Conservation of Momentum: Crash Lessons

Purpose:

To show and prove the conservation of momentum:  For a collision occurring between two objects, the total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision. That is, the momentum lost by one object is equal to the momentum gained by the other object.

Background:

Momentum is a physical quantity that determines the motion of a moving object. In effect, momentum measures how hard it is to stop a particular object’s motion. For example, it is easier to stop a fly moving at 6 m/h than a car moving at the same speed. However, it is easier to stop a car moving at 6 m/h than a car moving at 60 m/h. These examples illustrate momentum and the factors upon which it depends, that is velocity and mass. The momentum of an object at any given time is equal to:

p=mv

In addition to the above, momentum is a vector quantity, which means it has a direction (right, left, up, down, etc).

What we have said so far , though, applies for one object only. As we have been taught from countless movies and T.V. shows is that objects are meant to collide. Following a similar trace of thinking Physicists found the so-called law of conservation of momentum. This law states that in a given system, the total momentum of the system remains the same unless a force is applied in the system. For instance, let’s say we have two cars on two ends of a road and the one is moving at a speed of 10 m/h towards the other car, which is stationary (v=0 m/h). Before the collision takes place we can calculate the total momentum of the system, which will be equal to the sum of the two momenta of the cars. If both cars weigh 1000 pounds, then

p_a=m_av_a=1000*10=10000 kg*m*h^-1 and

p_b=m_bv_b=1000*0=0kg*m*h^-1

So the total momentum of the system before the collision is

Totalp_i=p_a+p_b =10000+0=10000 kg*m*h^-1.

Let’s say that when the two cars collide, both of them are moving with a velocity of 5m/h. If we repeat the calculations for the system then we will see that

p_a=m_av_a =1000*5=5000 kg*m*h^-1 and

p_b=m_bv_b =1000*5=5000 kg*m*h^-1 . Then the total momentum of the system after the collision is

Totalp_f=p_a+p_b =5000 +5000=10000.

 

Therefore, we can see that the momentum of the system did not change after the collision. From the above formula we can derive the velocity of an object after a collision, or the mass of an object, or anything that is relevant for that matter. In our experiments we tried to prove the law of the conservation of momentum when two carts are colliding. We calculated the total momentum of a system before a collision and after it and determined whether the momentum of the system remained the same or not, thus (hopefully)proving or disproving the law of conservation of momentum.

Procedure:

Setup: For this experiment you will need the following materials: Horizontal car ramp, two toy cars, masses, nxt processor, and motion sensors.

Data collection: Set up the horizontal car ramp and motion sensors (there should be two sensors on each end of the ramp). Measure the mass of each cart. Each sensor should record the velocity of a cart. Place a cart in the middle of the ramp and place a cart at the end of the ramp. One person should be in charge of pushing the cars for the collision and the other two should be responsible for starting and stopping the motion sensors. Once everyone is ready, push the cart at the beginning of the ramp towards the stationary cart in the middle of the ramp (it doesn’t matter how hard you push it but it is better not to push it very hard because the cars could fly off the track and injure a fellow group member!). When you push it, the member controlling the motion sensor of that end should start recording and right before the carts collide they should stop recording. Then, the second member of the group should initiate the second motion sensor . The computer should have recorded the data and placed it onto an excel file for your group. Repeat the process two more times and then find the average of the velocity measurements. From that you can derive the momenta of the carts before and after the collision. Finally add some masses on one of the carts and do the experiments again. You should do the process with 3 different mass setups and each mass setup should be repeated thrice, adding up to a total of 9 experiments.

Theoretical: Using the NXT software find the momentum of the system before the collision. The momentum of the system after the collision should be equal to the one before the collision, so use that as a measuring device.

