Tru Physics

Projectile Motion–Rubber Bands and Hex Nuts

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Tru Physics
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[This experiment can be completed at home without specialized equipment. The difficulty level is: Moderate.]

Weapons like the launcher shown above rely heavily on the physics of projectile motion.
Weapons like the launcher shown above rely heavily on the physics of projectile motion.

The purpose of this lab is to understand that motion in the x-direction is independent of motion in the y-direction. To do this, a projectile is launched horizontally off of a table into a cup or bowl some calculated distance away.

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Materials:

  • Phone with camera
  • Two-meter stick or measuring tape (one that measures in metric units is best)
  • Three binder clips (this set is nice because the small binder clips have a better grip for what we need and the large size is great for launching)
  • Rubber band (we will need a slightly thicker one, but it’s best to get the assorted pack so that you can get the size just right)
  • Hex Nut (Getting a pack like this is useful for other labs, but we will only need one hex nut for this lab)
  • Paper, single page only (8.5″ x 11″)
  • Clipboard (this is important because it makes the base of the launcher)
  • Ruler (optional)
  • Scissors/knife

Cost: I’m assuming that you already have some of this equipment. However, if you don’t, you can still get everything for under 50 USD.

Procedure:

  1. Assemble the projectile launcher. To do this, take the clipboard and clip a piece of paper to it.
  2. Cut the rubber band (choose a thicker one for best results). Now you have a long elastic band.
  3. At the bottom of the clipboard, attach the band using the two smaller binder clips. Then attach the larger binder clip around the band in the center. This is all shown in the figure below.
Figure 1. Proper connection of elastic band to clipboard (top) and launcher primed for launch (bottom). Projectile motion launcher.
Figure 1. Proper connection of elastic band to clipboard (top) and launcher primed for launch (bottom).
  1. Now you will want to locate the middle of the paper. Assuming that your paper is the general 8.5 inches width, mark a dot at 4.25 inches. This dot should be close to the bottom of the page (near the rubber band).
  2. Test the launcher by laying it on a flat surface (e.g. the edge of a table). Pull back on the large binder clip, place a hex nut flush with the binder clip, and then release. The binder clip should launch the hex nut straight forward.

Note: It is recommended to only pull back very slightly (depending on the rubber band being used). Start by only pulling the binder clip back by about an inch. Increase by a small increment if the launch is too weak. Continue adjusting how far you pull back until you are comfortable with the launch distance and speed.

  1. Once you have found a comfortable launch speed/distance, make a mark on the paper showing how far you need pull back. A straight line that aligns with the top of the hex nut is ideal. Always be consistent in pulling the binder clip to this same location.
  2. Now we need to calculate the launcher’s intitial velocity. In other words, we need to find out how fast the hex nut is traveling when it is launched. To do this, find a spare wall where you can rest your launcher on the ground such that it is pointing straight up. Check that the wall is free of items that may get damaged if shot by the launcher.
  3. Line up the two-meterstick or tape measure so that it is also going straight up the wall. It is best to have the numbers ascending as they go up the wall, so put the zero side at ground level if possible.
  4. Note the height of the clipboard. This is the initial height. Call it y_i and write it down.
  5. Pull the binder clip down and launch the hex nut from the straight line you drew earlier. Watch for how high it goes. You don’t need an exact value just yet.

Tip: Don’t release slowly. Try to let go all at once so that the launcher is as consistent as possible. Releasing slowly may cause the initial speed to be dampened unintentionally.

  1. Now that you know approximately how high the projectile will launch, set up your camera to record that portion of the two-meter stick. Recording the entire scene may make it difficult to read the values that you need.
  2. Start the recording, and launch the projectile ten times. Pull back the binder clip the exact same amount each time, and remember to release your grip quickly for each launch.
  3. Review the video footage and find the max height for all ten launches. If some of the launches were out of your video’s frame, that’s okay, as long as you have at least five good launches. Write down each max height.
  4. All of the launches should have a max height within a few inches of each other. If the variation is worse than this, try again with more care.
  5. Take the average maximum height from these launches. You need to determine \Delta y which is the average maximum height minus the clipboard height which you measured back in step 9. Write down this difference. It should be easy to see that this is how far the projectile actually traveled by the time it reached its max height.
  6. Apply the equation below to determine v_{i,y} which is the initial velocity of the projectile. [Note that v_{f,y}=0 m/s which is what actually allows you to solve for v_{i,y}.]

v_{f,y}^2 = v_{i,y}^2 + 2a \Delta y

using a=-9.8 \dfrac{m}{s^2} which is the acceleration due to gravity.

Note: Even though you will be launching the projectile horizontally in a moment, it will still have the same initial velocity. Firing the launcher upward has the advantage that the projectile slows down and turns around at the top of its flight path.

  1. Choose a table or desk to fire the projectile launcher off of. Be sure that the ground is clear and that nothing in the flight path could be damaged by the hex nut when you launch it.
  2. Measure the launch height (this would be the height of the table plus the thin clipboard on top of the table.) Call this value y_i.
  3. Get a small cup or bowl that you can launch the projectile into and measure the height up to the rim. We will call this y_f. Write it down.
  4. Determine the difference between these two heights: \Delta y = y_f - y_i
  5. Calculate the theoretical time of flight using the equation below:

t= \sqrt{\dfrac{2* \Delta y}{g}}

where:

  • g=9.8 \frac{m}{s^2}
  • \Delta y is the vertical distance that the hex nut will fall from the launcher to the bowl.
  1. Calculate the distance from the edge of the table at which you should place the cup (on the ground) using the equation below:

\Delta x = v_x t

where:

  • v_x is the initial velocity of the projectile. You obtained this value in step 16, but we called it v_{i,y} back then. It is the same value.
  • t is simply the time calculated in step 21.
  1. Use the two-meter stick to help you place the bowl the proper horizontal distance away from the foot of the table. This distance is just \Delta x from step 22. Align the center of the bowl with that distance.
  2. Use you best judgement to make sure that the projectile launcher is aligned well with the zero mark on the two-meter stick. Of course, the two-meter stick will be on the ground and the projectile launcher will be on the table, so you will have to estimate.
  3. Pull back the binder clip with the hex nut flush against it and release (quickly!) from the exact same mark as you used in all previous test launches. If done correctly (and with a bit of luck), the hex nut should land directly in the bowl! The most common error is not having the bowl and the launcher aligned properly, but the hex nut should still land just to the left or right side in either case.

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