Impulse Control - Studying Collisions
The unit on impulse and momentum is always a fun one to teach since it involves memorable demonstrations— like throwing an egg at a bed sheet. It also has great applications to driving safety, something that can never be reinforced too often with teenage students.
In the lab, a Force Sensor is essential to measure the force of a collision over time. A standard lab activity consists of colliding a cart into a Force Sensor while a Photogate measures the speed of the cart before and after the collision to determine the change in momentum. The change in momentum can be compared to the impulse by determining the area under the Force vs. Time curve.
In the case below, we are using a Discover Collision Bracket to hold a High Resolution Force Sensor in place while we measure velocity with a Smart Gate. A spring is attached to the Force Sensor to help extend the collision time.
The Discover Collision Bracket comes with two different types of springs to allow students to analyze two different collisions. To launch the PAScar at a consistent speed use the built-in plunger. When the springs are used, the resulting graph is a textbook example of an impulse curve.
Using the area tool in Capstone we can easily determine the area under the curve. Students can clearly see that the impulse is equal to the change in momentum and that the impulse for each spring is essentially the same.
We could stop here, but wouldn’t it be great to have the students do some additional exploring with their own bumpers? While you can use simple household materials for the bumpers, we used our 3D printer to create an accessory for the Force Sensor which allows us to print our bumpers. Thanks to 3D printer technology, it is now very easy to create all sorts of plastic parts without having to create a mold.
The accessory consists of five parts created by the 3D printer and a 6-32x0.5 screw. The screw and three of the parts are constructed together to make the base.
A rolled sheet of paper can be inserted into the base, which is then held in the base by a plug inserted in the paper cylinder.
Two different diameter plugs are available to accommodate the use of different thicknesses of paper. Using graph paper is a great way to start, since you can easily keep track of the length of the paper used in a bumper. The screw allows us to attach the accessory to the force sensor the same way we attached the spring.
Here is an example of a typical impulse graph you can get with a paper bumper:
As you can see, it is a bit different than the impulse curve with the spring, having more of a plateau for the force. However, the impulse-momentum relationship still holds!
A simple experiment to start off with is changing the length of the bumper. The number of squares in the legend represent the length of the bumper according to the squares on a piece of graph paper.
As one would suspect, the length of the bumper is inversely related to the maximum force on the cart. Again, the impulse remains the same in each case.
After smashing the bumper, the paper really cannot be reused since it is now crumpled.
But what happens to the impulse graph if the cart keeps smashing into the bumper over and over again? The data below shows the impulse for the bumper after being hit the first (Run #1), third (Run #3), and fifth time (Run #5).
Interestingly, the impulse remains the same, but as the bumper gets hit more and more times, the maximum force gets larger and the plateau gets narrower, showing a similar curve to the springs. This makes for a good argument why you should replace the bumpers on your car after a crash!
For a final test, what if the initial speed of the cart changed? The initial speed can be changed by using the different plunger settings in the PAScar.
There seems to be a lack of consistency between force and speed, but there is a very clear relationship between speed and impulse. What could be going on?
These are just some examples of what you can do with this type of an accessory. The great thing is that your students have the freedom to create their own experiments while at the same time exploring the relationship between momentum and impulse. If you are in a state which has adopted the Next Generation Science Standards, this would be a great activity to use some of those science and engineering practices!
If you have access to a 3D printer and would like to print your own bumper accessories, you may download the files from here:
Please feel free to share any additional ideas you or your students come up with using this accessory or ideas for another accessory!