AP Physics Lab Guide Labs consist of 40% of your grade You will usually have 2-3 labs per quarter Sometimes labs will be repeated using a different procedure to increase accuracy A lab group consists of 3-4 people, unless it is a partner lab Lab reports usually have to be typed Each person is responsible for writing their own lab report (you cannot turn in one for the whole group) unless otherwise stated Each Lab Report must have the following components: 1) Cover Page- The cover page must have the title of the lab, the date, and your name on it. Your lab partners’ names must be in parentheses underneath your name as well 2) Abstract- The abstract must give a basic overview of the lab. It must briefly explain what the experiment is designed to do and how you did it (not in great detail, though). A basic summary of your findings must also be included. The abstract should not be more than one paragraph long A example of an abstract This experiment is designed to prove whether or not momentum is conserved in explosions. The experiment was conducted with a frictionless track, two frictionless carts, and two photogates. Two mass scenarios were used for the explosion portion of the lab. Mass scenario one consisted of cart 1 having a mass of .50641 kg and cart 2 having a mass of .50613 kg. Mass scenario two consisted of cart 1 having a mass of 1.01042 kg and cart 2 having a mass of .50613 kg. These different mass scenarios are intended to prove that momentum is conserved no matter what the combination of masses of the carts is. For the explosion portion of the lab, the initial momentum was 0 kgm/s for both masses because they were both stationary. The lab proved that mass was conserved in both mass scenarios of the explosion portion of the lab because in both scenarios, final momentum was also 0 kgm/s. This is because the carts’ momentums were in opposite directions and cancelled each other out. C example of an abstract This experiment was designed to show whether or not momentum was conserved. After running the carts on a frictionless track, it was decided that momentum was actually conserved. We conducted explosions. We used carts of different masses. For the most part, the lab showed that momentum was conserved. 3) Introduction- The introduction must state what the intention of the lab is. This should be a very short paragraph. A+ Example of an Intro This lab was designed to show that momentum is conserved in explosions. This entire lab was driven by the theory that, in a closed system, momentum of the system before would be equal to the momentum after an explosion. The explosions in C Example of an Intro This lab was intended to show whether or not momentum is conserved. this lab were perfectly inelastic. The momentum equation used in this lab was P = mv. This lab was thus designed to show that the momentum of the entire system before the explosion was in fact equal to the momentum of the system after, thus proving the law of conservation of momentum. 4) Procedure- The procedure must be written in paragraph form. It must be a very detailed account of how you completed the lab. It must include the equipment that you used and how you used it. You should also include which units everything will be measured in. This should be approximately a paragraph long and should include enough detail that someone should be able to complete the lab exactly how you did. A+ Example of a Procedure Two carts were placed on a frictionless track. The way the carts are made allows one to attach them together by magnets. There is also a small button on top of one of the carts. Upon pressing the button, a small piece of metal protrudes from one of the carts at the point where they are attached. This button was effectively an “explosion button” because pressing it would cause the two carts to be propelled in opposite directions. Initial momentum was known because the carts started at rest and were stuck together. Thus, initial momentum was zero kgm/s because the velocity of the initial system was zero. Two photogates were placed on the frictionless track at an equal distance from the origin (where the carts were initially at rest). These photogates were used to help calculate the velocity of both carts after the explosion occurred. The photogates measured the time it took an index card that protruded from the top of each cart to pass through the gate. Since photogates were placed at both ends of the track, it is possible to calculate the final velocity for both carts. The final velocity can be calculated by dividing the length of the card by the time it took that card to pass through its respective photogate. Each card was the same length on each cart in order to maintain some consistency. Three