Question: These equations mathematically explain each scenario and how they differ. The velocity of each itern was determined by the height of the fall (1.5 meters)

These equations mathematically explain each scenario and how they differ. The velocity of each itern was determined by the height of the fall (1.5 meters) and gravity pulling the object toward Earth. Because both the test height and gravity are the same for each item, the velocity for the phone with different cases was consistent across the board. That velocity is then divided by the time it takes the item to fall in order to get the deceleration of the phone with each case. The greater the case's mass, the longer the fall took. When the fall took longer, the acceleration was a smaller number. One can extrapolate that the greater the mass, the smaller the acceleration, or change in velocity over time. The force of the cell phone falling was calculated by multiplying the combined mass of the phone and case by the object's acceleration when falling. Because an object with a higher mass had a significantly lower acceleration, those items also have a smaller force than objects with a lower weight. In other words, since the object is not increasing its velocity at a higher rate, its force is less. If the change in weights were more drastic, the higher mass value might balance out the smaller acceleration value, but the changes in mass are relatively small so this is not the case. In conclusion, the cases that have a greater mass had a lower acceleration and force than those that weighed less. Where there is less force, there is less damage to the item that has fallen because Newton's Laws say that the phone will be met with an equal and opposite force to that with which it falls. Based on these results, we recommend the rubber case as the best option to prevent breaking during falls. The rubber case had the highest mass of all cases, leading to the slowest acceleration and lowest force at -18.1N. This is a significant reduction from the 95.4N of the phone on its own or even the 37.4N of the hard plastic case. Because it has the lowest force, it is best designed to reduce breaks caused by the physical force of being dropped to the ground. That said, it is also the heaviest. If someone is willing to compromise some protection, the next best option would be the silicone case. This will still provide considerable protection but weighs 1.50z less. Overall, we recommend the rubber case for the highest protection level and the silicone case as a lighter alternative
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