E104 Newtons Second Law of Motion free essay sample

The experiment that was conducted was primarily about Newton’s second law of motion. Newton’s second law of motion states that a net force is required for a body to have acceleration. If a net force is applied on an object, then the object will accelerate with respect to the direction of the said force. The body’s acceleration is directly proportional to the net force and inversely proportional to its mass. The experiment conducted was used to verify the relationships specified in Newton’s second law of motion. There were 3 trials, and these were. Constant Mass, Varying Net Force B. Varying Mass, Constant Net Force C. Varying Mass, Varying Net Force In the said experiment, the formula used for the calculation of the experimental acceleration was: As for the accepted value, the formula used was: For the first trial, the net force changes when the mass of the mass hanger changes. The net force, N, is obtained by the equation of m2g, where m2 represents the hanging mass, and g is the constant gravitational pull, which is 9. 8m/s2. The results of part A can be seen in the table below. Mass of cart, m1 = 0.51kg Distance traveled, s = 0. 5m TRIAL m2 Net force, Accepted acceleration Time of travel Experimental acceleration % ERROR 1 0. 02kg 0. 19N 0. 36m/s2 1. 50s 0. 44 m/s2 22. 22% 2 0. 04kg 0. 39N 0. 71 m/s2 1. 06s 0. 89 m/s2 25. 35% 3 0. 06kg 0. 58N 1. 05 m/s2 0. 88s 1. 29 m/s2 22. 86% 4 0. 08kg 0. 78N 1. 32 m/s2 0. 72s 1. 92 m/s2 45. 45% 5 0. 10kg 0. 97N 1. 59 m/s2 0. 67s 2. 28 m/s2 43. 40% Figure A: The setup for Constant Mass – Varying Net Force There was a large factor between the accepted acceleration and the experimental acceleration. This was because in the experimental acceleration, the factors used were only the time of travel, t, and the distance s, which is the distance traversed by the cart, which were concepts of kinematics. As a commonly known and used example in the concept of kinematics, a rock drops to the ground in the same rate as a piece of paper; however, this is assuming that the rock and paper are placed inside a vacuumed tube without any air. In the said scenario, the forces pulling the objects downward would be equal; hence the objects would arrive at the ground at the same time. In the accepted acceleration, the formula used also considered the hanging mass, m2, not just the given acceleration due to gravity. The reason as to why there is a considerably large margin between the two accelerations will be explained later on. Based on the data, it can then be said that the net force is directly proportional to the acceleration. For the second trial, the constant term is the net force, which means that the hanging mass is also constant. N is again represented by m2g; the results of the second part of the experiment can be seen below. There were increments of 0. 1kg per trial, and the total hanging mass was 0. 1kg. Total hanging mass, m2 = 0. 1kg Net Force, m ­2 ­g = 0. 98N Distance traveled, s = 0. 5m TRIAL Total mass of cart, m1 Accepted acceleration Time of travel Experimental acceleration % ERROR 1 0. 51kg 1. 92m/s2 0. 62s 2. 60 m/s2 35. 42% 2 0. 61 kg 1. 61 m/s2 0. 67s 2. 23 m/s2 38. 51% 3 0. 71 kg 1. 38 m/s2 0. 74s 1. 83 m/s2 32. 61% 4 0. 81 kg 1. 21 m/s2 0. 77s 1. 69 m/s2 39. 67% 5 0. 91 kg 1. 08 m/s2 0. 81s 1. 52 m/s2 40. 74% Figure B: The setup for Varying Mass – Constant Net Force Similar to the first experiment, there was a relatively large margin with the experimental and accepted acceleration. In this part, the acceleration kept decreasing as the mass of the cart increased. This additional mass acts as a counteractive force to the force that is pulling it down, which is gravity. Since the counteractive force got stronger as the weight increased, while the acceleration due to gravity remains the same, the force that pulls it down is weaker due to the counteractive forces. A good analysis of this would be the usage of vectors and scalars; in the concept of vectors, if one traverses a distance of x N of E, and again, traverses a distance of y in the direction S of W. The displacement would be either N of E or S of W, depending on the magnitude of the said vectors. In the same way, since the force pulling downwards is stronger, the cart would be pulled in the direction of the mass, and in the same way, the acceleration decreases as the cart gets heavier. From this, it can be said that the mass is inversely proportional to the acceleration. As for the last trial, both the mass and the net force varied. The only factor constant in the second experiment is the distance. The results can be seen in the table below. Distance traveled, s = 0. 5m TRIAL m1 m2 m2g a (accepted) t a (experim. ) % ERROR 1 0. 51kg 0. 02 kg 0. 19N 0. 36m/s2 1. 5s 0. 44 m/s2 22. 22% 2 0. 61 kg 0. 04 kg 0. 39N 0. 60 m/s2 1. 09s 0. 84 m/s2 40. 00% 3 0. 71 kg 0. 06 kg 0. 58N 0. 75 m/s2 0. 94s 1. 13 m/s2 50. 67% 4 0. 81 kg 0. 08 kg 0. 78N 0. 88 m/s2 0. 87s 1. 32 m/s2 43. 12% 5 0. 91 kg 0. 10 kg 0. 97N 0. 96 m/s2 0. 82s 1. 49 m/s2 55. 21% The setup for Varying Mass – Varying Net Force In the final part of the experiment, there was still a relatively large margin of error. In this part, the acceleration still went up even if the mass that was being added on the cart was relatively larger than the hanging mass (20 times the hanging mass = cart’s additional mass). Again, the reason why the cart is getting pulled even with a considerable weight advantage is because of the concept of gravity. As it has been stated earlier, since the relationship of acceleration to mass and net force can be represented with: The said equation is Newton’s second law of motion; k is a constant in the said equation. The reason why there was a considerably large margin of error may be due to the fact that the distance used was only 0. 5m. Should the trial have gone any longer, and the results might have been toned down to as little as 10% error since the computations could have been more accurate with a prolonged test run on each trial. Additionally, the mass of the picket fence was not taken into consideration in the calculations. The string’s mass is considered negligible in this scenario. The rest of the possibilities lie on human error – the track’s movement, the photo gates’ movement, is a few good examples of the possible human errors. The group noticed the displacement of the dynamics track from the beginning of the experiment (aligned the edge with the table) and the end of the experiment (a few millimeters away from the table). The photo gates also sometimes when the track moved as well. Lastly, another major factor to consider is the fact that the cart might not have been aligned exactly to get an initial velocity of 0. E104 was concentrated on the analysis and application of Newton’s second law of motion. The group had successfully done all three parts of the said experiment, albeit with a large percentage error. The errors were factors that could have been altered, but were also factors too tedious to consider. Nevertheless, within the analysis of the said experiment, there was proof of Newton’s second law of motion. In the first part, it was seen that the net force is directly proportional to the acceleration. Additionally, in the second part, it was seen that the mass is inversely proportional to the acceleration. Lastly, in the final part of the experiment, the data gathered from the first two parts of the experiment showed the proof of Newton’s second law of motion. Overall, Newton’s second law of motion is essentially an in-depth version of the concepts of kinematics, where mass and net force is taken into consideration. With the addition of the said factors in the equation, then the results that can be yielded are potentially more mathematically accurate. The experiment has successfully verified the authenticity of the said law of motion.