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What is the value of the acceleration due to gravity on Earth?
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9) What would be the equation for the Conservation of Energy if you have only gravitational energy turning into only kinetic energy with no friction or other outside forces?
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10) According to the Law of Conservation of Energy, why does the first hill of a roller coaster have to be the highest?
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11) What are boundary conditions in a computer model?
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12) What is the butterfly effect in chaos theory?
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13) How do you calculate the efficiency of a device such as an engine?
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The acceleration due to gravity on Earth is approximately 9.81 m/s² (often rounded to 9.8 m/s²). This acceleration is directed toward the center of the Earth and varies slightly with altitude and latitude.
9) The conservation of energy for only gravitational potential converting to kinetic energy (no friction or external forces) is mgh = 1/2 m v². The mass cancels, giving v = sqrt(2gh), which relates speed to height lost.
10) By conservation of energy, the first hill must be the highest so the coaster has enough gravitational potential energy to convert into kinetic energy to reach subsequent hills. If any later hill were higher, the coaster would not have sufficient energy to climb it without an external energy input.
11) Boundary conditions in a computer model are the constraints or values specified at the edges of the simulation domain (and sometimes at initial or final times) that the solution must satisfy. They are necessary to obtain a unique and physically meaningful solution and strongly influence model behavior and stability.
12) The butterfly effect is the idea that tiny differences in initial conditions can lead to vastly different outcomes in deterministic chaotic systems. This sensitivity makes long-term prediction difficult even when the governing equations are known.
13) Efficiency is calculated as (useful output energy or power ÷ input energy or power) × 100% to express it as a percentage. It quantifies how much of the supplied energy is converted into the desired form, with the remainder lost to waste like heat or friction.
9) The conservation of energy for only gravitational potential converting to kinetic energy (no friction or external forces) is mgh = 1/2 m v². The mass cancels, giving v = sqrt(2gh), which relates speed to height lost.
10) By conservation of energy, the first hill must be the highest so the coaster has enough gravitational potential energy to convert into kinetic energy to reach subsequent hills. If any later hill were higher, the coaster would not have sufficient energy to climb it without an external energy input.
11) Boundary conditions in a computer model are the constraints or values specified at the edges of the simulation domain (and sometimes at initial or final times) that the solution must satisfy. They are necessary to obtain a unique and physically meaningful solution and strongly influence model behavior and stability.
12) The butterfly effect is the idea that tiny differences in initial conditions can lead to vastly different outcomes in deterministic chaotic systems. This sensitivity makes long-term prediction difficult even when the governing equations are known.
13) Efficiency is calculated as (useful output energy or power ÷ input energy or power) × 100% to express it as a percentage. It quantifies how much of the supplied energy is converted into the desired form, with the remainder lost to waste like heat or friction.
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