Data:

When we carried out the experiment we collected the data below:

Sensor at the End					Sensor at the Start
Mass1=500 Mass2= 900					Mass1=500 Mass2= 900
	Velocity	Momentum	Experiment Number			Velocity	Momentum	Experiment Number
	-6.349206	-8.518517933	1			24.25107	11.303302	1
	-5.494505					23.206751
	-6.410256					20.361991
average	-6.084655667				Average	22.606604
Mass1=500 and Mass2=500					Mass1=500 and Mass2=500
	Velocity	Momentum	Experiment Number			Velocity	Momentum	Experiment Number
	-10.50175	-13.1795	2			17.507	13.8303165	2
	-12.820513					27.431421
	-16.216216					38.043478
average	-13.179493				Average	27.660633
Mass1=900 Mass2=500					Mass1=900 Mass2=500
	Velocity	Momentum	Experiment Number			Velocity	Momentum	Experiment Number
	-11.71459	-20.84826567	3			22.072937	26.1902565	3
	-15.011547					28.53067
	-17.948718					36.697248
average	-14.89161833				Average	29.100285

 

 

 

 

 

 

 

 

 

 

 

 

Then we calculated the absolute momentum for both motion sensor measurements and for all experiments to produce the table below. Three columns make up the chart; the first column, is meant to represent the results of the absolute momentum after the carts collisions. The second column’s data represents the absolute momentum before the collisions. And the last column, connotes what experiment was repeated (1,2 or 3):

After obtaining our data, the group decided to graph the numbers in order to get a visual representation of the absolute momentum collisions. The graph below  shows both data collisions in the same graph, and it’s easier to grasp the similarity of the curves that are given. This similarity in the curves tell us that momentum was conserved but the existence of errors made it impossible to produce identical curves.

Analysis:

Does the experiment prove the conservation of momentum theory?

From our data we can see that the momentum of the two sides is almost the same, which points to the fact that momentum is conserved.

What variables could have skewed the results collected?

In our case friction was the primary source of error. due to the fact that we used a track, when the cars collide they have twice the amount of fiction they have when they are on their own. Therefore, there is an external force acting on the system which is why momentum is not conserved.

How does mass affect the results?

When the two carts collide, they stick together. When that happens their masses are added. As a result the force of gravity, which is the product of mass and acceleration increases. Therefore, the force acting on the system is greater than before, thus skewing our results.

Can you suggest things that might improve the experiment or the accuracy of the results?

If we used a frictionless track, there would be no external force acting on the system, so we would get the results we expected.

 

Conclusion:

In our hypothesis we expected momentum to be conserved. The experiments we conducted showed a pattern that indicates to the fact that momentum is conserved. Even though the existence of friction skews our results, we can still see why and how momentum is conserved.

Experiences:

Anestis Luarasis:

I believe that the experiments we conducted were successful, and they showed that momentum was conserved. The team cooperated adequately and were highly productive. If there was one thing i would  change it would be the track. Otherwise everything was fine.

Nurta Ibrahim:

I loved all my team members they all took the time to put this wonderful experiment together. They even took their own time out to work on the blogs and doing the whole experiment. I couldn’t have asked for better members than the ones i have worked with. The only issue was that the data was skewed due to the existence of friction from the track.

Darwin Huang:

Overall this project was a great experience for me. I made new friends and even learned something new. The members in the group were never mean and we had lots of fun when we were devising our outline and plan. One thing i would change about the project is get a frictionless track because it complicated our project results by a pretty big factor. Otherwise it was great.

Cristian Koch :

This project was a great opportunity for working as a team. Over the last few weeks the members and I worked hard and managed to accomplish a successful experiment. The experiment had me learn about the physical quantity that determines the motion of a moving object, momentum. I can conclude that the experiment was a success and not only had it taught me new things but also improved my work ethics with others.

Ramon Morales Pozo:

This was a very interesting experiment. We proved the conservation of momentum, and we found a way to prove it which I find was very creative and informative at the same time. Overall, I enjoyed the project, and I was glad to have such good teammates.

 

What is it?