trials were conducted with just the mass of the carts themselves. In order to be more thorough, a second set of trials was conducted with an additional mass added to one of the carts (see “results” below for specific mass scenarios). Also, it is important to note that the carts moved in opposite directions after the explosion occurred, meaning that one velocity must be considered negative in calculating final momentum. C Example of a Procedure Two carts were stuck on a frictionless track. Then an explosion occurred between the two carts and they went in opposite directions. The carts were at rest initially, but after the explosion they weren’t. A photogate was used to measure how long it took the carts to travel to the photogate. This was later used to calculate velocity. 5) Results- This section should include all data tables that you have. Data tables should include all data collected and the units should be accurate. This section should also include any necessary explanations required to fully understand what data was collected. This section should not just be filled with data tables, but should also include the occasional sentence or two of explanation (ex: if the initial velocity of a cart is zero, you should explain that that’s because all trials started at rest). This section is also intended to have all calculations needed. There should be one sample calculation for each calculation you completed. Sample calculations should show all steps in the calculation and should include units at all points (not just in the final answer). There should also be a table that includes all your calculated data as well. This section can be very lengthy if the lab required numerous calculations, or it can be short if the lab wasn’t too calculation-heavy. A+ Example of a Results Section Collected Explosion Data Total Mass Time for Cart 1 to Pass Through Photogate 1 Cart 1 Trial 1 Trial 2 Trial 3 Average .22786 s .23327 s .25945 s .24019 s .51976 s .43419 s .51599 s .48665 s Total Mass Cart 2 Time for Cart 2 to Pass Through Photogate 2 Trial 1 .32828 s .21952 s Trial 2 .27533 s .22365 s Trial 3 .26732 s .22499 s Average .29031 s .22272 s Explosion Velocity Sample Calculation: It should be noted that since the carts started at rest, their initial velocity is zero m/s. The carts final velocities (as an average) can be calculated by dividing the length of the index card (which was .126 m long) by the time it took that card to travel through the photo gate. The sample calculation below is for the final velocity of Cart 1 with its first mass scenario (no added weight). Also, Cart 2’s velocity is in the negative direction because it travels in a direction opposite to that of Cart 1. 𝑣𝑓 = .126 𝑚 .24019 𝑠 = .52459 𝑚/𝑠 Explosion Velocity Calculation Table: Cart Cart 1 (initial mass scenario) Cart 2 (initial mass scenario) Cart 1 (second mass scenario) Cart 2 (second mass scenario) Initial Velocity 0 m/s 0 m/s 0 m/s 0 m/s Final Velocity .52459 m/s -.43402 m/s .25891 m/s -.56557 m/s *it should be noted that the term “initial mass scenario” means the first three trials of each cart before the masses were changed. Initial mass scenario means the trials in which mass of cart 1 = .50641 kg and the mass of cart 2 =.50613 kg. Second mass scenario means when the mass of cart 1 = 1.01042 kg and the mass of cart 2 remains unchanged. Explosion Momentum Sample Calculation: The formula used for all momentum calculations is p=mv, where p is momentum, m is mass of the object (in kilograms) and v is velocity (in m/s). Momentum calculations in this lab are designed to prove that momentum is in fact conserved. Thus, momentum of the system before and after the explosion will be calculated. If momentum truly is conserved, then the momentum of the system before the explosion should equal the momentum of the system after the explosion. The sample calculations below are for Mass scenario 1 (in which the mass of cart 1 was .50641 kg and the mass of cart 2 was .50613 kg) 𝑚 𝑚 𝑘𝑔𝑚 𝑃𝑜 = (. 50641 𝑘𝑔) (0 ) + (. 50613 𝑘𝑔) (0 ) = 0 𝑠 𝑠 𝑠 𝑚 𝑚 𝑘𝑔𝑚 𝑃𝑓 = (. 50641 𝑘𝑔) (. 52459 ) + (. 50613) (−.43402 ) = 0 𝑠 𝑠 𝑠 Thus momentum is conserved because the momentum of the system before the explosion is equivalent to the momentum of the system after the explosion. Calculations for Mass Scenario 2 (in which cart 1 = 1.01042 kg and Cart 2= .50613 kg) 𝑚 𝑚 𝑘𝑔𝑚 ) + (. 50613 𝑘𝑔) (0 ) = 0 𝑠 𝑠 𝑠 𝑚 𝑚 𝑘𝑔𝑚 𝑃𝑓 = (1.01042 𝑘𝑔) (. 25891 ) + (. 50613) (−.56557 ) = 0 𝑠 𝑠 𝑠 𝑃𝑜 = (1.01042 𝑘𝑔) (0 Summary Table: Mass Scenario 1 2 Initial Momentum 0 kgm/s 0 kgm/s Final Momentum 0 kgm/s 0 kgm/s Momentum Conserved? Yes Yes C Example of Results Section Data: Collected Explosion Data Trial 1 .22786 .51976 Trial 2 .23327 .43419 Trial 3 .25945 .51599 Trial 1 .32828 .21952 Trial 2 .27533 .22365 Trial 3 .26732 .22499 calculation: 𝑣= . 