Notebook 1DM Kress Final

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Iowa State University *

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131L

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Physics

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Apr 3, 2024

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Lab 1DM - 1D motion Equipment  Motion detector  A cart that rolls on an aluminum track. The cart has an adjustable friction pad  Spirit level  Various masses, string and a pulley, to apply a force to the cart  A wood board (1" thick) that may be placed under the feet at one end of the track to tilt the track. The apparatus for this lab is depicted in the figure below. The string (when under some tension !) should be 162-164 cm long , including the loop at each end. Check its length by stretching it gently on the measuring jig, or use a meter stick. Adjust or replace it if necessary; string and scissors are available. Lab 1DM – Page 1

The cart and track  Handle and push the carts gently .  The two stops on the track (near the 20 cm mark and the 170 cm mark) prevent the cart from getting too close or too far from the motion detector.  The cart has a friction pad underneath it to produce friction if desired. Drag can be adjusted with the plastic screw located behind the reflecting plate. Please do not turn the screw all the way out. For today’s lab, the friction pad should be lifted so it does not touch the track. Is it lifted? Yes  Use the spirit level to check that the track is horizontal. Is this done? Yes  Check now and several times during today’s lab that the track’s feet are not too close to the end of the table. The track tends to slide about. The motion detector The motion detector system measures the distance to the nearest object in front of the detector. It emits short bursts of sound of ultrasonic frequency and detects any reflections of this sound that come back. It measures the time between the emission of the burst and the first reflected sound (above some threshold level), and transmits this time information to the computer. From this, the computer software calculates the distance to the reflecting surface by using the known speed of sound (in air at room temperature). This process is similar to that used by some auto-focus cameras, as well as the echo- location process that bats use. The motion detector fills a cone-shaped region with sound. The motion detector will measure the distance to the closest object within that cone. The object that should reflect the first sound received by the motion detector is the plate on the cart; when you are pushing the cart, be sure that you and your hand are farther from the motion detector than the plate. "Bad" data points often are the result of an unwanted object being in the "cone" of sound. Lab 1DM – Page 2

1. Velocity, acceleration For this first part of the lab, the string and hanging weights should be put aside. The cart will be moved with your hands. Download and open 1DM – 1D motion.cmbl Do a quick test of the motion detector by moving the cart along the track. In the following activities, different motions will be described to you. For each case, the activity has 3 steps: a. Prediction: Sketch a qualitative prediction of the v-t and a-t graphs that correspond to that motion. b. Experimental result: move the cart accordingly (several times if needed until you obtain a satisfactory data set). Insert images of the graphs produced by the motion detector. c. Compare and discuss interesting qualitative features and differences of the predictions and the experimental results. These might be due to a variety of factors:  Imperfections of the experimental setup (try to specify what is the problem)  Bad experimental setup (wobbly or unleveled tracks, unwanted echoes, etc.)  Oversimplified or incorrect prediction. Lab 1DM – Page 3

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1.1. Moving toward the detector at two different constant speeds: first slowly and then faster. Prediction: Experimental result: Lab 1DM – Page 4

Compare and discuss: From t=0 to t=3, our experimental graphs were very similar to what we predicted would happen. We predicted the velocity to start out at a small negative, but the experimental results was it started at 0. This could have been because our cart was too far away from the detector. Lab 1DM – Page 5

1.2. Starting halfway along the track, move slowly away from the detector at constant speed, stop for a couple of seconds, then move toward the detector at constant speed, but faster than before. Prediction: Experimental result: Lab 1DM – Page 6

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Compare and discuss: Overall similar, acceleration changes weren’t as dramatic as how we drew them, but we accurately predicted the direction and magnitude of the velocity changes. Our drawing depicted a straight line down as the velocity changes, which wasn’t how we saw it but it was as close as we could get them given our equipment. Lab 1DM – Page 7

1.3. Moving away from the detector, speeding up with a constant acceleration. Prediction: Experimental result 1 : 1 It is relatively easy to move your hand at constant velocity, but constant acceleration is hard! Do not spend too much time on this, just a couple of attempts and move on. Lab 1DM – Page 8

Compare and discuss: We attempted to get our velocity as linear as possible and without a linear fit showing the line, I would say that it is very close to linear. The magnitude of acceleration isn’t as large as we thought on the graph shown but it does appear to be constant, as we predicted. Lab 1DM – Page 9

