motion in 1D Lab

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1021

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Physics

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Jan 9, 2024

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M otion in One Dimension-1021 Group Members Goals The goal of this experiment was to understand the concepts of one-dimensional motion along with key parts of it such as displacement, velocity, acceleration, rate-of-change (RTC), and time intervals. Another main goal was to be able to collect, graph, and analyze data from the experiment and put all the results into a lab report. Procedure For Part 1 a 30cm long piece of tape was threaded into a Nakamura timer that was set to 10 Hz which makes 10 marks per second as a test to make sure that the machine is properly working but also to make a control group as the second step was to pull the tape completely through the time at any speed. A motorized cart was used to determine the length traveled by the cart in 6 seconds. A piece of tape, slightly longer, was cut and taped to the cart so that when turned on, the cart would pull the tape from the Nakamura timer. Once a consistent pattern of marks is made then stop. Error and precautions The ramp where the experiment was conducted may have some influence on the results given. The ramps were adjustable meaning that one side or the other could have been elevated one way or the other. The past students who used them may or may not have put them back level to the ground or level to the earth. To avoid a mistake like this, use a bubble level to make sure that it is completely level rather than using vision and estimating that it is accurate. In part 2, the acceleration was decreasing, so there may have been friction, or an error with the slope, but the acceleration gradually decreased before hitting the bridge at the end.

Results Part 1 Scatter plot Tabulated Data Part 2 Graph 1 time (s) interval distance(m) total distance (m) instantaneous speed(m/s) 1 0.797m 0.797 0.797 2 0.78m 1.577 0.78 3 0.78m 2.357 0.78 4 0.78m 3.137 0.78 5 0.795m 3.932 0.795 6 0.768m 4.7 0.768

Graph 2 Questions 1. How can one find the pulling speed using the dots. Briefly describe using the definition of speed. a. We can find the pulling speed by counting the dots created by the Nakamura timer that was set to 10 Hz which makes 10 marks for every second that passes. To find

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the speed we can use the equation: speed=distance/time. As we plug in the information given to us into the equation, we get speed=30cm/3seconds gives us 10 cm/sec. 2. Compare your two tapes, the one done manually vs. that done by the cart. How can you determine by looking at the spacing of the dots whether the cart was moving at a constant speed? Support your answer in one or two sentences with your observations. a. We can determine if the cart was moving at a constant speed by looking at the intervals between the dots. The one that was moving at a constant speed will have the same size gap between the dots in comparison to the manual one which had different size intervals between the dots. 3. Did the cart travel the same distance from one interval to the next? Use your data to support your statement. a. The cart did not travel the same distance from interval to interval. As seen in the Tabulated Data table there were differences in each of the trials from 0.797 to 0.78m and the lowest being 0.768m. 4. Did the cart’s instantaneous speed change from one interval to the next? Support your answer using your data a. The carts speed changed from one interval to the next. In the first interval it started at 0 and increased to a speed based on the acceleration and the interval. In the following interval it increased from the speed from the first interval to its max speed. 5. If an object moves at a constant speed, then its instantaneous speed at any given moment is the same as its average speed. Thinking about the speed of the cart during the entire 6- second trip, was the average speed equal to any interval’s instantaneous speed? Explain your reasoning. a. The average speed would be equal to the interval instantaneous speed because the average speed and the interval speed have the same relationship to each other in relation to the different intervals. 6. Is the slope value (the number m in y = mx+b) from the equation within about 10% of the value of average speed calculated in Step d? Would you expect these two values to be similar? Why or why not.

a. The slope value is within 10% of the average speed measured based on the information taken from the graph. They are expected to be similar because they follow the slope resulting in about the same speed. 7. How can the trend of the data on the chart allow you to conclude whether you observed motion with constant speed? a. When looking at the graph the slope of the line increases at a constant positive rate meaning that it holds a constant speed throughout the duration of the cart movement. If the cart were to increase in the middle of its run and turn back to normal, the graph would have a spike, and return to the original slope. 8. Compare the trends in the data in your three plots. In which of the plots, position, velocity, or acceleration, does the value increase linearly with time? In which, if any, is the trend nonlinear? Did any of the plots show a constant value over time? a. In the chart, the graphs that are increasing linearly with time are Velocity. Nonlinear is Position, and the constant is acceleration. 9. How does one obtain the acceleration value from the linear fit of a graph of velocity vs time? (Refer to your textbook if necessary. a. In the lab, the slope of the line for the Velocity per time graph is identical to the acceleration in the given graph. 10. The fit line is a way of incorporating all data into a single best estimate of the acceleration. Let’s compare this to the instantaneous acceleration calculated at each moment. Look in the acceleration column your Capstone data table, these are the instantaneous acceleration values. How are the instantaneous acceleration values similar or different to the single acceleration value obtained from the best-fit line? a. They are similar because they followed the same value of constant speed within each of the trials. Discussion Part 1: For Part 1 the scatter graph of the experiment in the results section, the cart moved at a constant rate throughout its initial movement proven by the straight and consistent positive line

throughout shown in the graph. As seen in the Tabulated Data, the interval distances remained relatively the same with exceedingly slight differences at the beginning of the experiment with an initial interval of 0.797m and towards the end where the cart was finishing its experiment with an interval of 0.768m. The middle of the experiment remained at a constant of 0.78m. In Part 1 the results that were obtained were consistent with the data that was expected to happen. The cart had a motorized engine that moved at one consistent speed. The slope of the line in the graph shows that the cart in the experiment was moving at a constant positive rate with no noticeable changes. The reliability of the experiment had little effect from human error but it was noticeable in the table. In order to time the 6 seconds done for the experiment a timer needed to be pressed at the same time that the cart was put into motion. It was not a noticeable change but it shows how human error can effect an experiment. Part 2: In Part 2 the wireless smart cart had to be connected to PASCO through a Bluetooth connection to make it operational. We created our own slope to be used in this experiment to get the acceleration, position, velocity, and time in the movement of the smart cart. Once the slope was set up, we recorded the cart going down the slope at a constant increase in position, velocity, but not acceleration. We redid the first test to get a new set of data because our first run had a delay response in the recording process. We expected at least two of the graphs to be similar to each other but each one had a drastically different slope. Position being in a curse, Velocity being a diagonal line, and Acceleration being a constant straight line horizontally. The data was close to what we were expecting to produce out this lab besides the acceleration being slightly off than expected. The acceleration had a constant decline that was barely noticeable unless you examined the data chart and compared it between each result. Instead of acceleration being truly constant it was slowly declining down.

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