. We then spun the object for 20 revolutions and timed how long it took. We then had the rotations per second data, while the force sensor measured the net force of the system. We had one person swinging the stopper, one person measuring time and rotations, and another capturing the net force through Logger Pro.
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Data Overview:The raw data was recorded exactly how designed in the procedure, measuring rotations per second while simultaneously capturing the net force of the system. The mass of the stopper and the radius of the string are constant in this lab. The speed is then calculated by multiplying the angular velocity (the rotations per second) by 2(pi)(radius). This then calculates the tangential velocity, which is the speed of the stopper. To calculate the acceleration, we divided the net force of the system while swinging the stopper by the mass of the stopper, because of Newton’s second law, F=ma. From here, we were able to plot our data, and begin to determine the relationship between speed and acceleration. We fitted our data to the model y=Ax^2, as this was the best fit that made sense for the data. The y-intercept needs to be 0, as there cannot be an acceleration when the speed is 0. The x-intercept also needs to be 0, as when there is a speed there must be an acceleration. This is why this model works.
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Conclusion:From this Whirly Durly Lab, we can ultimately conclude the relationship between speed and acceleration when an object is moving in a circular motion. We can determine that the centripetal acceleration = (speed)^2 / radius, written as ac = V2/r. This makes sense when we look at the line that best fits our data. The formula for that was y=Ax2, and now we know that y is ac, A is a constant equal to 1/r, and x is the speed, written as V. Our radius is 0.5 meters, which makes sense why our A value on our line of best fit is close to 2, as 1/0.5 = 2. This equation for centripetal acceleration is significant because we can calculate the acceleration or velocity for an object moving in a circular motion. From here, we can then determine the net force of an object moving with centripetal acceleration, using Newton’s second law. This is a significant application that will be very useful.
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Evaluating Procedure and Improving the Investigation:Our procedure certainly has room for improvement. The two main sources of uncertainty in our lab were the measuring of rotations and time, and the speed of swinging the stopper. We were measuring our rotations with a stopwatch and our eyes, meaning it is not as precise as it needs to be. Also, we cannot ensure that our speed of swinging the stopper fully matches the monotone, meaning our data will slightly deviate from the value it should be. These two limitations didn’t allow us to get fully accurate and precise data. To improve our investigation, we could make a slow motion video, where we could more accurately count out 20 rotations and just look at its corresponding time taken. It is hard to find another way to ensure our speed of swinging the stopper is fully accurate, rather than practice. If we had more time to practice and get comfortable swinging the stopper, we could better match the metronome.
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