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1.4. Moving toward the detector, speeding up. Prediction: Experimental result: Lab 1DM – Page 10

Compare and discuss: There was a slight error at the end, but from t=0 to t=1 the experimental graph looks like what we predicted. We correctly predicted the direction and magnitude of the velocity and our graph is as linear as we could make it. We also correctly predicted the acceleration and our experimental graph appears to be constant as well for acceleration. Lab 1DM – Page 11

1.5. Some conclusions for activity 1 True or false? Explain based on your results for activities 1.1 through 1.4. “When the cart is speeding up, the acceleration is always positive.” False, when the cart was moving towards the detector, it was technically moving at a negative x position, which results in a negative velocity. As it speeds up the velocity gets larger in the negative direction, resulting in a negative acceleration. “It is impossible to get a perfectly vertical line in any of these graphs.” True mostly, it was very challenging for us to be able to replicate the quick change in velocity that we predicted. It was also hard to have the detector pick up the immediate change in velocity. I’m sure with the correct equipment or tools we could get a better line. Lab 1DM – Page 12

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2. Speeding up with constant acceleration Cart pulled by hanging weight To obtain a constant acceleration, we will pull the cart with a string and weight, as shown in the figure below. Before you take a run, sketch a prediction of what your velocity and acceleration graphs will look like. Test your predictions! Lab 1DM – Page 13

Lab 1DM – Page 14

Quantitative results: determine the acceleration. In the interval where the acceleration is constant, we can determine its value in two different ways: a. In the v-t graph: use a linear fit to determine the slope. You need to select the data for the correct interval only! Insert the graph with the linear fit box below. Remember to include the standard error. (When the graph was included, the linear fit box could not be easily read so I only included the linear fit box but I understand if I needed both.) b. In the a-t graph: Select the appropriate data and use the Statistics tool to determine the average value. Insert the graph with the Statistics box below. c. Compare the two results. They are very close, so I would consider the experiment as a successful way of showing that the slope of velocity vs time is acceleration. They are minorly different, which could be a result of not using the right range or errors produced by the cart and detector. Lab 1DM – Page 15

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Lab 1DM – Page 16

Activity 3: Inclined track We will now study the motion of the cart as it goes up (after being given a gentle push) and down the track. Tilt the track by placing a 1” thick board under the feet of the track closest to the motion detector . As usual, sketch your predictions for the graphs: Run the experiment. The cart should be given a short push at the bottom of the track, strong enough so it goes up a reasonable distance, and gently enough so it doesn’t crash! Insert your graphs, calculations and results below. Lab 1DM – Page 17

The results of our linear fit slope compared to the acceleration statistics are very similar. The mean of the acceleration graph is just outside of the range of uncertainty but it is only 0.07 units away from being in the range so I consider them to be very close. Discuss any differences with your predictions. Our prediction didn’t look the same as our results. We thought the acceleration would be negative and then positive once the cart stopped moving towards the detector. We were incorrect, the acceleration was constant the entire time. I would also say that our velocity prediction was incorrect. We assumed there would be not a constant change in velocity (which goes back to our acceleration prediction) but Lab 1DM – Page 18

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instead we saw that there was a constant change in velocity and the velocity was 0 at the exact moment the cart turned around. Did the cart stop at the top? For a brief moment, yes it stopped at the top of the motion as it was moving towards the detector and then after it stopped it began moving away from the detector again. How much time did the cart spend at its highest point top before it started back down? It stopped for less than a second. On our velocity vs time graph, it stopped when the velocity was zero and according to our graph, it did not spend more than half a second there. Is the acceleration positive, negative or zero at the instant when the cart reaches the top? Justify your answer based on the graphs. Positive, our graph shows a positive constant acceleration. This is because gravity is acting on the cart and gravity is always constant. Because the incline is starting at the origin of our positive x axis, the cart is being pulled in the positive direction. It slowed down as it was going in the negative direction and then sped up. Compare the accelerations of the cart while going up and while going down. Are they equal within experimental precision? Discuss why or why not. They are very similar but the mean value of the acceleration statistic is just outside of the uncertainty range given by the linear fit. This could be due to our errors such as interfering with our motion during the trials or even just not getting an accurate reading with the motion detector. Lab 1DM – Page 19

Notebook 1DM Kress Final

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