Here are the essential concepts you must grasp in order to answer the question correctly.
Gravitational Potential Energy
Gravitational potential energy (GPE) is the energy an object possesses due to its height above the ground. It is calculated using the formula GPE = mgh, where m is mass, g is the acceleration due to gravity (approximately 9.81 m/s²), and h is the height. In this scenario, the aluminum sphere's GPE will convert to kinetic energy as it falls, and upon impact, some of this energy will be transformed into thermal energy.
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Energy Conservation
The principle of energy conservation states that energy cannot be created or destroyed, only transformed from one form to another. In this case, the gravitational potential energy of the sphere is converted into kinetic energy as it falls, and upon hitting the ground, a portion of that energy is converted into thermal energy, which raises the temperature of the sphere.
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Specific Heat Capacity
Specific heat capacity is the amount of heat energy required to raise the temperature of a unit mass of a substance by one degree Celsius. For aluminum, this value is approximately 900 J/(kg·°C). To find the temperature increase of the sphere after absorbing thermal energy, the formula ΔT = Q/(mc) is used, where ΔT is the temperature change, Q is the heat absorbed, m is the mass, and c is the specific heat capacity.
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