A quarter-pound hamburger with all the fixings has a mass of 200 g. The food energy of the hamburger (480 food calories) is 2 MJ. By what factor does the energy equivalent exceed the food energy?

검증된 단계별 안내

Convert the mass of the hamburger from grams to kilograms, as the SI unit for mass is kilograms. Use the conversion: 1 g = 0.001 kg. Thus, the mass \( m \) in kilograms is \( m = 200 \times 0.001 \, \text{kg} \).

Use Einstein's mass-energy equivalence formula \( E = mc^2 \) to calculate the energy equivalent of the hamburger's mass. Here, \( c \) is the speed of light in a vacuum, approximately \( 3 \times 10^8 \; \text{m/s} \). Substitute the mass \( m \) and \( c \) into the formula.

Calculate the food energy of the hamburger in joules. Since 1 food calorie (kcal) = 4184 joules, the food energy \( E_{\text{food}} \) in joules is \( E_{\text{food}} = 480 \times 4184 \; \text{J} \).

Determine the factor by which the energy equivalent exceeds the food energy. This factor is given by \( \text{Factor} = \frac{E}{E_{\text{food}}} \), where \( E \) is the energy equivalent calculated in step 2 and \( E_{\text{food}} \) is the food energy calculated in step 3.

Simplify the expression for the factor and interpret the result. This will show how many times greater the energy equivalent is compared to the food energy.

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주요 개념

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Energy Units

Energy can be measured in various units, including joules (J) and food calories (cal). One food calorie is equivalent to approximately 4.184 joules. Understanding these conversions is essential for comparing different energy values, such as the energy content of food and the energy equivalent of mass.

Mass-Energy Equivalence

Mass-energy equivalence is a principle from Einstein's theory of relativity, expressed by the equation E=mc². This concept states that mass can be converted into energy and vice versa, allowing us to calculate the energy equivalent of a given mass. In this context, it helps determine how much energy is contained in the mass of the hamburger.

Food Energy

Food energy refers to the energy that food provides to the body, typically measured in calories. In this question, the hamburger's food energy is given as 480 food calories, which indicates the amount of energy available for metabolic processes. Understanding food energy is crucial for evaluating dietary intake and energy expenditure.