Studying Gravity like Galileo
As part of my Grade 10 Integrated Science course we do a unit on Mechanics, and we start that big unit with gravity. While I do many labs in that unit, one of my favourites is an open-ended lab in which students investigate the effect of mass on the acceleration due to gravity. I find Physics to be one of the best branches of Science in which to teach and reinforce experimental design skills and this lab in particular has many teachable moments which I use to help my students better understand things like constants (or controlled variables), sources of error (methodological error in particular) as well as how to make sure their data is both reliable and valid.
The Inspiration
In my opinion one of the best ways to help students understand the creativity and problem-solving components of the scientific method is for them to analyze famous historical experiments, especially those which led to significant discoveries. One such experiment is that of Galileo, when he disproved Aristotle's statement that the acceleration of an object due to gravity is dependent on mass. Galileo used a long ramp at a low incline to slow down the movement of a ball rolling down a ramp enough to get accurate data. He also used the flow of water into a cup to measure the time it took the ball to roll down different intervals of the ramp. With careful analysis he was able to determine that the balls accelerated at a constant rate. You can find a great video of this experiment from Spark here.
The Methodology
With Galileo's experiment as inspiration I explain to my students that their task is to work in groups of three to investigate how mass affects the acceleration of a ball down a ramp. They are given different balls of a similar size, I use golf balls, ping pong balls and squash balls for the smaller types of balls and then baseballs, tennis balls and floor hockey balls for the second size. As a class if there are at least 3 groups collecting data on each size of ball then we have more than enough data to ensure that the results are reliable.
They are each given a 3 meter piece of PVC pipe which has been cut in half (best ramp ever) as well as a buret on a ring stand with a clamp, a beaker and a graduated cylinder to allow them to recreate Galileo's method of measuring time without a clock or stopwatch.
I tell the students to set the ramp up at a low incline of their choice and to collect data on the time (or volume of water) it takes for each ball to go down the ramp. In their groups of three most teams have one student who is responsible for releasing the ball at the top of the ramp & says "go", a second student who catches the ball at the bottom of the ramp & says "stop" and the third who opens and closes the buret based on these cues from their teammates. This methodology has enough information to allow for students to get started, but is vague enough to allow them to make their own methodological choices and learn from their mistakes.
The Materials (list per group of 3 students)
One half piece of PVC pipe 2.5 to 3 m long
One tennis ball
One floor hockey ball
One baseball
One squash ball
One golf ball
One ping pong ball
One ring stand
One buret clamp
One buret
One 100 ml graduated cylinder
One 250 ml beaker
One small funnel
A mass balance
Access to a sink for water
You may allow students to use their phones to take pictures if you like (but they should not use it as a stopwatch!)
The Teachable Moments
#1: Constants
Once each group has begun to collect data I check in with them about their methodology and ask them questions which are designed to point out potential sources of error &/or lacking constants (controlled variables). For example, it is important that the buret is opened and closed in the same manner each
time to ensure that the time is accurately measured. This can be done by having the same student open the stopcock completely each time. Another important constant is if the ball is pushed down the top of the ramp or just let go. Ideally students figure out that pushing the ball down the ramp will introduce a confounding variable which makes their data less valid and they will just let it go down the ramp without any applied force
#2 Measurement & Trials
Since students will use the volume of water which has flowed out of the buret during the time it took the ball to roll down the ramp (remember this is their measurement of time) they need to ensure that their measurements are accurate. There are three common ways to measure the volume of water lost using the provided equipment. The first two measure the volume of water which has flowed into the beaker or graduated cylinder placed under the buret and the third is to measure the change in volume of the buret. This is an excellent moment to talk about uncertainties of the tools used in Science. Which tool gives the most accurate measurement of volume? The beaker, the graduated cylinder or the buret? How does increasing the number of increments increase the validity of the data? You can also check with your students about how many trials of data they plan to collect, my standard minimum number of trials for most labs is three, but with a lab like this with so much reliance on human reaction time I tell my students that five is much better. We then take some time to talk about why five trials is more reliable than three.
#3 Velocity vs. Acceleration
Many students collect five trials of data on the amount of water (which represents time) it takes for each of the three balls to roll down the full 3 m ramp and then calculate the velocity of each ball's movement and think that they are done. This is an excellent moment to discuss and reinforce the difference between velocity and acceleration, then have the students brainstorm how to determine the acceleration of the ball using the water timer method. I often guide my students to divide their ramp into three 1 meter sections, and to use the same technique they used earlier to determine the velocity of each section, from point A to B and from B to C and from C to D then from A to D (their original data).
Once they have this information they can calculate the acceleration using the final velocity (m/ml) and the initial velocity (m/ml) over the time it takes the ball to roll down the entire ramp (volume of water from A to D). Each group of students should have a data table with 5 trials for each of these different increments of distance, as well as the mass of each of the balls.
The Data Analysis
Once each group has their data collected I have the students create a single data table for the entire classes data set, this allows for a further increase in reliability, we then calculate the acceleration together (using the talk aloud method) for one or two raw data sets to model the calculations for those students who need it. If each group calculates the acceleration for each of their 5 trials of each of their 3 different balls we will then have lots of data to use to calculate the mean. Depending on the level of your students you can take this moment to do standard deviation of the.data set as well. I encourage my students to graph their data using a scatterplot with line of best fit, graphing mass vs. acceleration. At this point I usually take a moment to remind students that when graphing the independent variable goes on the x-axis and the dependent variable goes on the y-axis as someone always forgets. I ask my students to graph their data digitally in Google Sheets or Excel so that we can then calculate the regression of the data set, this is something that we do quite a bit in this unit.
Now that students have a complete data table, calculations and graph they can begin to interpret their findings. Is their hypothesis supported or refuted and how can they tell? Did they find that the acceleration is independent of mass? How reliable and valid is their data? How big is the standard deviation of each ball's acceleration? Is the regression value high enough to imply significance? Which sources of error can they identify?
More Teachable Moments
#4 Sources of Error
At this point I usually facilitate a class discussion about their sources of error as well as the reliability and validity of the data set. I try to discourage discussion of human error, saying that we need to focus on methodological error - things that we could have planned for differently to reduce error. I have found that it helps students to think of this in terms of what they would do in an idea world... would they conduct the lab in a vacuum? Would they have balls of the same surface texture and size but different masses? Would they use a photo-gate or other method to measure time?
#5 Constants Round 2
After our discussion of sources of error we can discuss a common solution - which is keeping things which we cannot change constant, so at least they are affecting all of the trials in the same way. A great example of this is the friction of the pipe they have used, it would be ideal if the ramp had little to no friction, but it also works if the same ramp is used for every trial...so the friction affects all the balls in the same way. Another constant that could be addressed is the angle of the ramp, did every group in the class use the same angle? Or did everyone use a slightly different shallow angle? How might this have affected the data set?
I hope that this blog post inspires you to use labs such as this one to help your students develop their investigation skills and understanding of the differences between velocity and acceleration as well as the impact of mass on the force of gravity rather than the acceleration due to gravity. If you would like a full student lab sheet with detailed instructions for this lab you can find it in my TPT shop.
Thanks for reading teachers, travelers & curious souls of all kinds.
The Roaming Scientist
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