Throughout the day we constantly use electricity. From turning on the lights to using the microwave oven, we continuously consume electricity. It is understable that during some periods our demand for electricity increases. For instance, in the summer we usually consume more electricity due to the fact that the temperature is high and we use air conditioners all day. These periods that electricity consumption reaches a peak are called peak usage times. The past years though our demand for electricity has grown larger and according to the Energy Information Administration it will increase by 40% by 2030. In order to limit our demand some programs called Demand Response programs have been created. These programs allow the users(us) to voluntarily decrease energy consumption during times that electricity cost is high(peak usage times). As a result of this we can both save money and electricity.

 

 

Implications:

 

The United States release approximately 150 million tons of carbon dioxide in the atmosphere for electricity generating purposes(source U.S. Department of Energy). By using demand response programs, the amount of energy needed to be produced will be less, hence the release of pollutants and greenhouse gasses will reduce as well.

”In a yearlong, small-scale study in homes on the Olympic Peninsula in Washington, the Department of Energy (DOE) found that when consumers were equipped with     smart electric meters, thermostats, water heaters and dryers, they reduced their energy usage and associated costs — on average, participants saved 10 percent on their electricity bills, and there was a 15 percent reduction in peak load usage”

The quotation above from howstuffworks.com indicates that we would use approximately 15% less energy in peak times. This means that we would avoid releasing millions of greenhouse gasses to the atmosphere if we adopted demand response programs.

Important Note:

One of the most promising concepts surrounding demand response programs is that of smart houses. In this concept houses are equipped with direct response energy, which is a system that constantly regulates the amount of energy used in various time-periods. For instance, direct response will decide to produce less energy during peak hours(when the price of electricity is high) and turn off appliances such as the thermostat, or the washing machine to save money and energy. This automatic power control used in direct response energy is used in smart houses, that use a smart grid which ” has  a web of access points that could be identified and contacted. Through these contact points, the grid would automate the flow of electricity as needed, identify and isolate load problems.”(source How Stuff Works.com)

In conclusion:

It seems to be that demand response is one of the most intriguing and lucrative new technologies right now. Not only can it help us save money-a fact that is even more appreciated in our times of economic crises-but it can also help us lower our greenhouse emmisions considerably. It is a win-win situation that we must not turn our back to.

Approximately six months ago the entire world was holding its breath over one of the most dangerous contemporary disasters, the Fukushima Daichi Nuclear Plant Disaster. A massive eathquake of magnitude 9.0 richter degrees, set off a tsunami which hit the eastern coast of japan and obliterated everything in its way. Amongst of the victims of the tsunami was the Fukushima Nuclear Plant.

Basics First:

Before an analysis of the events that unfolded is provided, i think it would be better to provide a short description of how nuclear plants work in order achieve a better understanding of the problem.

The main premise of a nuclear reactor is quite similar to that of the typical coal-burning power plants, with the main idea being the heating of water into pressurized steam that drives a turbine generator. The difference between the two power plants is the way that water is heated. In a nuclear plant, water is heated through the use of nuclear fission in which one atom splits into two and releases energy. In a nuclear plant that is achieved by firing a neutron on a uranium-235 atom, which then splits into two atoms while releasing heat and gamma radiation(radiation from high-energy photons). The uranium-235 atoms are all stored in fuel rods that are assembled together and form bundles of fuel rods that emit heat. However, for us  to harnest the vast amounts of energy released, a mechanism is required to control the flow of energy and limit it to desirable levels. In the nuclear plant, this mechanism is  found in the use of control rods. Control rods are specifically designed rods that can absorb neutrons and help avoid overheating. These rods can be raised and lowered to absorb less and more neutrons respectively. If raised, less neutrons will be absorbed which means that more energy will be released. The controlled release of energy,then, heats water and turns it into steam, which,in turn, drives a turnine, that is connected to a generator, thus producing energy that we can use. (This is a basic description of the way nuclear power plants work. For further details, allude to http://www.popsci.com/science/article/2011-03/whats-happening-japans-nuclear-power-plants).

