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Ch 36: Special Relativity
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
All textbooksKnight Calc 5th EditionCh 36: Special RelativityProblem 69b
Chapter 36, Problem 69b

The sun radiates energy at the rate 3.8 x 1026 W. The source of this energy is fusion, a nuclear reaction in which mass is transformed into energy. The mass of the sun is 2.0 x 1030 kg. What percent is this of the sun's total mass?

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Determine the energy radiated by the sun per second, which is given as 3.8 × 10^26 W. Recall that power (P) is the rate of energy transfer per unit time.
Use Einstein's mass-energy equivalence formula, E = mc^2, to calculate the mass equivalent of the energy radiated. Rearrange the formula to find m = E / c^2, where c is the speed of light (approximately 3.0 × 10^8 m/s).
Substitute the energy radiated per second (E = 3.8 × 10^26 J) and the speed of light (c = 3.0 × 10^8 m/s) into the equation m = E / c^2 to calculate the mass lost per second.
To find the percentage of the sun's total mass lost, divide the mass lost per second by the total mass of the sun (2.0 × 10^30 kg) and multiply by 100%. Use the formula: percentage = (mass lost / total mass) × 100%.
Simplify the expression to determine the percentage of the sun's total mass that is converted into energy per second. Ensure all units are consistent and calculations are performed step by step.

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Key Concepts

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

Energy-Mass Equivalence

Energy-mass equivalence is a principle derived from Einstein's theory of relativity, encapsulated in the equation E=mc². This concept states that mass can be converted into energy and vice versa, highlighting the relationship between mass and energy. In the context of the sun, this principle explains how the mass lost during nuclear fusion is transformed into the energy radiated by the sun.
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Nuclear Fusion

Nuclear fusion is a process where two light atomic nuclei combine to form a heavier nucleus, releasing a significant amount of energy in the process. This reaction powers stars, including the sun, where hydrogen nuclei fuse to form helium. Understanding fusion is crucial for calculating the energy output of the sun and its implications for mass loss over time.
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Percentage Calculation

Percentage calculation is a mathematical process used to express a number as a fraction of 100. In this context, it involves determining what fraction of the sun's total mass is converted into energy. This requires dividing the mass equivalent of the energy output by the sun's total mass and multiplying by 100 to obtain the percentage, providing insight into the efficiency of the sun's energy production.
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Related Practice
Textbook Question

Let's examine whether or not the law of conservation of momentum is true in all reference frames if we use the Newtonian definition of momentum: px = mux. Consider an object A of mass 3m at rest in reference frame S. Object A explodes into two pieces: object B, of mass m, that is shot to the left at a speed of c/2 and object C, of mass 2m, that, to conserve momentum, is shot to the right at a speed of c/4. Suppose this explosion is observed in reference frame S' that is moving to the right at half the speed of light. Use the Lorentz velocity transformation to find the velocities and the Newtonian momenta of B and C in S'.

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Textbook Question

The sun radiates energy at the rate 3.8 x 1026 W. The source of this energy is fusion, a nuclear reaction in which mass is transformed into energy. The mass of the sun is 2.0 x 1030 kg. Fusion takes place in the core of a star, where the temperature and pressure are highest. A star like the sun can sustain fusion until it has transformed about 0.10% of its total mass into energy, then fusion ceases and the star slowly dies. Estimate the sun's lifetime, giving your answer in billions of years.

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Textbook Question

An electron moving to the right at 0.90c collides with a positron moving to the left at 0.90c. The two particles annihilate and produce two gamma-ray photons. What is the wavelength of the photons?

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Textbook Question

A rocket is fired from the earth to the moon at a speed of 0.990c. Let two events be 'rocket leaves earth' and 'rocket hits moon.' Repeat your calculations of part a if the rocket is replaced with a laser beam.

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Textbook Question

The nuclear reaction that powers the sun is the fusion of four protons into a helium nucleus. The process involves several steps, but the net reaction is simply 4p → 4He + energy. The mass of a proton, to four significant figures, is 1.673 x 10-27 kg, and the mass of a helium nucleus is known to be 6.644 x 10-27 kg. What fraction of the initial rest mass energy is this energy?

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Textbook Question

At what speed, as a fraction of c, is the kinetic energy of a particle twice its Newtonian value?