PHY 150 Project Two Case Material Evaluation Report Template

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Southern New Hampshire University *

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150

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Physics

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Apr 3, 2024

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A&L ENGINEERING Case Material Evaluation Report Newton’s Laws of Motion Newton’s first law states: (Inertia) An object at rest remains at rest, and an object in motion remains in motion at constant speed and in a straight line unless acted on by an unbalanced force. Newton’s second law states: The force applied on a body is given by the rate of change of linear momentum of the body. In Math term is looks like this, Momentum is p=m*v, where m is the mass of the body and v is the velocity of the Body. We can calculate force by using the following formula, F=dp/dt=d/dt(m*v) =m(dv/dt)+v(dn/dt) If the mas is constant, we use this formula, where a is the acceleration of the body. F=m(dv/dt)=ma Newton’s third law states: For every action there is an equal and opposite reaction. So, if object A acts as a force upon object B, then object B will exert an opposite yet equal force upon object A. In my analysis of the impact of the mobile phone and cases on the ground, when dropped from a certain height involves the understanding and application of each of the 3 laws of motion. Newton’s laws of motion can be applied to my analysis, when an object is at a height, it poses some energy due to its elevation, and it is called potential energy. As the object is released from its position, it will fall under the influence of gravitational force. Newtons first law state that the object will stay in motion in the same respect if it is not affected by another force. During my testing, I concluded that the external forces working against the object's motion are impact force and air drag. Force Diagrams

A. Phone without a case: The mass of the phone - m = 6.2 oz = 0.175 kg The collision time, t = 0.01s We then apply conservation of energy between the two positions shown in the FBD. That can be calculated by, (Total energy(initial)) = (Total energy(final)) PE +KE= PE + KE mgh + 0 = 1/2mv^2 + 0 V = velocity of the phone before impact mgh = 0.5 * mv^2 v = sqrt (2*9.81 m-s^2 * 1.5 m) v = 5.425 m-s^-1 Deceleration at impact can be calculated as: Vf = v + at Vf is the velocity of the object after the impact which is given zero and a is the deceleration. 0 = 5.425 + 0.01 * a a = -542.5 m-s^-2 B. Phone with a silicon case: The mass of the phone – m1 = 6.2 oz = 0.175 kg The mass of the silicon case – m2 = 1.7 oz = 0.048 kg Total mass – m = m1 + m2 = 0.175 + 0.048 = 0.223 kg The collision time - t = 0.05s Then we apply conservation of energy between the two positions shown in the FBD (Total energy(initial)) = (Total energy(final)) PE +KE = PE + KE mgh + 0 = 1/2mv^2 + 0 mgh = 0.5 * mv^2 v = sqrt 2*9.81 m-s^2 *1.5 m v = 5.425 m-s^-1 The deceleration at impact can be calculated as: Vf = v + at 0 = 5.425 + 0.05 * a a = -108.5 m-s^-2 C. Phone with hard plastic case: The mass of the phone – m1 = 6.2 oz = 0.175 kg The mass of the silicon case – m2 = 1.1 oz = 0.031 kg The total mass – m = m1 + m2 = 0.175 + 0.031 = 0.206 kg The collision time - t = 0.03s Apply conservation of energy between the two positions shown in the FBD

(Total energy(initial)) = (Total energy(final)) PE +KE = PE + KE mgh + 0 = 1/2mv^2 + 0 mgh = 0.5 * mv^2 v = sqrt 2*9.81 m-s^2 *1.5 m v = 5.425 m-s^-1 Deceleration at impact can be calculated as: Vf = v + at 0 = 5.425 + 0.03 * a a = -180.83 m-s^-2 D. Phone with a rubber case: The mass of the phone – m1 = 6.2 oz = 0.175 kg The mass of the silicon case – m2 = 3.2 oz = 0.0907 kg Total mass – m = m1 + m2 = 0.175 + 0.0907 = 0.2657 kg Collision time - t = 0.05s Then we apply conservation of energy between the two positions shown in the FBD (Total energy(initial)) = (Total energy(final)) P.E +K.E = P.E + K.E mgh + 0 = 1/2mv^2 + 0 mgh = 0.5 * mv^2 v = sqrt 2*9.81 m-s^2 *1.5 m v = 5.425 m-s^-1 The deceleration at impact can be calculated as: Vf = v + aΔt 0 = 5.425 + 0.08 * a a = -67.81 m-s^-2 Force Calculations Calculated force of impact for #3 A-D: A. Phone without a case: The force of impact can be culated with the following formula – F-impact = m(v-u) t = 0.175(5.425-0) 0.01 F-impact = 94.93N B. Phone with a silicon case: The force of impact can be culated with the following formula – F-impact = m(v-u) t = 0.223(5.425-0)

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0.05 F-impact = 24.19N C. Phone with a hard plastic case: The force of impact can be culated with the following formula – F-impact = m(v-u) t = 0.206(5.425-0) 0.03 F-impact = 37.25N D. Phone with a rubber case: The force of impact can be culated with the following formula – F-impact = m(v-u) t = 0.2657(5.425-0) 0.08 F-impact = 18.01N Modeling Motion A. Velocity before impact: As I’m showing from my calculation above the velocity before collision stays constant with each of the cases, because velocity is independent of mass and collision time of the object. Making me conclude that the velocity before impact stays constant. B. Acceleration: The object's acceleration will remain constant, equal to the acceleration influenced by gravity. Deceleration of impact on the other hand is influenced by the collision time by inverse relation. Meaning that when collision time decreases the deceleration time will increase. C. Impact Force: The impact force is similar to the mass of the object and the opposite to the collision time. Since the velocity is not changing, it will not affect the force. Material Recommendation A. I recommend the rubber case. The rubber case is the one that offers the best protection against impact do to only transmitting 18.01N of force.

B. The best material I recommend for the phone case is silicon. I believe this is the best material because it is easy to produce, silicon is lighter than rubber and is an ergonomic material.

https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/newtons-laws-of-motion/ #:~:text=Laws%20of%20Motion-,1.,on%20by%20an%20unbalanced%20force . https://spacecenter.org/science-in-action-newtons-third-law-of-motion/#:~:text=Newton's %20third%20law%20simply%20states,equal%20force%20upon%20object%20A .

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