126 = .5 . 24019 calculation table: Cart Initial Velocity 0 0 0 0 Cart 1 Cart 2 Cart 1 Cart 2 Final Velocity .52 -.43 .25 -.56 Explosion Momentum Sample Calculation: 𝑃 = (. 50641 )(0) + (. 5)(0) = 0 𝑃 = (. 50641 )(. 52) + (. 506)(−.43) = 0 Momentum is clearly conserved. 6) Discussion and Conclusion- This is the final section of the lab and should be the place where you wrap everything up. You should talk about your data; discuss any and all trends you discovered. This is also where you should talk about errors. Errors can be classified as systematic or random, and you should include possible solutions to correct this error. Overall, your discussion and conclusion section should talk about whether your data supported what you were trying to find. You should always include data in this section. If your data supports what you expected, make sure you include a few examples of your data that support this (ex: if you thought that momentum would be conserved and it was, include some data from a trial in which it was clearly conserved). This section should be 1-2 paragraphs long and should be as detailed as you can possibly make it. A+ Example of Discussion and Conclusion The explosion experiment proves that momentum is conserved during a closed system of an explosion. In the first mass scenario (in which cart 1 had a mass of .50641 kg and cart 2 had a mass of .50613 kg), the momentum before the explosion was 0 kgm/s. The momentum of the system after the explosion was also 0 kgm/s. This is because the explosion caused the two carts to travel in opposite directions. The two carts’ momentums cancelled each other out because they were travelling in opposite directions, thus resulting in a final momentum of zero. This means that momentum was conserved. When an additional weight was added to cart 1 (in the second mass scenario), momentum was also conserved. The initial momentum of this explosion was zero, because both carts started at rest. Again, the momentum after the explosion ended up cancelling each other out. The cart with the larger mass traveled with a smaller velocity. The cart with the smaller mass traveled with a greater velocity. Thus, these equaled the same momentum in opposite direction because the equation for momentum is p=mv Possible sources of error in this lab include the fact that the “frictionless” tracks could not possibly be frictionless. The track that was used was dusty (which is one of the more visible signs of friction present). Also, it’s very hard to develop a truly frictionless surface. Although the track may have been very smooth; it must have still possessed friction. This could have skewed the data in a systematic manner, as it would cause the velocities of the carts to be lower than their theoretical values. Unfortunately, this is an error that cannot be feasibly solved, as perfectly frictionless tracks do not exist. Another source of error was the fact that two different photogates had to be used each time. It’s impossible to tell whether or not each photogate had the same reaction timing. One may have been less calibrated than the other. This would be a random error. This error could be solved by using checking that both photogates are equally sensitive by running controls through them and seeing if both show the same time value. Another source of error in this lab would be environmental conditions. There could have been randomly generated gusts of winds from the air conditioning units. This would cause a random error. The only solution to this error would be to conduct the lab in a vacuum free of environmental errors. Unfortunately, this would be impossible to do because the people conducting the experiments would probably asphyxiate. Another source of error is air resistance. Air resistance is not taken into account in these momentum calculations. Air resistance would be a systematic error because it would cause the velocities of the carts to be less than they theoretically should be. Again, the only proper solution to this (other than calculating air resistance and taking that into account) would be to conduct the experiment in a vacuum. C Example of Discussion and Conclusion This experiment proved that momentum was conserved in explosions. Momentum was the same before and after the explosion. Different masses were used on the carts and momentum was still conserved. See calculation section for proof of this. We used p=mv. There was probably some error in this lab. Sources of error include human error and dust on the track. Human error cannot be fixed. Another error was probably air resistance. Overall this lab confirmed that momentum is conserved in explosions.