Not only do we get the “shape” of the acceleration curve of the colliding cart, but we also get the maximum acceleration -6.67 meters/second squared. This acceleration and the mass of the cart (0.566 kilograms) result in a maximum impact force of 3.73 Newtons.
This is not exactly the same value you get from the force sensor, but that’s okay. There are two main reasons why the maximum force differs with this method. First, the video frame rate was 30 frames/second, so position points were only collected every 1/30 second. It’s entirely possible to increase this frame rate, but I kept it at a normal value because this is what you usually see in real videos.
The second problem is that when you calculate velocity and then acceleration, you are actually only looking for acceleration values for a few points at a time. This can introduce small errors that cause the final value to be slightly off.
Anyway, this video method is great. This is non-invasive and can be done after the fact. All you really need is a video. (It is also helpful to know the mass of an object.)
Accelerometer
If you don’t want to use video analysis, there are other ways to obtain acceleration data (and use it to find forces). It is possible to measure acceleration directly, and you probably have a device that can do it right now. It’s called a smartphone. Cell phones have accelerometers that can measure their movements, which are used for things like LIDAR, augmented reality, and even long exposure photography.
In my opinion, the best apps that can get acceleration data from your phone are: fifox. (It’s free.) You can actually get the data. all This app allows you to operate your phone’s sensors such as pressure, magnetic field, rotation, etc.
Anyway, what would happen if you stuck your phone on a cart that crashed into a barrier? Here’s the data I got:
Illustration: Rhett Alleyne
From now on, the maximum acceleration will be 6.55 m/s.2. We can use the mass of the cart (and the iPhone, which increases in mass) to find the maximum impact force again. This results in a maximum force of 5.32 newtons upon impact.
Of course, acceleration can be measured with sensors other than smartphones. In fact, almost every modern car has some type of accelerometer that is used to determine when to deploy the airbags, i.e. when high acceleration is sensed during an impact. Other acceleration sensors can also be installed inside the car to measure acceleration at various points inside the car. This produces data that shows how the car deforms or moves relative to itself during a collision.
Here are some fun and safe experiments you can try at home. You take a cell phone with the PhyPhox app installed and drop it onto a pillow from a very close distance, measuring the acceleration. Next, drop the phone from the same height onto another soft object and compare the impact acceleration. Hopefully, you will find that the softer the landing target, the lower the value of acceleration (and therefore force) upon impact.