My presentation to a Grade 11 physics class consisted of 5 main parts:
- Lecture
- Worksheet
- Predictions
- Demonstration
- Discussion
Lecture
Click here to download the presentation slides!
These slides cover all 5 sections, but most of the slides focus on the first part. They explain what a concussion is, and the key differences between concussions and skull fractures. Then I derive the equation for impulse from Newton's 2nd Law. We analyze the variables of the equation for impulse to see how we can reduce the average force of a collision by wearing a helmet. The key point is that wearing a helmet will increase the time duration of the collision, which will cause a decrease in the average force of the collision. I derive a formula for the work-energy principle, and perform a similar activity analyzing the variables of this formula. The key takeaway is that the helmet will increase the distance over which the collision takes place, which results in a decrease in the average force of the collision. The slides also introduce the Force vs. Time graph, and show that the impulse of a collision is the area under the curve of this graph.
Worksheet
After going over the key concepts, the students can work on the worksheet for about 10 minutes. The worksheet will ask the students to analyze two different force vs. time graphs and decide which one had a helmet and which one didn't. Then there are two simple calculations that will make the students apply the concepts discussed earlier.
The worksheet and solutions are attached below, and can also be found on the Resources page.
Predictions
The bottom part of the worksheet includes a spot for predictions. In this space, the students are given the mass of the ball and the height it will be dropped from, and are asked to calculate what the impulse of the collision will be. After the demonstration, we will come back and discuss how good our predictions were, and why.
For my mass of 10.6 kg and height of 0.1 m, the predicted impulse is 14.85 Ns. We predict that the impulse will be approximately the same for the two collisions, if we ignore the mass of the helmet (about 500g compared to the 10.8kg mass).
Demonstration
The demonstration can be done quite quickly. First drop the mass onto the force plate without a helmet, and save the data in LoggerPro. If possible, show the data collection on a projector screen so the students can see the Force. vs. Time graph constructed in real time. Once this data has been saved, repeat the drop, but this time with the mass protected inside a helmet.
Once the data has been collected, use LoggerPro to calculate the impulse of each collision. Below is the data I collected when performing this demonstration:
Discussion
Once we have our Force vs. Time graphs, it is important to discuss the results. As we predicted, the two collisions have approximately the same impulse. The collision with a helmet (shown in blue above) clearly takes place over a longer time duration, and has a smaller peak force. However, the measured impulse is about 2x greater than our prediction. Ask the students for their thoughts on why this happened.
I believe there are two significant reasons why we got twice the predicted impulse:
We made our prediction assuming that the ball had a final velocity of 0.
In reality, this is not true. It is clear in both videos above that the ball bounces off the force plate with an upwards velocity. This means that there is some additional change in momentum, and therefore a greater impulse. However, for this to cause the measured impulse to be twice the predicted impulse, the ball would need to bounce all the way back to its initial height, so there must be something else at play.
The force plate appears to bounce into the air slightly.
In addition to the ball having a final upwards velocity, the force plate also appears to jostle into the air during the collision. Using the conservation of momentum, this is an additional change in momentum that would need to be considered when calculating the impulse.
There may be other factors involved that I haven't thought of - maybe your students will come up with some better ideas!