We Crashed a Dynamics Cart into a Target! What the Graphs Reveal About the Secret of “Speed Squared” (A Kinetic Energy Experiment)
“If your speed doubles, how much harder is the crash?”
When car accidents make the news, “excessive speed” is often blamed. That’s because even a small increase in speed makes the impact far worse than you’d expect. The secret behind it is something familiar from physics class: kinetic energy.
So what does kinetic energy depend on? When I asked my students for their hypotheses, the words “mass” and “velocity” came up.
This experiment is usually done on a small scale, rolling a marble down a rail into a target. My twist this time was to crash a 1 kg dynamics cart into a target box and work out the answer from how far the box gets pushed. Going bigger makes the results much easier to interpret. Here’s how it works.
What You’ll Need
- Dynamics cart… It has a mass of 1 kg.
- Weights (500 g) x 2… I used two 500 g blocks of oil-based clay as a substitute. Put one on the cart and it becomes 1.5 kg, put on two and it’s 2 kg, so you can easily change the cart’s mass.
- Beespi… A simple speedometer.
- Bamboo ruler
- Disposable chopsticks
- Ticker timer
- Masking tape… Used to mark spots on the desk.
- Target (box)… I made mine by stuffing some oil-based clay into a bento lunch container. It’s nice that you can build it from everyday items.
How to Do It
1. Tape a chopstick to the dynamics cart with masking tape. Then set up the target and run the cart through the Beespi to measure its speed right before it hits the target.
2. Vary the speed (between 0.20 and 0.80 m/s), crash the cart into the target, and record how far the target gets dragged.
3. Once you have four data points, add one weight to make the cart 1.5 kg and repeat. When you’re done, add the second weight to make it 2.0 kg and run the experiment again.
Result 1: Speed vs. Distance Moved
Now it’s time to analyze the results and turn them into graphs. This is where students start to wonder and debate which kind of function fits the data, and it’s honestly the most fun part of the whole experiment.
Let’s start with speed and distance. Put the distance the box moved on the vertical axis and the speed on the horizontal axis.
Most of my students guessed a linear function. But when you actually plot the graphs for 1.0 kg, 1.5 kg, and 2.0 kg, they don’t come out as straight lines. Instead, you get a graph that curves upward.
A curve like this might be a quadratic function, so let’s dig deeper. To test that idea, we square the speed on the horizontal axis. Plot the distance moved against the square of the speed, and you’ll find that the distance is proportional to the square of the speed.
Result 2: Mass vs. Distance Moved
Next up is mass. To compare masses fairly, you need to compare them at the same speed. But getting the 1.0 kg, 1.5 kg, and 2.0 kg carts to hit the Beespi at exactly the same speed is next to impossible. So we use the graphs we just made and read off the distance the target moved at the same speed.
When you graph that (distance moved on the vertical axis, mass on the horizontal axis), you get a straight line.
The Big Reveal: What Kinetic Energy Really Is
Putting it all together, we can conclude that kinetic energy is proportional to the square of the speed and proportional to the mass. Written as a formula, it starts to look like the famous “1/2 × m × v²”.
There’s a catch, though: this experiment can’t tell us anything about that 1/2. Some students tried to squeeze it out of the slope of the graph, but when the cart and the box stick together and move as one, mechanical energy isn’t conserved. That means the experiment simply can’t pin down the coefficient.
This is a valuable lesson in itself, too. Knowing what an experiment can tell you, and what it can’t, is a hugely important part of thinking scientifically.
These results connect directly to everyday life. Take a car’s brakes, for example.
If your speed doubles, your kinetic energy quadruples. That means the distance it takes to stop after hitting the brakes also becomes roughly four times longer. Stopping from 30 km/h and stopping from 60 km/h are very different stories. The “proportional to the square of the speed” graph we drew in this experiment ties right into road safety.
How You Read the Graph Changes Your Conclusions
By the way, some students look at the graph with the target’s distance on the vertical axis and speed on the horizontal axis and decide it’s a linear function.
The same goes for mass, where some students wonder whether it might be a quadratic function.
Depending on how you collect your data and what range you cover, a curved graph can sometimes look like a straight line. How you interpret that is a great example of how your analysis shapes your conclusions.
That said, because this experiment uses a cart and makes for a big, dynamic demonstration, careful work gives you remarkably clean graphs. You’ll be able to reach the conclusions you’re aiming for with confidence. Give it a try with everyday materials!
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