v Levitated Puck on Ramp Interactive @ This video shows a superconducting puck levitated above a magnetic ramp. When released, the puck glides nearly frictionlessly to the bottom of the ramp. We'll use these videos to create a mathematical model that describes the relationship between release height and velocity at the bottom of the ramp. @ 1. The video below shows a description of the apparatus we'll be using, a superconducting puck and a magnetic track. The puck is cooled to -196C in a liquid nitrogen bath. Then the puck is placed above the track, held in position by a wood spacer. Through a process called "quantum locking" the puck remains the same height above the track. The puck can move along the track with virtually no friction. Watch the short video below to familiarize yourself with this apparatus. @ 4. Now your equation should show that v is proportional to some power of h times a numerical coefficient. Think about the units that this coefficient must have and the fact that this coefficient must be related to the acceleration due to gravity, 9 = 98Ocm/s2 Can you figure out how the coefficient is related to g? In other words, is it 1/29 , is it 29 , is it 9 , etc? Of course, there is experimental error so the value of the numerical coefficient won't be exactly one of these relationships with g, but using what you think is the correct relationship, calculate what we'll call our experimental value of g. Show all your work. BIQx,x'E EEEEE @WBPEFEEI Score: 0/2 @ 5. Finally, if your were to do this experiment over and take new data from the video, explain at least one thing you would do differently to reduce errors. 5 BIHX1X'EiEEEEECO7WBmE Score: 0/2 5. Finally, if your were to do this experiment over and take new data from the video, explain at least one thing you would do differently to reduce errors. BIUXX=BEE @ Vx POF Score: 0/2@ 2. This next set of videos allows you to explore and experiment with this apparatus. You can select the mass of the puck, and the height from which the puck is released. You can measure the speed of the puck as it slides along the horizontal portion of the track. / '0 (V V l . "' , '\\V 'r " ' Mass: #1 Height: K Frame rate: 240 frames per second HEIGHT MASS Height K mass #1 ange 0 I4 > M I \"El\" @ 3. Use this data table and graph to collect and analyze data. Follow the instructions in the sections below. Name units var v Graph 1 Title 10 Vertical Axis v Graph 1 Title 10 Vertical Axis Horizontal Axis Go Back to the Table 1' + Add Another Graph 10 v Tips for Making Measurements with this Interactive @ There are several features of this Interactive that allow you to make accurate measurements of the release height and velocity. Let's look at these. @ 1. For the release height, we'd like to find how much higher the puck is at release compared to the bottom of the ramp. Here are some tips: 1. Click the red dot tool icon to deploy a red marker 2. Position the marker on the center of the puck before release. When the marker is selected, you can use the arrow keys on your keyboard to adjust the position. 3. Play the video and pause when the puck is sliding along the flat portion of the track. 4. Deploy another red marker and place it on the center of the puck. 5. Use the vertical ruler tool to measure the change in height between the two locations 6. You can also deploy the horizontal line to use as a reference. For example, you can place the horizontal line on the lower marker and use it to measure the height. 7. Here's an example of how the tools could be set to measure a release height: 30 cm sl Ae 0cm AA 30 cm 20 cm E4 DOD 10 cm 10 cm 2. To measure the velocity as the puck slides across the flat portion of the track, we'll need a displacement and time interval. Here are some tips for that: 1. Use the horizontal ruler to measure the position of the puck as it slides. 2. Measure position using either the right or left edge of the puck, which is easier to see rather than the middle of the puck. 3. Use the stopwatch to measure time. 4. Estimate the change in position to the nearest 0.1 cm.@ 3. Use the data table to simplify your calculations. For example, rather than calculate each velocity, make a column on the data table that will calculate velocity using the displacement and time measurements. Here's how: 1. Make columns for displacement and time in the data table. 2. Enter the displacements and times for each trial. 3. Click the menu tool in the data table column heading an add a new column to the right. 4. Label the new column velocity 5. Press the menu icon in the column heading again and choose change column formula 6. Use the calculator to make a formula for the velocity v Part 1: Collecting Data @ Let's make measurements and enter the data into the data table in first section. @ 1. As stated in the introduction, our goal is to find the relationship between the velocity at the bottom of the ramp and the release height. That is, we are looking for the function v(h) . Which variables will get graphed on which axis to find this relationship? @ v on the horizontal axis, h on the vertical axis h on the horizontal axis, 11 on the vertical axis 1 / 1 submissions remaining Cray-AI n [9 @ 2. Using the instructions in "Tips for Making Measurements..." collect data and enter it in your data table. Collect at least seven measurements for different release heights and the corresponding velocity at the bottom of the ramp. Make sure to include trials that start near the top of the ramp and near the bottom. v Part 2: Linearize your Data to Find the Relationship @ We'll use the process of linearizing to find the mathematical relationship between release height and velocity at the bottom. @ 1. Which kind of relationship does your graph appear to show? @ linear: '0 oc h inverse: 11 0c % sideways parabola: 17 0c x/E parabolic: v 0: h2 inverse squared: 1) oc le? Score: 0/2 @ 2. Based on your answer above, create a calculated column in your data table so that you create a linear relationship. Use the linear regression tool to find the equation for your relationship. Write your equation in the space below, @ Hint: your equation should show velocity, v as a function of release height, h. So it should be of the form v(h) I: I: '7' ll BIHXIX1 Ecpm Score: 0/5 @ 3. Given the fact that if the initial height was zero lie the puck started at the bottom of the ramp) then the velocity at the bottom would be zero, are there any numbers in your experimental equation above that should be zero? Explain, and if so, write the new equation (now corrected for v = 0 when h = O). BIHX,X'EE Ecwpm Ill 7 Score: 0/2 @ 4. Now your equation should show that v is proportional to some power of h times a numerical coefficient. Think about the .I III- rr~- I .I III r III .II- (In-I .I I. I. .I