Prelab: Complete the prelab section BEFORE class Purpose:

Transcription

1 Lab: Projectile Motion Prelab: Complete the prelab section BEFORE class Purpose: What is the Relationship between and for the situation of a cannon ball shot off a with an angle of from the horizontal. Theory: After writing the purpose, we need to think about what we expect the relationship to be. This will be stated in the theory. In this lab, we are looking at the relationship between the horizontal position and the vertical position of a cannon ball shot horizontally from a position on top of a table. Complete each of the following tasks. 1. Sketch the shape y vs. x graph that you expect. In this case, you cannot predict specific values. The shape of the graph is the important thing. Notice that because there are no scale values, the units are not necessary on the axes labels. y y-position vs. x-position 2. Look up in your text a sentence that talks about motion for an object in projectile motion. Give the quote. In parentheses after the quote place: authors, year, page number as in (Knight, Jones, & Field, 20xx, p. #). x 3. What is the value (with units) of each of the following constants for a situation of an object in projectile motion? a x = a y = 4. With a horizontal launch, what is the value of the initial (at t=0) y-component of the velocity, v iy? v iy = Phys. 114: Lab-Projectile Motion-Report Page 1 of 8

2 Procedure: Procedure steps are primarily given in the lab instructions document. Summarize the main steps in the following space. Draw a diagram of your cannon for the initial situation where is it shot from the top of a table. Include in the drawing the following: The table and launcher. Indicate the locations of the cannon ball at t=0, xi and yi, and the locations of x=0 ad y=0. Indicate what you need to measure to find the actual value of yi. Both x and y coordinate systems. Include x=0 and y=0 on the coordinates. Indicate, on the drawing, the launch angle for this lab. Phys. 114: Lab-Projectile Motion-Report Page 2 of 8

3 Fill out the following sections and turn in as Lab 3 Report. See calendar for due date. Part I: Initial Conditions, Muzzle Velocity Calculations, and Theoretical Trajectory Calculations After taking measurements, show your calculation for finding the initial y value. Set the cannon to a medium range and assure that the cannon is going at least 2 meters horizontally. Shoot the cannon 10 times (at least) to measure the time it takes the cannonball to travel past the two photogates in the barrel. List the times here and show your calculation for the best average time and uncertainty. Hint: To save time in lab, you can get these time measurements while taking other range data. However, you must not change the range setting or the muzzle velocity will change and, therefore, your times. Calculate the muzzle velocity for your cannon on a medium range setting using the average time you found above. Fill the initial values for kinematic quantities into the table below. x-components y-components xi = yi = vxi = vxf = vyi = axi = axf = ayi = ayf = Phys. 114: Lab-Projectile Motion-Report Page 3 of 8

4 Consider the situation where your cannonball has travelled 1.5 meters horizontally from the starting position. Calculate the height, y, of the cannon ball at this location. Show your work keeping all equations separated into x-component and y-component equations. Show all your steps and draw a box around your answer. Be sure to include units. x-component equations and work y-component equations and work Consider the situation where your cannonball has travelled to a height of 0.30 meters from the ground. Calculate the horizontal position, x, of the cannon ball at this location. Show your work keeping all equations separated into x-component and y-component equations. Show all your steps and draw a box around your answer. Be sure to include units. x-component equations and work y-component equations and work Phys. 114: Lab-Projectile Motion-Report Page 4 of 8

5 Consider the situation where your cannonball has travelled to a height of 0 meters from the ground. Calculate the horizontal position, x, of the cannon ball at this location. This is the expected maximum range of your cannon at its current setting. Show your work keeping all equations separated into x-component and y-component equations. Show all your steps and draw a box around your answer. Be sure to include units. x-component equations and work y-component equations and work Repeat calculations for theoretical positions of the cannonball during flight. Be sure to calculate at least 7 more values between the launch and the final location. Order these values and place in your data table (Part II) as theoretical positions. You should have at least 11 values including x=0. Note that you will not have to include uncertainty in the table headers for theoretical values. You will need to include units. You are not required to show work for the addition 7 sets of calculations. Part II: More Uncertainty and Formal Data Table To find uncertainty for x position, use single reading analog. Include a pdf diagram with values and also a clear statement of the uncertainty. Use this value of uncertainty in your table. x = ( +/- ) cm. Phys. 114: Lab-Projectile Motion-Report cm cm Page cm 5 of 8

6 To find the uncertainty for the y position, use the technique shown in the lab directions. Give an example of the uncertainty for y at the location x=2.0 meters, a location near this that your measured. You may include a photograph of your scatter pattern or draw a reasonable copy. Show any values that appear to be outliers. Show your visual approximation of the average value and indicate the uncertainty on both sides (top and bottom) of this average. Then state the value and uncertainty in the standard format. Note that your uncertainty is probably different for each different position you measure. It would be most appropriate to report them all. HOWEVER, for this lab, you may use this uncertainty as the y uncertainty in your table for all measurements. For those interested in more detail about this, see the bonus section for this lab. Place picture (or drawing) here. Part y III: = ( Graph and Comparison +/- ) cm. Create a FORMAL table of theoretical and measured x and y values. Be sure to add the necessary elements to the table headers (uncertainty is not needed for theoretical values). Be sure to order your table values to be in trajectory order increasing in x and y. Add rows as necessary and be sure to include your initial location as a measured value. Be sure to also include the measured location where y=0. Phys. 114: Lab-Projectile Motion-Report Page 6 of 8

7 Theoretical Values from calculations x Measured values from cannon shooting. Part III: Comparing Theoretical and Experimental Graphs Using your many theoretical (calculated) (x,y) paired values, plot a y vs x graph of your predicted cannon ball path (trajectory). Include a plotted dot for your x=0 position also. Now using you many measured (x,y) paired values, plot, on the same y vs x graph, your measured cannon ball path (trajectory). Use different color or shaped point protectors and best-fit lines and a key so that the two lines can be distinguished. Attach your graph and make sure to put your name and group number on it. Use engineering paper!!! Phys. 114: Lab-Projectile Motion-Report Page 7 of 8

8 Answer the following questions regarding your comparison of the two graph lines. 1. Are the shapes similar or not. If they differ, explain how they are different. 2. Are the ranges similar or not. If they differ, is the theoretical one longer or shorter? 3. If drag were to have an effect, would you expect it to make your experimental trajectory shorter or longer than your theoretical one? Bonus: When uncertainty values are different for every point, then simply listing one uncertainty value in the graph header is not sufficient. In that case, one could list it with every value in the table. However, a better system is to use error bars in the graph. Error bars are the graphed length of the uncertainty. See the example plot. It is showing error bars for y only for simplicity. Generally, x-error bars would be shown also. Notice that the error-bar for the largest y value is +/- 15 units. Its length is 15 units long above the dot and also 15 units long below the dot. However the bars on the dot at y=34 is only 5 units above and below the dot, indicating +/- 5 units of uncertainty. For bonus credit, include error bars with your graph and also include the different y value uncertainty in the table with each value. X (cm) Y (cm) +/ / / / / Phys. 114: Lab-Projectile Motion-Report Page 8 of 8