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Lab 1: Motion In One Dimension Group members: Jenny Sim, Tiffany Kho Goals: The primary goal of part I is to measure the instantaneous speed and distance between each interval in order to determine whether or not the cart is moving at a constant speed. The primary goal of part II is to determine a cart’s constant acceleration by measuring the changes in velocity and acceleration as it moves down a ramp. Procedure: For Part 1, a 30-cm long piece of paper tape was threaded into a nakamura timer set at 10 Hz to create 10 sparks per second. Dots were then generated onto the tape by pulling it through the timer at a random speed, creating a pattern used to determine the pulling speed. This procedure was then repeated but instead of being pulled manually, a motorized cart was used to pull the tape. Prior to pulling it, the cart’s distance traveled in six seconds was estimated by measuring with a ruler. For Part II, a PASCO smart cart was released from the top of a ramp in order to determine changes in velocity and acceleration as it descended. The cart was connected to an online Capstone application, which captured and recorded three trials of the cart’s rolling down motion in a positive direction. Using the recorded data, Capstone then generated tables and three graphs for each trial showing position, velocity, and acceleration. A linear fit was applied to each, combining all of the data for the best estimate of acceleration. This data was then used to compare instantaneous acceleration values to the single acceleration value obtained from the best-fit line. Error and Precautions: A possible error that can affect the results of this experiment is the incorrect adjustment of equipment. For instance, if the Nakamura timer from Part I was not set precisely to 10 Hz before starting the experiment, it can affect the calculation of pulling speed which in turn can have an impact on other measurements. In addition, this error can also apply to Part II because if the Capstone application is malfunctioned or not set up properly, it can also affect the accuracy of any recorded data. In order to avoid this error, it is important to calibrate the timer and ensure that it is generating sparks at the desired frequency as well as confirming the accuracy of the motorized cart’s speed and distance measurement. Thus, a few precautions that can be taken for this lab include verifying that the timer is set to 10 Hz, pulling the paper tape at a stabilized speed, and making sure to connect the correct PASCO cart code to the Capstone program application.

Results: Position (m) VS Time (s) Time (s) Interval distance (m) Total distance (m) Instantaneous speed (m/s) 1 s 0.0136 m 0.0136 m 0.0136 m/s 2 s 0.0142 m 0.0278 m 0.0139 m/s 3 s 0.0148 m 0.0426 m 0.0142 m/s 4 s 0.0154 m 0.0580 m 0.0145 m/s 5 s 0.0160 m 0.0740 m 0.0148 m/s 6 s 0.0166 m 0.0906 m 0.0151 m/s Average Instantaneous Speed: 0.01435 m/s Total Distance Traveled VS Time time (s) total distance (m) 1 s 0.0136 m 2 s 0.0278 m 3 s 0.0426 m 4 s 0.0580 m 5 s 0.0740 m 6 s 0.0906 m

Calculations: Total Distance: example: 0.0136 m/s + 0.0142 m/s = 0.0278 m/s 0.0136 m/s + 0.0142 m/s + 0.0148 m/s = 0.0426 m/s (continue adding the interval distances starting from 0 to get total distance for each second) Instantaneous Speed: example: instantaneous speed = total distance / time (s) 0.0142 m / 2 s = 0.0139 m/s Average Instantaneous Speed: 0.0136 m/s + 0.0139 m/s + 0.0142 m/s + 0.0145 m/s + 0.0148 m/s + 0.0151 m/s = 0.0861 m/s ÷ 6 = 0.01435 m/s Questions: Part I Question 1: How can one find the pulling speed using the dots? Briefly describe using the definition of speed. With speed being the rate of change of an object’s position over time, we can find the pulling speed using the dots by measuring the distance between each dot. The further apart the dots are, the slower the pull is while the closer the dots are, the quicker the pull is. Thus, we can also find the pulling speed by dividing the time taken to travel by the distance traveled. Question 2: Compare your two types, 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. We can determine by looking at the spacing of the dots whether the cart was moving at a constant speed by looking at the patterns after being pulled. With the tape that was pulled manually, the patterns were very inconsistent with some dots being closer to each other and others being further apart. As for the ones pulled by the cart, the pattern was consistent and the dots were evenly spread apart which means that the cart was moving at a constant speed.

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Question 3: Did the cart travel the same distance from one interval to the next? Use your data to support your statement. Yes, the cart traveled the same distance from one interval to the next with approximately 6 cm in between each. Question 4: Did the cart’s instantaneous speed change from one interval to the next? Support your answer using your data. The cart’s instantaneous speed did change from one interval to the next. As the interval distance increases in meters, the instantaneous speed also gets faster which is demonstrated at second where the interval distance is 0.0136 meters with a speed of 0.0136 m/s while second 6 has an interval distance of 0.0166 meters and a speed of 0.0151 m/s. Question 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. Yes, the average speed of the cart during the 6-second trip is equal to the instantaneous speed because as we mentioned earlier, the cart was moving at a constant speed since the distance between each interval was consistent. Therefore, the instantaneous speed would be the same as its average speed. Question 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? The slope value from the equation y= 0.0154x+0.0028 is not within 10% of the value of average speed calculated in step D because the slope value (0.0154 m/s) represents the constant speed of the cart during the entire trip while the average speed (0.01435 m/s) is calculated by taking into account the total distance traveled and the total time taken. Question 7: How can the trend of the data on the chart allow you to conclude whether you observed motion with constant speed? The trend of the data on the chart allows us to conclude whether we observed motion with constant speed by examining the relationship between time, position, or distance. If there is a straight line trend on the graph with a constant slope (straight line), this suggests that the cart was moving at a constant speed. Whereas a curved or non-linear trend indicates that the speed of the object was inconsistent over time.

Part II Question 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? The plot graph whose value increases linearly with time is velocity. The point where the trend is nonlinear is at approximately 1.43 seconds since it starts curving downwards from that point on. Question 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.) To obtain the acceleration value from the linear fit of a graph of velocity vs time, we have to look at the slope of the graph. The slope of the velocity graph shows the acceleration. For example, if an object is moving at the speed of +3 meters per second then the slope of the line will be +3 meters per second. Question 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 of 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? In Run 1, the instantaneous acceleration values are similar to the single acceleration value obtained from the best-fit line in that the slope value (0.485) is the same as most of the instantaneous acceleration values ranging from seconds 3 to 6. Velocity VS Time (TRIAL 1)

Discussion: After completing this lab, we were able to measure the instantaneous speed and distance by evaluating the collected data from the experiments in Parts I and II. In Part I, we used the dot patterns on the paper tape, which was generated from the cart and pulled manually, to measure the speed. A ruler was then used to measure and compare them. The results determined that the manually pulled tape was faster than the cart because the dots were inconsistent and closer together whereas the tape pulled by the cart moved at a constant pace. In Part II, we noticed that the acceleration of the cart as it was traveling down the ramp was changing slightly initially. However, it slowly began to stabilize at a certain value since there were no other forces acting on it. As for velocity, our graphs demonstrated that the velocity data was linear and how it increased over time as the cart traveled down the ramp.

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