Lab 3 - This is lab report #3, Newton\'s Second Law. PDF

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This is lab report #3, Newton's Second Law....

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Introduction: The goal of this lab was to understand the Newton’s 2nd law and to understand how force would be applied and how the mass of the system would affect/determine the acceleration. Also, how using two different methods the acceleration can be obtained leading it have to similar acceleration values. Apparatus: For this lab, air track, two carts with the 10cm flags, pulley and a string was needed. Also, two photogates, computer with the software Pasco interface and Capstone software. In addition, Set of different masses were required. Procedure: Part 1: Setup. ● First step was to position the pulley at the end and hangs over the edge of the table refer to the picture below to set up:

● Set up the photogate, as usual but this time 50 cm apart and align them so that a flag therefore that the cart will be able to pass through the beam and record values. ● Measure the mass of cart(which came out to be 196g) and measure the mass of the hanger (which came out to be 4.71g). ● Attach the pulley to the end of tack and hang the mass hanger and cart over pulley. Part 2: Constant Force, Varying System Mass. ● Plug the photogate and set up the pre-configured timer that includes two photogates and one flag and enter correct flag length. ● One person release the cart and other person catch it before it crash, and record data. ● Make a data in Excel with the data. ● Add 10g to the mass hanger provided the pulling force., Release cart and record five data for five different cart, and have 40g on the cart at the end. ● Copy all data in excel to make graphs. ● Do calculations using method 1 and method 2 to get the acceleration and then use that information to get gravitational acceleration. Part III: Verifying both force and system mass

● Find the m2/m1+m2 by using data from part II ● use gravitational acceleration and m2/m1+m2 to graph the data for part III. ● Make sure the m1 and m2 is in kg not g Precautions: To make this lab better, human errors could be prevented. Also, the friction between the cart and the surface could be minimized. etc. Source of Errors: Source of errors for this lab would be human error, errors in measurement, and force/air resistance because the acceleration is lower than the ideal. Also, it could be error in the system or set up of the lab, it can not be 100% correct. Data: PartII: Table 1: Cart Weight (g)

Method 1

Method 2

Gravitational Acceleration

196

0.5805

0.5733

2.95

206

0.8316

0.8181

4.39

216

0.1515

0.1829

1.02

226

0.0575

0.0694

0.402

236

0.3335

0.3709

2.22

Part III: Table 2: Acceleration

m2/(m1+m2)

2.95

0.1937

4.39

0.1861

1.02

0.1790

0.402

0.1725

2.22

0.1663

Calculations: Two methods were used in order to find the acceleration. The sample calculation using first method: Vf2 -Vi2 =2ax 0.892 -0.462 =2a(0.5) 0.5805=1a a=0.5805m/s The sample calculation using second method: V f −V i = 0.5733 m/s = 0.89−0.46 t 0.75 Gravitational Acceleration:

a=

m2 m1+m2 g

0.5733 = g=2.95

0.0471 0.196+0.0471 g

Questions: 1. Does one of the two methods give a more accurate value for? Hypothesize as to why this might be (there is no single correct answer here). Using the second method give a more accurate value for g because the equation vf^2-vi^2=2ax, the velocity is squared and any error in the velocity measurement gets squared too leading us to grow mistakes, with the other method (vf-vi/t) the vf is linear which gives precise answers. Also, it would measure the time precisely and we are limited to the precision of ruler to measure the distances and that is why vf-vi/t) works better than the other method. 2. According to the two different calculations of average velocity, does the system appear to be undergoing constant acceleration? Briefly explain. According to two different calculations of average velocity, the system appear to be undergoing constant acceleration to a good approximation because while using the two different methods almost same results were obtained which confirms that the acceleration was constant throughout the experiment. 3. From your graph what is the trend for how the acceleration changes as the system gets more and more massive? Is this consistent with Newton’s Second Law. According to the newton’s second law the f=ma therefore a=f/m and it tells us that as mass increase the acceleration decreases and in our case this was not happening due to the source of errors. 4. If you look closely at the graph, you will see it asymptotically approaches zero acceleration. Does this mean there will still be nonzero acceleration for extremely large system mass? There will still be nonzero acceleration for extremely large mass system mass because the acceleration becomes smaller and smaller as the total mass gets bigger, a very large mass would still move just that it would be accelerating very slowly. We would need to put infinite amount of mass theoretically in order to have a static cart. Therefore it would have non zero acceleration, because no matter how big the mass is since we can not put infinite amount of mass. 5. Theoretically, what should the y-intercept be for your graph in Part III? Explain. The y intercept should be 0 for the graph in Part III because if there is no hanging mass to accelerate the system, then there would be no net force, which does not make sense therefore y intercept has to be zero.

6. Make a prediction: if we were able to keep adding mass to the mass hanger, would we eventually reach a maximum for the acceleration? What did you predict would occur? No, the maximum acceleration can not be reached because when the mass values increases the acceleration also increases until it gets to a point where it would just level off at free fall acceleration, basically it would fall if there is no other mass involved. Results and Discussion: This lab was done to understand the Newton’s second law and understand how acceleration can be found by using two different methods and get similar answers, in the data above the two methods that were used the results came out to be almost close to each other this could be due to the photogate, and then the second method was used to find the gravitational acceleration by plugging in either method 1 or method 2. Looking and the graphs, our graph for part II seems somewhat off then what was expected the expected was that the graph would go down and that can be seen in our graph and we get negative slope -11.306 and the grah for part III was not even close to what was expected because the slope of the graph is 0.0038 which is way off then what was expected. The expected was that the graph would increase and that can be seen in our graph but overall both of the graphs we obtained are not 100% accurate due to sources of errors....