Group5_6_ch6

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Law of Conservation of Energy Lab
__**Members:**__ Dani Rubenstein (Period 2) and Molly Lambert (Period 6)

__**Objectives:**__ What is the relationship between changes in kinetic energy and changes in gravitational potential energy?
 * 1) If the cart starts at the top of the ramp, what is its speed at the position of the photogate?
 * 2) What is the speed of the ball when it leaves the launcher at short range?
 * 3) What is the speed of the pendulum at the bottom of its path, if released from h = 20 cm?
 * 4) What is the highest point the ball will reach when released from the top of the shorter incline?
 * 5) What is the speed of the ball when vertically launched at short range?
 * 6) What is the speed of the ball at the top of the loop?

__**Hypothesis:**__ The Law of Conservation of Energy states that the amount of initial energy will be equal to the amount of final energy. Knowing this, we can expect our initial energies to be equivalent to our final energies. The law also says that energy can neither be created nor destroyed, however, it can change forms. Our lab is considered to be successful if our calculations for initial and final energies come out to be equal or close.

__**Methods and Materials:**__

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 * Station 1:** We first found the mass of the cart and the diameter of the top black part of the plastic picket fence. Then, we measured the initial and final heights of the cart on the ramp with the meter stick. At the top of the ramp, we released the cart with a plastic picture of a picket fence. The cart then passed through the photogate, giving us the ability to record the time and calculate it's velocity.

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 * Station 2:** We massed the ball and measure the height of the launcher with a meter stick. We then measure the diameter of the ball and placed it into the horizontal launcher at short range. When we shot the ball it went through the photogates, giving us the ability to record the time between the two gates. We then measured the distance between the photogates in order to calculate or velocity.

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 * Station 3:** After massing the wooden cylinder and recording its diameter, we attached it to a string to swing through the photogate. We used a meter stick to first measure the initial heigh of 20 cm above the photogate. We then calculated velocity using the diameter of the cylinder and the time recorded by the photogate.

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 * Station 4:** After massing the ball, we used a meter stick to measure the initial height of the ramp. We then released the metal ball and measured the height it reached on the other side of the ramp, which was used as final height.

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 * Station 5:** We massed and recorded the diameter of the ball and then inserted the ball into a vertical launcher. After setting it to short range, we recorded the time it was in the gate by using a photogate. We also recorded the initial height of the ball and its maximum height, which was the final height.

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 * Station 6:** After first massing and measuring the diameter of the ball, we measured the initial height of the roller coaster ramp. We also recorded the final height, which was at the location of the photogate. Finally, we found the time the ball was in the gate, at the top of the loop, by using the photogate.

__**Data:**__


 * Our Data:**


 * Class Data:**

Data Table for Station One

Data Table for Station Two
 * Groups 1-4 were determined void due to faulty data

Data Table for Station Three

Data Table for Station Four

Data Table for Station Five

Data Table for Station Six

__**Analysis, Sample Calculations, and Percent Differences:**__


 * Sample Calculation for Average: (Average of Class Data, Station Six, Initial Height)**
 * Sample Calculation for Velocity: (Our Data, Station One, Final Velocity)**
 * Analysis of Station One:**
 * Analysis of Station Two:**


 * Analysis of Station Three:**
 * Analysis of Station Four:**
 * Analysis of Station FIve:**


 * Analysis of Station Six:**

Through this analysis, we were able to see that initial energy is in fact equal to final energy. To find the accuracy of our results, we used a percent difference equation. We chose to use percent difference instead of percent error because there was no theoretical value that we were comparing our experimental results to. However, we were finding the difference between two results that were supposed to be equal, therefore, we chose to use percent difference.

