A particle has rest mass $6.64 \times 10^{- 27}$ kg and momentum $2.10 \times 10^{- 18}$ 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?

검증된 단계별 안내

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.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

10m

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.

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.

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.