 

What Went Wrong:

In the video posted above, you will find a simpe experiment conducted by nuclear engineer Arnie Gundersen that serves as a representation of the way Fukushima’s fuel rods melted and shattered, which led to the spill of radioactive Uranium.

Implications:

The radioactive material that leaked in Japan from the Fukushima Nuclear Plant had grave implications for Japan. Firstly, the area around fukushima was evacuated immediately and Japan’s prime minister Naoto Kan was quoted saying “I can’t deny the possibility that it could be a long time before people can return to and live in regions with high radiation levels,”. Furthermore, ”in a meeting with local officials on Saturday, the government estimated it could take more than 20 years before residents could safely return to areas with current radiation readings of 200 millisieverts per year, and a decade for areas at 100 millisieverts per year.”(quotation by http://www.reuters.com/article/2011/08/27/us-japan-nuclear-uninhabitable-idUSTRE77Q17U20110827). The above information seems to verify that people that lived in or near those areas will not be able to return home for a long time.

Also, the leak of radioactive material has polluted the Pacific ocean, the soil and the air near the power plants. It was announced by Japanese authorities that in March 2011,  “radioactive iodine-131 exceeding safety limits for infants had been detected at 18 water-purification plants in Tokyo and five other prefectures”, thus indicating to a water contamination in Japan. In addition to this, an article in the New York Times reported ” radiation that exceeds safety levels has been detected in tea, milk, fish, beef and other foods produced outside that zone, and as far as 200 miles from the plant.”. Furthermore, Japan also imposed a ban on beef from Fukushima and nearby prefectures, due to traces of radioactive cesium being detected in meat samples. The above facts prove that radioactive material has escaped into Japan’s natural resources, which makes them a danger for the health of Japanese people as well as Japanese fauna(a more detailed analysis of the disaster on animals and the environment can be found in an article by the Scientific American located here; http://blogs.scientificamerican.com/guest-blog/2011/03/22/impact-of-the-japan-earthquake-and-tsunami-on-animals-and-environment)/. It was reported that radioactive waste was spilled in the Pacific Ocean which additionally endangers aquatic animals nearby. A considerable effect of the above is that Japan’s credibility and commerce have been facing a steep decline, thus increasing the financial burden that Japan has to bear. It seems, therefore, that the nuclear meltdown in Fukushima, had severe implications for Japan that could turn out to be condemning for Japan’s natives, economy and ecosystem. If the results of such disasters are as unbearable as they are made out to be, why do we still invest in nuclear power, when the risks associated with it are so grave?

Reflection Time:

Japan will have to spend approximately 300 billion dollars to eradicate the results of the Fukushima nuclear plant disaster and at the same time the damage to Japan’s ecosystem cannot be undone. Apparently the risks of running a nuclear plant are high, (even when compared to the vast amounts of energy produced by nuclear plants) and Japan’s disaster underlined the gravity of the situation, which seems to have taught us a lesson. After, the nuclear disaster, Prime Minister Naoto Kan declared that he wanted to diminish the country’s dependence on nuclear energy, increase safety features and invest in safer alternative sources for energy. His example, has been followed by people all around the world who in light of the disaster, have decided either to reduce nuclear energy dependence or increase safety measures in nuclear plants. Such countries include Germany, Italy, Switzerland, France, India, etc. An elaborate analysis on the effect of the Fukushima disaster on the nuclear industry is provided in the article below; http://spectrum.ieee.org/tech-talk/energy/nuclear/fukushimas-impact-on-nuclear-power. In conclusion, it seems  that Japan has just faced one of the worst disasters in recent history. However, what is left for us now, is to pick up our pieces and think carefully about the consequences of our actions. Nuclear power plants need to be safer before they can be regarded as the future of energy and that can be achieved by further research and investment on them. Noone wants to witness a repeat of what happened in Japan, so maybe it is time to learn from our mistakes, and be patient with this subject.