Copy of Lab 2 - Kinematics

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Lab 2 - Kinematics Learning Objectives ● Understanding the concepts of position, displacement, and velocity ● Develop skills of graphical representation and analysis of motion ● Learn techniques of numerical differentiation and integration. Overview Kinematics is a field of physics that describes how things move. The language that describes how an object moves is given by its displacement and velocity . Displacement is the change of an object's position; where it starts and where it ends. Velocity is how fast the object moves and what direction it moves. iOLab You are going to use the iOLab to test your understanding of kinematics. First make sure your iOLab is set up correctly. ● Launch the iOLab software on your computer. ● Connect the USB dongle to a USB port on your computer. The dongle indicator at the top of the iOLab software should turn on from gray to white. ● Turn on the power button on the iOLab device. The remote indicator at the top of the iOLab software window should turn on from gray to white. ● In the list of sensors on the left side of the iOLab software window, put a check in the box next to the “Wheel.” Make sure there are checks next to “Position” and “Velocity.” Uncheck “Acceleration.” ● Uncheck any other sensors. Now test the iOLab device by recording some data. Place the iOLab on its wheels on a smooth level surface. Click the Record button on the iOLab software window and give the iOLab a push so it rolls a distance of about 0.5 - 1 meter, then click stop. UMass Amherst Physics 151 Fall 2023

Click on the Zoom Tool to zoom in on a portion of a graph you want to see better. There are three types of zoom: zoom in on a selected box, zoom vertically, and zoom horizontally. Clicking on the Analysis Tool will allow you to analyze a selected portion of a graph. Click and hold the left mouse button and drag horizontally along a portion of the graph to analyze. The iOLab software will return the following values: ● is the average of the selected range. ● is the uncertainty of the selected range. ● a is the shaded area of the selected range. ● s is the slope of the selected range. ● In analysis mode the vertical line that tracks with the mouse pointer gives the value of the graph at time t . UMass Amherst Physics 151 Fall 2023

Position to Velocity Once the iOLab is set up and working, it is time to do the experiment. Below is a set up of graphs of position vs. time. Based on the graph, you are going to predict what the corresponding graph of velocity vs. time would look like. Remember the relationship between position and velocity. Velocity is the rate of change of a moving object’s position: So when you are looking at a graph of position vs. time, the slope of the graph is the velocity at that point in the graph. Here are some things to consider when looking at the slope of position vs. time: ● Is the slope positive or negative? ● Is the slope steep or shallow? Now you will make a series of predictions, then test your predictions using the iOLab. ● On a piece of paper sketch your predicted graph and take a picture of it. Then paste your picture into your copy of the report document. You must sketch your prediction FIRST, before you test your prediction with the iOLab. ● Next, use the Kinematics - Simulation spreadsheet to perform a numerical differentiation of the position vs. time data and simulate the velocity vs. time you are predicting. ● Next take the iOLab and record the motion of it moving in a similar way as the graph of position vs. time. Then look at the iOLab graph of velocity vs. time. Does the graph of velocity vs. time match your prediction? If it does explain why. If it does not, explain what assumptions you made in your prediction. Take a screenshot of your iOLab software window and insert it into your copy of the report document. UMass Amherst Physics 151 Fall 2023

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1. Sketch a prediction of the velocity vs. time graph that corresponds to the position vs. time graph below. a. Insert a picture of your predicted graph of velocity vs. time here: b. Generate a graph of velocity vs. time with your simulation. Copy/paste your graph here: UMass Amherst Physics 151 Fall 2023

c. Insert a screenshot of your iOLab software window with graphs of position vs. time and velocity vs. time here. Describe what you did to make the iOLab move the way it did to produce the graphs. d. Does your prediction of velocity vs. time agree with your recorded velocity vs. time of the iOlab? Explain why or why not. Yes, my predicted graph does agree with the recorded graph. My prediction was a UMass Amherst Physics 151 Fall 2023

constant line and the outcome of the recorded graph also was constant. 2. Sketch a prediction of the velocity vs. time graph that corresponds to the position vs. time graph below. a. Insert a picture of your predicted graph of velocity vs. time here: UMass Amherst Physics 151 Fall 2023

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b. Generate a graph of velocity vs. time with your simulation. Copy/paste your graph here: c. Insert a screenshot of your iOLab software window with graphs of position vs. time and velocity vs. time here. Describe what you did to make the iOLab move the way it did to produce the graphs. UMass Amherst Physics 151 Fall 2023

d. Does your prediction of velocity vs. time agree with your recorded velocity vs. time of the iOlab? Explain why or why not. Yes, my predicted graph does agree with the recorded graph. My predicted graph was constant and my recorded graph was slightly shifty but also had a constant outcome . 3. Sketch a prediction of the velocity vs. time graph that corresponds to the position vs. time graph below. UMass Amherst Physics 151 Fall 2023

a. Insert a picture of your predicted graph of velocity vs. time here: b. Generate a graph of velocity vs. time with your simulation. Copy/paste your graph here: UMass Amherst Physics 151 Fall 2023

