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Ch 37: Special Relativity
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoYoung & Freedman Calc 14th EditionCh 37: Special RelativityProblema 37a
Capitolo 37, Problema 37a

A particle has rest mass 6.64×10−276.64\(\times\)10^{-27} kg and momentum 2.10×10−182.10\(\times\)10^{-18} kgm/s.
(a) What is the total energy (kinetic plus rest energy) of the particle?
(b) What is the kinetic energy of the particle?
(c) What is the ratio of the kinetic energy to the rest energy of the particle?

Guida verificata passo dopo passo
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Step 1: Understand the concept of total energy in relativistic physics. The total energy \( E \) of a particle is given by the equation \( E = \sqrt{(pc)^2 + (m_0c^2)^2} \), where \( p \) is the momentum, \( m_0 \) is the rest mass, and \( c \) is the speed of light.
Step 2: Calculate the rest energy of the particle using the formula \( E_0 = m_0c^2 \). Substitute \( m_0 = 6.64 \times 10^{-27} \) kg and \( c = 3 \times 10^8 \) m/s into the equation.
Step 3: Use the total energy formula to find the total energy \( E \). Substitute the given momentum \( p = 2.10 \times 10^{-18} \) kg•m/s and the calculated rest energy into the equation \( E = \sqrt{(pc)^2 + (m_0c^2)^2} \).
Step 4: Determine the kinetic energy \( K \) of the particle. The kinetic energy is given by \( K = E - E_0 \), where \( E \) is the total energy and \( E_0 \) is the rest energy.
Step 5: Calculate the ratio of the kinetic energy to the rest energy using the formula \( \text{Ratio} = \frac{K}{E_0} \). Substitute the values of \( K \) and \( E_0 \) obtained from previous steps.

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Relativistic Energy-Momentum Relation

The relativistic energy-momentum relation is a fundamental concept in physics that connects a particle's total energy (E), momentum (p), and rest mass (m₀) through the equation E² = (pc)² + (m₀c²)², where c is the speed of light. This equation allows us to calculate the total energy of a particle when its momentum and rest mass are known, accounting for relativistic effects at high speeds.
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Kinetic Energy in Relativity

In relativistic physics, kinetic energy (K) is defined as the difference between the total energy (E) and the rest energy (m₀c²) of a particle. It is given by K = E - m₀c². This definition extends the classical concept of kinetic energy to account for the effects of relativity, which become significant at velocities close to the speed of light.
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Rest Energy

Rest energy is the energy inherent to a particle due to its rest mass, given by the equation E₀ = m₀c². This concept, introduced by Einstein's theory of relativity, highlights that mass itself is a form of energy. Rest energy is a crucial component in calculating the total energy of a particle, especially when considering relativistic effects.
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A proton (rest mass 1.67×10−271.67\(\times\)10^{-27} kg) has total energy that is 4.004.00 times its rest energy. What are (a) the kinetic energy of the proton; (b) the magnitude of the momentum of the proton; (c) the speed of the proton?

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