Velocity Lab Objective: Be able to explain how to calculate velocity of an object moving at constant velocity. Note: This Lab does not require a full lab write-up as outlined in the syllabus. You need submit your completed table and graph, answer the questions included in the lab and write a short paragraph summary. Students are allowed to do this lab individually or with a partner. If with a partner, both partners must write and submit their own labs and indicate who their lab partner is. Background Information: You will probably find this lab the most difficult of the labs in this course, especially if math is not your favorite subject. It is the only lab that requires using some basic physics and graphing. The future labs will be easier, but I suggest NOT using your drop one lab ability because you may need it later in the semester for an emergency. I have included a tutorial on graphing for those of you that may need a refresher. The tutorial is located in this module under Lab. In the lab once the ball leaves the ramp there is no longer the effect of gravity, therefore the ball’s velocity is no longer increasing but rather a constant velocity. In this lab, we will be measuring this constant velocity. Note that slower velocities may occur in your longer distance runs due to friction. When scientists perform experiments, they do a test multiple times and then average the results to achieve the best accuracy possible. If there is a test run that is very different from the others, a scientist may discard that test run believing that there was an error in its measurement. If you have a result that is very different from the others, you need to think about why it was different and whether that test run’s measurements should be discarded. In this lab we are going to use 2 methods to find the average velocity of the test runs. Method 1 requires calculating each test run’s velocity and taking the mathematical average of the velocities. This is similar to what was done in Lab 1. Method 2 requires graphing the test run data and using the slope of the best fit line to calculate the average velocity. Watch the tutorial if you want a graphing refresher. Materials Required: Ramp to roll a ball down (possibilities include a wrapping paper tube and with some books under one end) Smooth surfaced ball (that can be rolled down the ramp you chose, smooth to reduce friction and not bouncy. For example, a marble) Long smooth surface (for ball to roll on after leaving the ramp, examples smooth floor or table) Tape (to hold ramp and measuring device in place) Metric tape measure or meter stick Method of timing (must measure time from end of ramp to desired distance, can use clocks, watch, some cell phones or stop watch if available) Calculator Graph Paper Pencil Ability to take a Digital Picture Steps: 1. Use the following table to record your data. Test Run # Time Distance Velocity (d/t) 1 2 3 4 5 6 7 8 9 10 Average N/A N/A 2. Create a ramp as shown in the Velocity Lab Diagram. A suggestion to create a ramp is to use a wrapping paper card board tube with some books under one end. There should be no bumps on the ramp or floor. Assure that your ramp will not move between test runs by taping it in place. Question #1: Why is it important to not have bumps in the ramp or floor? Question #2: Why is it important that the ramp is not moved between test runs? 3. Choose a smooth ball of the appropriate size to roll down the ramp you have constructed. For best test results a ball with minimum bouncing ability is suggested. Question #3: From what you have learned of basic physics, why will a less bouncy ball give better test results? 4. Mark the starting point of the ball on the ramp. Each test run needs to start at the same point on the ramp so that the velocity of the ball when it reaches the floor is the same for each test run. The lower on the ramp the starting point the slower the velocity. Slower velocity may be better if you do not have a very accurate timing device. 5. Try a test run. The ball should go straight once it leaves the ramp unless the floor or table is slanted. Position the ramp to get the ball to travel as straight as possible. If needed, place something on each side of the ball’s path as side rails to keep it going straight. 6. Place metric tape measure or measuring device on the floor with the 0 point at the position the ball hits the floor. 7. Time to do 10 test runs. For each test run, release the ball from the same starting point. Start timing the ball when the ball hits the floor and finish timing at a predetermined location. (Make sure to vary your distances (final location) so that you have varied distances in your table and graph. Distances might be start around 70 cm and then add 10 or 20 cm each test run, but will vary on each student’s available floor space and timing device). Record each test run distance and time in the table. Method 1 for calculating average velocity: 8. Calculate the velocity in the last column using the formula v=d/t. Question 4: Are any of the result velocities very different from the others? If so, why do you think it is and do you think the run should be discarded? 9. Calculate the average velocity of the test runs by adding all velocities in the last column and dividing by the number of runs. Record. Method 2 for calculating average velocity: For those students needing a refresher in graphing and best fit line, watch the graphing tutorial found in this modules lab section. In addition these sites may be helpful: http://www.mathgoodies.com/lessons/graphs/line.html http://www.mathsteacher.com.au/year10/ch16_statistics/09_linebestfit/24line.ht m http://illuminations.nctm.org/ActivityDetail.aspx?id=146 10. On a piece of graph paper, create a graph similar to the one shown in PhysicsPlace.Com Interactive Figure 3.01 or the graphing tutorial. Time will be on the x-axis (horizontal axis on the bottom) distance on the (y-axis). In order to use graphing to find the average of a ratio as in our velocity ratio v=d/t, the numerator (number on the top of the fraction) must go on the y- axis and the denominator (number on the bottom of the fraction) must go on the x-axis. 11. For best accuracy of your results it is better to use as much of the graph paper as possible, this means choosing what each square of the graph represents wisely. It is important to note that the scale (how much each scale represents) of the x –axis and y-axis can be different. Start both the x and y axis at 0 and the largest possible number for each your distance and time must fit on the axis. Number your x and y axis. 12. Plot the points of each test run and label the data points on your graph. To plot each point, simply follow from each axis the distance and time of the test run horizontally and vertically on the graph paper until the 2 lines meet. 13. Once all the data points are plotted you are to place a best fit line through the dots plotted. A best fit line is a straight line. In this case, the best fit line must go through the point (0,0) and then roughly through the middle of all the other data points. (Note: A best fit line goes through (0,0) if it makes sense for the experiment. In our case the (x,y) coordinate pair is (time,distance), if the time =0 it makes sense that the distance = 0) 14. Once the line is plotted, the slope of the line will give you the average velocity. To find the slope pick 2 points on the line that are NOT points from a test run. For better accuracy pick points that aren’t close together on the line. Slope is designated by the letter m and the formula is: m=(y2-y1)/(x2-x1) 15. Record the calculated slope. This is your average velocity calculated by the graphing method. Compare Method 1 and Method 2 Results: 16. Compare the average velocity calculated in the table to the average velocity calculated by graphing. Question #5: Are the average velocities of the 2 methods close in number? If not, what do you think is the cause of the difference? Oil Reserve Lab Objective: To explore the amount of oil reserves left on Earth and to predict when the reserves will run out. Notes: Make sure to answer the questions in the lab in the lab write up. Students are allowed to do this lab individually or with a partner. If with a partner, both partners must write and submit their own labs and indicate who their lab partner is. Lab writeups should not be identical otherwise it is considered plagiarism. Lab write-up format is given in the syllabus. Materials Required: Map of the globe (flat version, can get online and print but larger is better) A list of the top 20 oil reserve countries (See Energy Source and Energy Conservation Part C, second to last slide) Enough of the same object to represent the total billions of barrels of oil (Each object could represent 1 or 2 or 5 billion if desired, suggested object would be pennies) Ability to take and upload a digital picture (edit your pictures so less pixels for submission) Steps: 1 Calculate how many billions of barrels left by adding up the countries reserves in your list. 2 Determine how many billions of barrels each of your objects will represent. 3 Place objects on map to represent Oil Reserves. 4 Take a picture and submit with your lab. 5 What observations can you make? 6 Oil consumption is estimated to be 30 billion barrels a year. With current resources and consumption rate, when will oil reserves run out? (Divide total amount of reserves by 30)
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