Notebook 1DM - 1D motion hc

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Iowa State University *

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Feb 20, 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: The velocity came out as expected, leaving room for human error. The curve has a positive slope that increases as time goes on. The acceleration is almost what we expected to happen. Constant acceleration is hard to achieve using only your hands as the source of acceleration, but the graph still shows a relatively constant acceleration for the first second, followed by a period of increase, then followed by another slightly larger constant acceleration. Acceleration is measured independently of direction, and an acceleration graphed on the negative y-axis is indictive of a negative acceleration. The velocity graph should have remained under the x-axis since we are moving towards the detector and in the negative direction, as shown by the negative slope of the distance graph. 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: The velocity graph worked perfectly and matched what we predicted, is shows the constant velocity in the positive x-direction, followed by a time of no movement, followed by a continually decreasing velocity in the negative direction. The second velocity should have been more constant. Acceleration almost follows what we expected, with a constant slope to start which is very close to the positive y-axis, then a period of no movement lying on the y=0 line, followed by a greater constant acceleration than in the beginning that returns to the positive y-axis. This graph shouldn’t have dipped below the x-axis. 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: Our prediction for velocity matches what we said would happen it constantly goes up as speed increases. Acceleration is not as constant as we predicted, but it is most likely due to human error. 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: Our prediction for velocity matched completely with our data that we collected, it has a negative slope under the x-axis moving in the negative direction. The acceleration should not have gone under the x- axis, as it was intended to be increasing continuously. 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.” True, acceleration is measured independently of direction. Acceleration is only negative when it is decreasing. “It is impossible to get a perfectly vertical line in any of these graphs.” True, all velocities and acceleration take place over a change in time, signified by a change in the x- position. A perfectly vertical line would have to occur faster than instantaneously. 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. 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. When acceleration is constant as the velocity increases at a linear positive slope. Lab 1DM – Page 15

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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 16

Discuss any differences with your predictions. There were no differences between our predictions and the data we received. Lab 1DM – Page 17

Did the cart stop at the top? Yes. How much time did the cart spend at its highest point top before it started back down? At most 1 second, then it went backwards, more like 0.5 secs. Is the acceleration positive, negative or zero at the instant when the cart reaches the top? Justify your answer based on the graphs. Positive, when it reached the top, the acceleration stays constant at the peak. 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 equal and opposite as seen by the data we collected. (means) Lab 1DM – Page 18

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