By completing this lab, we were able to conclude that our original hypothesis, which stated that the initial energy was going to be equal to the final energy, is correct. Not only did we prove that this hypothesis is correct in one situation, but by completing six different activities we were also able to show that this concept applies to all situations. Also, although some of our percent differences were rather high, this only shows that there must have been sources off error in those situations, because in stations where we received initial and final numbers closer to each other we had the lowest percent differences. For each station, the percent differences (in numerical order) were as follows: 2.54%, 86,4%, 48.9%, 14.15%, 14.18%, and 34.2%. Although two of these stations had very high percent differences, all of the other stations fell within the 20 percent range, proving that overall we had accurate results that were able to prove our hypothesis correct. However, although we received good results, there were clear sources of error that we were able to point out at each station. At a majority of the stations, friction was definitely the main source of error. Although friction was clearly present at most of the stations, we did not consider friction while completing our calculations, therefore leaving out the work component that would have been added to our initial side of the equation. To erase this source of error, we could have used a force sensor to determine the coefficient of friction, along with our prior knowledge, that would allow us to include friction/work into the equation, which evidently would have made our results more precise. Additionally, for stations where friction was not present, such as stations two, three, and five, air resistance caused the same source of error that the stations with friction caused. Also, basic human errors could have caused high percent differences as well. Due to the fact that we had to measure both initial and final heights with just a meter stick or a ruler, we were not able to obtain results that were as precise as possible. To fix this, we could have used a measuring device with more significant figures that would have allowed us to get more accurate results for our measurements. As implied by the experiment, the Law of Conservation of Energy applies to all real life situations. Because we used the same concept at many stations during the lab, we showed that this same concept can be applied in many different instances. For example, station one can be related to a sled going down an incline. At first, it starts up higher and has no kinetic energy, however, by the time it gets to the bottom the amount of energy does not change, only the form of energy does. Station two can be applied to the real life situation of throwing a ball of a tall mountain, and just like in station one, the Law of Conservation proves that the amount of initial energy is equal to the amount of final energy.
 * Conclusion:**

=Ballistic Pendulum Lab=
 * __Members:__** Katie Dooman (Period 6) and Maxx Grunfeld (Period 4)

Objective: What is the initial velocity of a ball fired into a ballistic pendulum?

Hypothesis: The three difference measurement techniques will produce similar initial velocities. The photogate will probably produce the most accurate results, while the LCE technique will probably be a little less accurate since there is only a little energy lost.

Methods and Materials: We tested and measured the initial velocity of the ball fired into the ballistic pendulum in three different ways. The first was measured with a photogate timer. To do this, we connected the photogate to a computer and then calculated how much time it took for the ball to go through it. The photogate timer was put just past the tip of the launcher and was held in a secure position so that it would not move around. We measure the diameter of the ball with a meterstick, and simply found the initial velocity using the equation v=d/t. For kinematics, we used a meterstick to find the height to the ground and the horizontal distance to the ground. the exact points were recorded by carbon paper taped to the floor. Doing projectile kinematics gave us the initial velocity. Finally, we did conservation of energy and momentum, launching the ball into a pendulum that swung up to a certain angle theta, which we measured. We also found the center of mass of the pendulum and calculated the length to the end of it. We then massed the ball and pendulum in order to solve the work-energy and momentum equations. After finishing the calculations, we found that the three initial velocities were all very similar, which holds true to our hypothesis.



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 * __Video:__**


 * __Sample Calculations:__**





Analysis Questions
 * 1) According to your calculations, would it be valid to assume that energy was conserved in that collision?
 * No, we cannot assume that energy is conserved. There is actually energy lost in the collision.
 * First calculate the ratio M/(m+M). Then we can compare this ratio with the ratio calculated in part (b). In theory, these two ratios are expected to be the same.
 * 1) Go to [] Select “Ballistic Pendulum” from the column on the left. What is the effect of increasing the mass of the ball? What is the effect of increasing the pendulum mass? Try it. (NOTE: You have to read “Student Notes” first before you can run the simulation.)
 * An increase of the mass would in turn increase the final height and theta of the pendulum. However, if you increased the mass of the pendulum, it would do the opposite- the height and theta would decrease. This occurs due to the fact that momentum must remain constant, and a higher mass is compensated by lower velocity. Therefore, the height is reduced.
 * 1) Is there a significant difference between the three calculated values of velocity? What factors would increase the difference between these results? How would you build a ballistic pendulum so that momentum method gave better results?
 * 2) No, there is not a significant difference between the calculated values of velocity. For each of the trials, using different methods to calculate the velocity, we were able to get small percent differences. No matter what the case is, the velocity should be consistent from the launcher, which it is. However, if the percent difference was larger, it could be due to factors such as inconsistency of the launcher, poor measurements or not rounding correctly, and a bad photo-gate timer. If we needed to improve the pendulum, we could have a digital reader to measure theta so it is more accurate, as it is fairly easy for someone to misread the measurement. Misreading the angle could lead to bad results, which would then lead to a larger percent difference.