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0. Math Review31m
- Math Review
  31m
1. Intro to Physics Units1h 29m
2. 1D Motion / Kinematics3h 56m
3. Vectors2h 43m
4. 2D Kinematics1h 42m
5. Projectile Motion3h 6m
6. Intro to Forces (Dynamics)3h 22m
7. Friction, Inclines, Systems2h 44m
8. Centripetal Forces & Gravitation7h 26m
9. Work & Energy1h 59m
10. Conservation of Energy2h 54m
11. Momentum & Impulse3h 40m
12. Rotational Kinematics2h 59m
13. Rotational Inertia & Energy7h 4m
14. Torque & Rotational Dynamics2h 5m
15. Rotational Equilibrium3h 39m
16. Angular Momentum3h 6m
17. Periodic Motion2h 9m
18. Waves & Sound3h 40m
19. Fluid Mechanics4h 27m
20. Heat and Temperature3h 7m
21. Kinetic Theory of Ideal Gases1h 50m
22. The First Law of Thermodynamics1h 26m
23. The Second Law of Thermodynamics3h 11m
24. Electric Force & Field; Gauss' Law3h 42m
25. Electric Potential1h 51m
26. Capacitors & Dielectrics2h 2m
27. Resistors & DC Circuits3h 8m
28. Magnetic Fields and Forces2h 23m
29. Sources of Magnetic Field2h 30m
30. Induction and Inductance3h 38m
31. Alternating Current2h 37m
32. Electromagnetic Waves2h 14m
33. Geometric Optics2h 57m
34. Wave Optics1h 15m
35. Special Relativity2h 10m

35. Special Relativity

Consequences of Relativity

Physics

35. Special Relativity

Consequences of Relativity

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Problem 37b

Textbook Question

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?

Verified step by step guidance

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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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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