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c. Insert a screenshot of your iOLab software window with graphs of position vs. time and velocity vs. time here. Describe what you did to make the iOLab move the way it did to produce the graphs. HINT: what if the iOLab moves on a ramp? Construct a small ramp for the iOLab to move on. d. Does your prediction of velocity vs. time agree with your recorded velocity vs. time of the iOlab? Explain why or why not. Yes, my predicted graph does agree with the recorded graph. My predicted graph has UMass Amherst Physics 151 Fall 2023

a positive velocity and so does the recorded graph which is also a positive velocity. 4. Sketch a prediction of the velocity vs. time graph that corresponds to the position vs. time graph below. a. Insert a picture of your predicted graph of velocity vs. time here: b. Generate a graph of velocity vs. time with your simulation. Copy/paste your UMass Amherst Physics 151 Fall 2023

graph here: c. Insert a screenshot of your iOLab software window with graphs of position vs. time and velocity vs. time here. Describe what you did to make the iOLab move the way it did to produce the graphs. d. Does your prediction of velocity vs. time agree with your recorded velocity vs. UMass Amherst Physics 151 Fall 2023

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time of the iOlab? Explain why or why not. Yes, my predicted graph does agree with the recorded graph. I have a negative velocity in my predicted graph and that matches the recorded graph as it's also going down. Velocity to Position Now you are going to make predictions of the iOLabs position based on a graph of velocity vs. time. Below are graphs of velocity vs. time. For each graph you are going to sketch a prediction of the corresponding position vs. time graph. In the previous part of the lab, you used the slope of position vs. time to help you predict the velocity vs. time, but how do you predict the reverse? Consider again the relationship between position and velocity. The mathematically velocity is the derivative of position and graphically it is the slope of position vs. time. But we can do the inverse to find the position: So mathematically the displacement is the integral of velocity with respect to time. Graphically the area bound between the velocity graph and the time axis across some time interval is equal to the displacement of an object. Now look at the graphs of velocity vs. time below: and sketch your prediction of the corresponding position vs. time graph. Once you have your prediction, use the iOLab device to move with a velocity like the graph and compare your prediction of position vs. time to the position vs time from the iOLab. ● On a piece of paper sketch your prediction of the corresponding position vs. time graph and take a picture of it. Then paste your picture into your copy of the report document. You must sketch your prediction FIRST, before you test your prediction with the iOLab. ● Next, use the Kinematics - Simulation spreadsheet to perform a numerical integration of the velocity vs. time data and simulate the position vs. time you are predicting. UMass Amherst Physics 151 Fall 2023

● Next take the iOLab and record the motion of it moving in a similar way as the graph of position vs. time. Then look at the iOLab graph of velocity vs. time. Does the graph of velocity vs. time match your prediction? If it does explain why. If it does not, explain what assumptions you made in your prediction. Take a screenshot of your iOLab software window and insert it into your copy of the report document. 5. Sketch a prediction of the position vs. time graph that corresponds to the velocity vs. time graph below. a. Insert a picture of your predicted graph of position vs. time here: UMass Amherst Physics 151 Fall 2023

b. Generate a graph of position vs. time with your simulation. Copy/paste your graph here: c. Insert a screenshot of your iOLab software window with graphs of position vs. time and velocity vs. time here. Describe what you did to make the iOLab move the way it did to produce the graphs. UMass Amherst Physics 151 Fall 2023

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d. Does your prediction of position vs. time agree with your recorded position vs. time of the iOlab? Explain why or why not. Yes, my predicted graph does agree with the recorded graph. My predicted graph was constat then positive velocity which exactly matched the recorded graph as it was also constant then suddenly took a spike up. 6. Sketch a prediction of the position vs. time graph that corresponds to the velocity vs. time graph below. UMass Amherst Physics 151 Fall 2023

a. Insert a picture of your predicted graph of position vs. time here: b. Generate a graph of position vs. time with your simulation. Copy/paste your graph here: UMass Amherst Physics 151 Fall 2023

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d. Does your prediction of position vs. time agree with your recorded position vs. time of the iOlab? Explain why or why not. Yes, my predicted graph does agree with the recorded graph. My predicted graph was constant then it was negative velocity, which is also the same for the recorded graph. 7. Sketch a prediction of the position vs. time graph that corresponds to the velocity vs. time graph below. a. Insert a picture of your predicted graph of position vs. time here: UMass Amherst Physics 151 Fall 2023

d. Does your prediction of position vs. time agree with your recorded position vs. time of the iOlab? Explain why or why not. Yes, my predicted graph does agree with the recorded graph. My predicted graph was constant for a small period then had a positive velocity and back to constant, which matched the recorded graph as it had the somewhat similar. UMass Amherst Physics 151 Fall 2023

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