Textbook Question
A laboratory experiment shoots an electron to the left at 0.90c. What is the electron's speed, as a fraction of c, relative to a proton moving to the right at 0.90c?
1
views
Ch 36: Special Relativity
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
Not the one you use?Change textbookSelect a different textbook
Table of contents
- Ch 01: Concepts of Motion35
- Ch 02: Kinematics in One Dimension75
- Ch 03: Vectors and Coordinate Systems58
- Ch 04: Kinematics in Two Dimensions60
- Ch 05: Force and Motion23
- Ch 06: Dynamics I: Motion Along a Line53
- Ch 07: Newton's Third Law27
- Ch 08: Dynamics II: Motion in a Plane52
- Ch 09: Work and Kinetic Energy56
- Ch 10: Interactions and Potential Energy50
- Ch 11: Impulse and Momentum56
- Ch 12: Rotation of a Rigid Body71
- Ch 13: Newton's Theory of Gravity52
- Ch 14: Fluids and Elasticity44
- Ch 15: Oscillations55
- Ch 16: Traveling Waves37
- Ch 17: Superposition39
- Ch 18: A Macroscopic Description of Matter53
- Ch 19: Work, Heat, and the First Law of Thermodynamics60
- Ch 20: The Micro/Macro Connection53
- Ch 21: Heat Engines and Refrigerators34
- Ch 22: Electric Charges and Forces40
- Ch 23: The Electric Field39
- Ch 24: Gauss' Law32
- Ch 25: The Electric Potential63
- Ch 26: Potential and Field57
- Ch 27: Current and Resistance42
- Ch 28: Fundamentals of Circuits39
- Ch 29: The Magnetic Field47
- Ch 30: Electromagnetic Induction60
- Ch 31: Electromagnetic Fields and Waves32
- Ch 32: AC Circuits63
- Ch 33: Wave Optics32
- Ch 34: Ray Optics57
- Ch 35: Optical Instruments30
- Ch 36: Special Relativity38
- Ch 37: The Foundations of Modern Physics25
- Ch 38: Quantization49
- Ch 39: Wave Functions and Uncertainty31
- Ch 40: One-Dimensional Quantum Mechanics35
- Ch 41: Atomic Physics18
- Ch 42: Nuclear Physics27
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
Chapter 36, Problem 37b
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 guidance1
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.
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Was this helpful?
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.
Recommended video:
Guided course
07:46
Unit Conversions
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.
Recommended video:
Guided course
4:52Gravitational Potential Energy for Systems of Masses
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.
Recommended video:
Guided course
04:10Intro to Energy & Types of Energy
Related Practice
Textbook Question
What are the rest energy, the kinetic energy, and the total energy of a 1.0 g particle with a speed of 0.80c?
3
views
1
rank
Textbook Question
The star Alpha goes supernova. Ten years later and 100 ly away, as measured by astronomers in the galaxy, star Beta explodes. An alien spacecraft passing through the galaxy finds that the distance between the two explosions is 120 ly. According to the aliens, what is the time between the explosions?
1
views
Textbook Question
Two events in reference frame S occur 10 μs apart at the same point in space. The distance between the two events is 2400 m in reference frame S'. What is the velocity of S' relative to S?
Textbook Question
A proton is accelerated to 0.999c. By what factor does the proton's momentum exceed its Newtonian momentum?
Textbook Question
A modest supernova (the explosion of a massive star at the end of its life cycle) releases 1.5 x 10⁴⁴ J of energy in a few seconds. This is enough to outshine the entire galaxy in which it occurs. Suppose a star with the mass of our sun collides with an antimatter star of equal mass, causing complete annihilation. What is the ratio of the energy released in this star-antistar collision to the energy released in the supernova?