Building Bridges

Written by Devansh Taori, Anshul Mathur, and Ryan Wei (period 4).

Introduction
In Mrs. Roemer's 4th period physics class, we built a bridge out of popsicle sticks and wood glue. We spent a significant amount of time in class as well as outside of class constructing the huge bridge. We met up at Anshul's house twice for nearly 11 hours in total to complete the bridge. In the end, it was an extremely successful project that was tons of fun.

The main objective for this experiment was to create a bridge weighing less than 0.454 kg that could hold more than 40 times its weight. 

We successfully created such a bridge. In the end, our bridge was 0.444 kg in weight and held more than 300 times its weight. 

Strategy and procedure
When we first started creating the bridge, we were unsure where to start. Our first two attempts started by creating the sides of the 60 cm pathway on the top of the bridge. However, after constructing more of the bridge, we realized that these two models weren't feasible. Our third attempt was the one that ended up becoming successful.

Once we figured out the general structure of the bridge, we made a quick sketch to make the building process a lot easier. We decided to go with a general truss structure for the sides and bases, since that would balance the weight better and make the bridge lighter but also more durable. We used approximately 16.5 trusses in total for the sides.

We decided to first start by building the individual trusses of the bridge that would help to carry the weight on the sides. Because the trusses were criss-crossed, they effectively balanced out the weight across the entire bridge and made it more stable. Also, the trusses transferred the force more effectively to the bases, which took most of the weight.

After building the trusses, we connected all of them together by using lots of wood glue. This structure formed the side of the rectangular prism at the top of the bridge. After building the sides of the bridge, we decided to build the 60 cm roadway on top, since we were afraid of going over weight and wanted to see how much weight we would have left for the base.

Now that we had weighed the entire rectangular prism on the top, we decided to build the bases. Because we knew exactly how much weight we had left, we adjusted the structure of the bases to reduce weight. Instead of putting a ton of popsicle sticks that had little function, we had a few popsicle sticks that were effective in holding up a lot of force.

Eventually, we constructed our entire bridge using a truss structure for the sides, a 60 cm solid roadway for the top, and bases that were extremely light but also used a criss-crossed structure to balance the weight. To make sure we weren't overweight, we used one of Anshul's weighing machines.

Going into Mrs. Roemer's class on the day of the Bridge Test, we were actually extremely scared. When we weighed the bridge at home, we were at 0.450 kg. We thought that maybe we would be overweight. Regardless, we were still so happy to be finally done with the bridge.

Results
When we weighed the bridge in Mrs. Roemer's class, it was luckily only at 0.444 kg. Thank goodness!

Here is the very final picture of the bridge right before we placed it for the weight test.

When we were doing the actual weight test, we were extremely careful when placing down the weights, because we thought that our bridge would collapse immediately. As you can see in the picture above, the bases were tilting slightly inward, and we thought that any amount of weight would cause the bridge to collapse inward. Luckily, our bridge held a significant amount. In fact, it held around 300 pounds before it collapsed! That's about 307 times the weight of our bridge!

Here's a picture of the bridge being finally destroyed under the sheer force of the weights. 

Concluding Remarks
As can be clearly seen, our bridge project was extremely successful. By utilizing a truss structure for the sides and bases, we made our bridge light and stable. Our bridge, weighing 0.444 kg, held 300 pounds, which is approximately 307 times its weight. Because of our ingenuity, planning, and hard work, we were successfully able to pass the test! If we were to do this experiment again, we would try to build the bridge by setting a limit on popsicle sticks, rather than the weight. This would force students to experiment with designs to make them extremely efficient.

Devansh did the lab report, took pictures, and created the 60 cm top roadway.
Anshul did the side, the bases, and helped with the lab report.
Ryan took pictures, created the sketch of the bridge design, helped with the bases, and did the sides.

Wave Investigations - 4th Period

Written by Devansh Taori, Anshul Mathur, and Eddy Lai.

Introduction

In Mrs. Roemer's 4th period physics class, we conducted an experiment to understand the properties of waves and examine whether changing some factors of the wave (such as amplitude, frequency, etc...) could affect other factors (such as speech, reflectivity, etc...). 
We began our experiment by asking three main questions and then using video recordings to detail our observations and come to an answer.


Data and Analysis
1) What affects the speed of a wave? Frequency? Amplitude?

