Lab 1 report

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Apr 3, 2024

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Experiment 1: Acceleration on an Inclined Plane Sandi Mitra, Polina, Roofida, Laura June 6 th , 2023
Objective This experiment involves rolling a small metal ball down an inclined surface. The objective of the experiment is to understand the relationship between distance and time. Students should also recognize and be able to calculate acceleration and utilize graphs. Apparatus 2-meter ramp 2 wooden blocks Small metal marble / ball Meter stick Stopwatch Sketch Data and Calculations
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Sample calculation from row 1 (page 19) Mean time = t 1 + t 2 + t 3 3 = (1.79 + 1.70 + 1.65)/ 3 = 1.71 seconds t 2 = 1.71(s) 2 = 2.92 s v = x/t = 100 cm / 1.71 s = 58.4 cm/s Graphs
Analysis In this experiment, students are to recognize any relationships between the angle of the ramp, velocity and acceleration by rolling a marble down an inclined plane. They measured three-time trails for each of the seven distances for both angles (a total of 14 distances). The advantages of recording three-time measurements for each distance is to reduce the amount of error that can take place in the experiment. The reason for this is because the higher number of measurements, the closer the data is to the true mean time. If a student took more time measurements, like 4- or 5-time values for each distance, the value would be more precise and accurate to the true value it takes for the marble to go that specific distance.
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Some sources of errors can take place that can lead the measurements being not precise. They include the human error of reading the measurements off by a millimeter on the meter stick, reaction to the stopwatch being too early or delayed, and other errors that include the presence of unaccounted friction. Students were then tasked to calculate the velocity, angle , slope of the graph, and acceleration from the slope of the graph. From the data above, students can compare both the velocity and acceleration values after calculation. In the first data set, the average velocity ranged from 36.5 cm/s to 46.7 cm/s and the acceleration was 17.3 cm/s 2 , whereas in the second data set, the average velocity ranged from 58.4 cm/s to 71.3 cm/s and the acceleration was 43.8 cm/s 2 . Comparing the two, students can safely make an inference that the second data set is approximately double the values from the first data set. Using this information, if they were to compare the calculated angles between the two (angle from data set 1: 1.84 ; angle from data set 2: 4.14 ), students could make a hypothesis that if the angle was doubled, then so would the velocity and acceleration values. This is also displayed on the graphs where both the slopes look approximately proportionate based in their scale. Due to the sources of error, some of the measurements would not be exact but students can assume that there is a correlating relationship between the angle of the ramp and velocity & acceleration values. Review questions 1. The difference between distance and displacement is that distance is a scalar quantity (only magnitude without direction) and displacement is a vector (with direction) 2. Average velocity is the change in displacement (distance and direction away from the starting point) over time, and acceleration is the change in average velocity over time. 3. An assumption would be that the initial velocity in this experiment would be zero because it starts from a resting position and not moving. The experimental procedure that would be followed would be releasing the ball and starting the stopwatch. 4. Using the equation x= 0.5at 2 we would be able to find the distance a ball travels from rest since v 0 = 0. 5. To get the acceleration, it is easier to get the value using a x vs. t 2 graph since it is equal to 0.5a rather than having to find another set of values.
6. The acceleration of a ball that rolls 220cm in 5 seconds would be 17.6 cm/s 2 because using the formula x= 0.5at 2 we can rearrange the equation to a=2x/t 2 so a= 2*220/25 = 17.6 cm/s 2 .

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