A brief outline for a horizontal projection lab

A teacher was asking about projectile motion labs in a Facebook teaching group; I thought I’d outline how I might do this. The teacher’s class is a traditional math-based class, looking for student-centered learning.

Introductory demonstration

1. Roll a ball along a table and let if fall off.
   • Ask students to draw what the path looks like along the table and after it leaves the table.
     • Hopefully they will draw a horizontal line followed by a curved line.
   • Ask them to add a motion map next to the path showing the ball’s position at equal time intervals.
     • Remind them that arrows on the dots show the direction, and the length of the arrows shows the relative speed.
   • Remember that many of them may not show constant Δx.
2. Ask what details about the motion we could measure. They should get some of these:
   • Distance the ball fell from the base of the table
   • Time it was in the air
   • How far down it fell (height of the table)
   • Mass of the ball
   • Speed of the ball (hint: remind them that we can’t measure speed, only change in position and change in time).
   • Distance the ball traveled (this would be a curved path; we won’t be measuring it, but they might suggest it).
3. Ask “Which of these measurements seem practical to collect with the tools we have?”
   • Δx (both on table and through air) and Δy
   • Times
   • launch speed (distance across the table and time needed)
   • Mass

Developing the experiment

1. Ask “Look at your motion map. Which parts of the motion seem to change the most? Which seem to stay the same?”
   • Students will say things like:
     • “It speeds up as it falls.”
     • “It moves sideways faster at first.”
     • “It slows down after it leaves the table.”
     • “It curves more later.”
2. Ask “What could we change the to make the ball fall further from the table?”
   • They might generate:
     • make it go faster
     • raise the table
     • use a different ball
3. Agree that the distance the ball falls from the table will be our dependent variable.
4. Explore how these would affect the distance.
   • If they have previously learned that all object fall with the same acceleration, ask them if the mass of the ball should change the distance (hopefully they will answer that it won’t).
5. Ask “Which of these changes would be easiest to control and repeat?”
   • The speed of the ball or the height of the table.
     • Unless you have tables that rise up easily, you can settle on speed being an easy ‘independent variable.’
6. Agree that the speed of the ball will be our independent variable.
7. Start a discussion of how you might change the speed of the ball in a controlled way.
   • They may come up with some creative ways, but I’d guide them towards rolling the ball down a ramp from different heights.
8. Ask “How could we measure the speed of the ball?”
   • If they have used motion sensors, they might suggest this. Ask them how they would position the motion sensor so it could measure the speed of the ball without getting in the way or being angled from the ‘straight forward’ motion of the ball.
   • If they have used photogates, they might suggest using those. Using just one just before it leaves the table would introduce significant uncertainty: How certain can they be that the photogate is on the exact center of the ball???? If you want to use photo gates, one near the bottom of the ramp and one right before it leaves the table might work (recording the time between the two positions).
   • A ‘low tech’ method is to mark off a distance along the table from the edge to close to the ramp. Demonstrate this. You might see the ball bounce a few times, so remind the students that they should try for a position when it is not bouncing.
     • What assumptions are we making here? The table should be level, but is it? Ask for other assumptions students might think of.
   • They can now calculate the speed of the ball.
9. How many trials, etc.
   • Discuss how many trials they should make for each speed (I usually suggest three).
   • How many different speeds do they want to record (the length of your tables and how many times your ball bounces before it just rolls across the table may help you decide how many is practical).
   • Ask them ‘launching’ it with a zero speed is possible (i.e. they should realize they can just drop the ball off the edge!)
10. Now I think the class is ready. A few other tips
    • You can use a plumb bob (any object hanging from a string tied a the launch point) if the edge of the table doesn’t have a straight wall down to the floor).
    • Data, data, and more data: Suggest that they measure the height of their launch position, as well as the mass of the ball. If you’ve taught energy, they can look at the height of the ball on the ramp (gravitational energy) and compare this to the speed (kinetic energy)–but caution that some of the energy is now stored as rotational energy of the ball–might be a good way to bring this out if they haven’t already studied rotational energy!
    • They can also time the ball’s projectile motion, although getting accurate times for this may be difficult…but worth a discussion of uncertainty in measurements.

Data analysis

1. Students can now plot speed and x-distance on a graph; they should find that the slope is the time the ball is in the air (Δx / speed -> m/(m/s) -> the time units go to the top and the distance units cancel). Time is a constant!

Resources/documents (coming soon)

Here are some documents you can use:

• Slideshow to walk students through the point of collecting data (“guided inquiry”)
• Google Doc worksheet (six pages).
• Google Sheet for processing data.
• Amplify activity with Desmos embeded