To answer this, we first tested amplitude --

Next, we tested frequency --

In the first video, we clearly see that increasing amplitude has no effect on the speed of a wave. Although it may initially look like the wave is gaining velocity, when looking closely, one can see that the amplitude ultimately does not effect velocity. This is mathematically correct as well, since the formula for a wave's velocity is v = f • λ (v = velocity, f = frequency, λ = wavelength). Since increasing the amplitude does not increase f or λ, v stays the same.

In the second video, it appears that when the frequency is increased, the speed of the wave increases as well. However, this is mathematically not the case, because although v = f • λ, when f of the wave increases, λ simultaneously decreases (since f and λ are inversely proportional). This means that v technically remains the same, because although f does increases, λ proportionally decreases and neutralizes the increase in f. Why then does the velocity of the wave in the video appear to increase? This is because when Eddy and Anshul were increasing the frequency, they were inadvertently also increasing the force applied to the wave. Since an increase in F increases velocity, we see a higher velocity for the wave. Therefore, although it appears that a higher f results in a higher v, such is not the case. The only reason why v is higher is because there is a higher F being applied.

Therefore, it's clear to see that amplitude and frequency do not have an effect on the velocity of waves, while force does.

2) How do waves reflect at a fixed or open end?

To answer this, we first tested a fixed end --

Next, we tested an open end --

In the first video, we see that when a wave has a fixed end (in this case, the fixed end was Anshul holding the end of the slinky), the wave actually inverts and goes back the way it came from in that inverted fashion. When looking at the wave closely, it appears as though the wave is going both towards and away from Anshul. This is because the wave being created by Eddy is moving towards Anshul. Then, the wave inverts when it hits the fixed end, and moves towards Eddy in that inverted way. Therefore, the appearance of the wave going both ways is actually a demonstration of the inversion that occurs with when waves reflect at fixed ends.

On the other hand, in the second video, we see that when a wave has an open end, there is no inversion. The wave does not appear to be going both ways. It only seems to be going from Eddy's hand outward. This is because the wave does not invert (although it does get reflected back towards Eddy), since there is no "end" (like Anshul's hand) to invert the wave. Thus, it's clear that waves with open ends reflect but do not invert.

From these findings, we can summarize that waves with fixed ends reflect in an inverted fashion, while waves with open ends reflect without inverting.

3) What happens when waves collide?

To answer this, we first tested destructive interference --

Next, we tested constructive interference --

In the first video, we see something called 'destructive interference' happening when two waves collide. Destructive interference occurs when the waves coming from each side (one from Eddy and one from Anshul) are not aligned, and thus the crest of one wave gets dragged down by the trough of the other wave. The resulting wave has crests that are shorter and troughs that are shallower. This is clearly apparent in the video, as we see the waves getting in the way of each other and not producing one harmonious wave. Everything appears to be filled with chaos, because the waves do not perfectly align.

However, in the second video, we see something called 'constructive interference' happening when two waves collide. Constructive interference occurs when the waves from each side are aligned, and thus the crest is equal to the sum of the crests of the waves coming from each side. The same goes for the troughs. This leads to the creation of a wave that is bigger than the original waves. We can very clearly see that in the video, where Anshul synchronizes his hands to produce waves that are perfectly aligned. The crests are much larger, and the troughs much deeper.

Therefore, we see that when waves collide, they can either interfere destructively or constructively.

Conclusion

In all, the physics experiment in Mrs. Roemer's class was extremely educational and allowed us to study the properties of waves as well as the impact that certain factors have on other factors of a wave. Through our analysis of videos 1 and 2, we determined that although it appears that amplitude and frequency affect the velocity of a wave, in reality, these factors don't. Other factors such as force are the ones that affect the velocity of a wave. Additionally, by analyzing videos 3 and 4, we saw that waves reflect inversely when they hit a fixed end, and reflect without inversion at an open end. Finally, in videos 5 and 6, we evaluated that when waves collide, they either interfere destructively (in which the crests and troughs are shortened) or constructively (in which the crests and troughs are increased). By using qualitative analysis, observations, and formulas, we were successfully able to come to our conclusions regarding the properties of waves.

Because this experiment did not involve any quantitative calculations, our scientific error was most likely extremely small. There was some error (for example, when we were figuring out whether f affected v) that caused problems, but through using formulas and analysis, we were able to identify our errors and account for them. Error could have occurred while we were shaking the slinkies, as we might have changed more factors than just the ones we intended to (for example, when trying to change frequency, we also changed force). Thus, while scientific error did exist, it was largely minimal.

If we were to do this experiment again, we would try using a larger slinky to magnify our results and make them more clear. Additionally, we could try using other mediums aside from a slinky to see whether velocity and other factors of the wave would change.