10 Projectile Range vs. Launch Angle Page 1 of 5

Written by Stuart Loucks

Projectile Range vs. Launch Angle Introduction In this lab, students use a Mini Launcher to measure the range of a projectile on a horizontal surface for various angles. The average range is calculated for each angle, and average range vs. angle is graphed. A user-defined curve fit is used to predict the maximum range and the angle at which it should occurs. These values are then tested with a final launch.

Equipment

Qty Items Part Number 1 Mini Launcher ME-6825B 1 Table Clamp ME-9472 1 Large Rod Base ME-8735 1 Rod, 45 cm ME-8736 1 No-Bounce Pad SE-7347

Required, but not included: 1 Meter Stick (Only 2 needed), or Measuring Tape SE-8827, or SE-8712A. 1 Carbon paper (Only 1 sheet needed) SE-8693 1 550 Universal Interface UI-5001 1 PASCO Capstone software

You will also need several sheets of white paper, and some type of non-marring tape, such as painter's tape. You will need a table at least 1.5 m to 2 m long.

Figure 1: Setup for Launch from Tabletop Height

10 Projectile Range vs. Launch Angle Page 2 of 5

Written by Stuart Loucks

Setup

1. Wear safety glasses and avoid looking down the barrel of the Mini Launcher.

2. Make sure the Mini Launcher is mounted on the bracket in the lower position as shown in Figure 2. Slide the launcher all the way back so that it pivots about the launch position of the ball.

3. Fasten the launcher to the

table using the Table Clamp. It is easier to adjust the launcher angle if you remove the knob as shown in Figure 2.

4. Use the No-Bounce Pad with Rod

Base and 45 cm Rod (see Figure 3) as a backstop to help stop the ball.

5. It is critical that you read/set the

angle of launch (see Figure 4) very carefully and precisely. You should be able to read/set the angle to 0.2 degrees (see Figure 5).

Figure 2: Launcher Mount

Figure 3: Backstop to Stop Ball

Figure 4: Launch Angle Figure 5: Precise Angle Measurements

10 Projectile Range vs. Launch Angle Page 3 of 5

Written by Stuart Loucks

Procedure

1. Confirm that the launcher is mounted in the lower position on the bracket, and that the launcher is pulled all the way back (see Figures 2 & 6), so that the ball is launched from tabletop height.

2. Set the angle for about 20°. Carefully read

the angle to 0.2 degrees (see Figure 5) and record its value.

3. Place the ball in the opening at the top of the launcher, and use the loading rod (stored in the holder at the front of the launcher bracket—see Figure 6) to push the ball in and so depress the plunger one "click" to the short range setting. Note that the plunger has three settings: short range (one click), medium range (two clicks), and long range (three clicks).

4. To make your results more consistent when launching the ball, always pull with a quick

short pulse when pulling the thick cord (attached to the trigger—see Figure 6). Do NOT pull slowly. Always make sure that everyone is clear before firing!

5. Pull the launch cord to launch the ball and note the landing location. Place a blank sheet of paper at this location and tape it in position as shown in Figure 7. Pay attention to how you pull the launch cord, and try to repeat the pull exactly each time. Be careful to not pull so hard as to change the angle. Check the angle after launching. If it changed, you may be pulling too hard, or the thumbscrews securing the launcher are not tight enough.

6. Now cover the white paper with a sheet of face-down carbon paper as shown in Figure 7. You do NOT need to tape the carbon paper.

7. Launch the ball again, and confirm that the contact point is marked. Repeat several times.

Figure 7: Landing Area

Figure 6: Launching Ball

10 Projectile Range vs. Launch Angle Page 4 of 5

Written by Stuart Loucks

8. Create Table I in Capstone. In the first column, create a user-entered data set called “Range 20°” with units of m. Turn on the statistics in the table and choose mean and standard deviation.

9. Use a Meter Stick to measure the range to each landing point made for the 20° launch (see Figure 8). This distance should be measured from the center of the launch position of the ball as shown in Figure 9, and NOT from the edge of the table. Measure each landing point separately (see Figure 10), each to the nearest millimeter. Enter them into the Range 20° column of Table I, in units of meters.

10. Use a pen to mark each landing point on the white paper, so you know these were already measured.

11. Create Table II in Capstone. In the first column,

create a user-entered data set called “Angle” with units of degrees in the first column. Enter your measured angle, precise to 0.2° (for example, 20.2°) in this column. In the second column, create a user-entered data set called “Average Range” with units of m. Enter here the mean value from the Table I Range 20° column.

12. In Table I, in the second column, create a user-entered data set called “Range 30°” with units of m. Adjust the launcher angle to about 30°, and repeat the procedure. Record the precise angle and the average range in Table II.

13. Add new columns to Table I for Range 40°, 50°, 60°, and 70°. Repeat the procedure for each angle, recording the final results in Table II.

Figure 10: Spread of Landing Points

Figure 8: Measuring Range

Figure 9: Measuring from the Center of the Launch Position

10 Projectile Range vs. Launch Angle Page 5 of 5

Written by Stuart Loucks

Average Range vs. Angle

1. Create a graph of Average Range vs. Angle, to plot the data from Table II.

2. Turn on the curve fit tool on the graph toolbar, and then select User-Defined from the list. Open the Curve Fit Editor on the left toolbar. If it tells you to select a curve fit, click on the curve fit annotation box on the graph. The default user-defined curve fit equation might be “y = A*x +B” where A and B are constants that can be adjusted. In theory, the range equation for this setup is:

Average Range = Rmax sin(2∙Angle) Here Rmax is the maximum range. To use this as the curve fit, edit the right side of the curve fit equation to read:

Rmax*sin(2x) Click on Apply. (Note: If the curve fit seems off, go to the in the Calculator and select “DEG” mode, then return to the Curve Fit Editor and click Apply again.)

3. Does the curve go nicely through or very near all the data? If not, double-check your curve fit equation. (To make the curve fit look nicer, you can change the graph settings for the data appearance: Make the data point size large, and disable connecting lines.)

Angle for Maximum Range

1. Record the value of Rmax from the curve fit.

2. In theory, the maximum range should occur when the angle is 45°. Does your graph appear to confirm this? To answer this question more precisely: On the graph, add a Coordinates tool from the toolbar. Change the tool properties for the coordinates so the Snap-to Pixel Distance is 1, so it does not snap to data points. Move the Coordinate tool cursor to the highest point on the curve, where the range is equal to Rmax. Record the Angle at that point.

3. Set the launcher to this Angle you just found from your graph. Launch, and then measure

and record the range. How well does it agree with the value of Rmax from your curve fit?