PHY 150 Project Two Case Material Evaluation Report Template (2)

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Dec 6, 2023

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A&L ENGINEERING Case Material Evaluation Report Newton’s Laws of Motion Newton's First Law asserts that unless acted upon by a force, a body in motion continues in motion and a body at rest remains at rest. The body in motion/rest in this situation is the phone, and the force acting on it to cause it to stop/move is gravity as it pulls the phone down to the earth. According to Newton's Second Law, force equals mass times acceleration, meaning that the rate of change is proportional to the force applied to the object. In this situation, we will be able to determine that the phone's acceleration as it descends will be in the same direction and magnitude as the force of gravity on the phone until it strikes the ground. According to Newton's Third Law, every action has an equal and opposite reaction. In this situation, we will witness this rule when we drop the phone and it collides with the ground, since the force exerted on the phone when it collides with the ground is the same as the force exerted on the ground as the phone collides with it. Force Diagrams
Velocity Calculations Tip : To begin, think about the drop in two phases: The first phase is from the drop to the moment of first contact with the floor. The second phase is the deceleration at impact. The collision time is the time from first contact with the floor to the instant the phone is momentarily at rest. Velocity = Displacement/Change in Time, Displacement = 1.5 m & Change in Time= 0.08 s
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Velocity = 1.5 m/0.08 s= 18.75 m/s Acceleration = Change in Velocity/Change in Time, (18.750 – 5.42)/ (0.08)= 166.63 m/s2 Force = Mass * Acceleration, Mass = 0.27 kg & Acceleration = 9.80 m/s2 Force = 0.27 kg * 166.63 m/s2 = 44.98 N a) Phone without case: Mass = 6.2 oz = 0.175 kg Collision time Δt= 0.01s Velocity before impact V = √ (2*9.81m/s*1.5m) V = √ (29.54) = 5.425 m/ s 2 Deceleration at impact Vf = v + aΔt Vf = final velocity b) Phone with Silicon Case: Mass = 6.2 oz = 0.175 kg Silicon = 1.7 oz = 0.048 kg Total Mass (Mt) = 0.223kg Collision time Δt= 0.05s Velocity before impact: V = √ (2*9.81m/s*1.5m) = 5.425m/ s 2 Deceleration at impact: Vf = v + aΔt
Vf = -5.425 + 0.01*a a = -542.5 m/ s 2 Vf = -5.425 + 0.005*a a = -108.5m/ s 2 c) Phone with Hard Plastic Case: Mass = 6.2 oz = 0.175kg Hard Plastic = 1.1oz = 0.031 kg Total Mass (Mt) = 0.175 + 0.031 = 0.206 kg Collision time Δt= 0.03s Velocity before impact: V = √ (2*9.81m/s*1.5m) V = 5.425 m/ s 2 Deceleration at impact: Vf = v + aΔt Vf = -5.425 + 0.03*a a = -180.83 m/ s 2 d) Phone with Rubber Case: Mass = 6.2 oz = 0.175kg Hard Plastic = 3.2 oz = 0.0907 kg Total Mass (Mt) = 0.175 + 0.0907 = 0.2657 kg Collision time Δt = 0.08s Velocity before impact: V = √ (2*9.81m/s*1.5m) V = 5.425m/ s 2 Deceleration at impact: Vf = v + aΔt Vf = -5.425 + 0.08*a a = -67.81 m/ s 2 Force Calculations a) Phone without case: m(v-u)/ t = 0.175(5.425-0)/ 0.01 = 94.93 N b) Phone with Silicon Case: m(v-u)/ t = 0.223(5.425-0)/ 0.05 = 24.19 N c) Phone with Hard Plastic Case: m(v-u)/ t = 0.206(5.425-0)/ 0.03 = 37.25 N d) Phone with Rubber Case: m(v-u)/ t = 0.2657(5.425-0)/ 0.08 = 18.01 N Modeling Motion A. Velocity before impact: The calculations above show that the velocity before the collision remains constant in each of the cases because velocity is independent of object mass and collision time. Therefore, we can deduce that the velocity before impact is constant. B. Acceleration: The object's acceleration remains constant, which equals gravity's acceleration. However, impact deceleration is inversely proportional to collision time. As a result, as the collision time decreases, the deceleration increases.
C. Impact Force: This is proportional to the object's mass and inversely proportional to the collision time. Because the velocity is constant, it has no effect on the force. Material Recommendation If we are only considering the option that provides the best protection, I would recommend the rubber case. The rubber case provides the best impact protection because it transmits only 18.01N of impact force. However, other considerations may be made outside of this evaluation. Silicon for example is more attractive and appealing than rubber, is easy to manufacture, and is lighter than rubber.
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References Urone, P. P., & Hinrichs, Roger. (2022). Chapter 4. In College Physics 2e . OpenStax. https://openstax.org/books/college-physics-2e/pages/1-introduction-to- science-and-the-realm-of-physics-physical-quantities-and-units

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