Question

The passage states that which of the following causes an increase in particle mass? A. A particle reaching the speed of light B. Acceleration of a particle in a vacuum C. Using heavier particles D. Injecting energy using electric fields

Short answer

Option D: Injecting energy using electric fields.

Step-by-step solution

- Understanding the Problem

Determine what the passage is asking for: identify which of the given options causes an increase in particle mass.

- Analyze Each Option

Go through each of the options to see how it affects particle mass: A. A particle reaching the speed of light B. Acceleration of a particle in a vacuum C. Using heavier particles D. Injecting energy using electric fields.

- Relate to Physical Principles

Recall that according to the theory of relativity, as particles gain energy, their mass increases. So, evaluate each option in light of this principle.

- Evaluate Option A

A particle cannot reach the speed of light as its mass would become infinite, making this option invalid.

- Evaluate Option B

Accelerating a particle in a vacuum does not inherently increase its mass unless the acceleration involves adding energy.

- Evaluate Option C

Using heavier particles presupposes the particles are heavy; it does not increase their mass.

- Evaluate Option D

Injecting energy using electric fields increases the energy of the particle and, according to relativity, increases its mass.

- Conclusion

Based on the analysis, injecting energy using electric fields (Option D) is the correct answer as it causes an increase in particle mass.

Key concepts

theory of relativity

The theory of relativity, developed by Albert Einstein, fundamentally changed our understanding of physics. One key aspect of this theory is the relationship between energy and mass. Einstein's famous equation, \( E = mc^2 \), shows that energy and mass are interchangeable: energy can be converted into mass and vice versa.
When a particle gains energy, such as through acceleration or interaction with an electric field, its mass increases. This phenomenon is most noticeable at speeds close to the speed of light. Here's how:

• Rest Mass vs. Relativistic Mass: A particle's rest mass is its inherent mass when not in motion. As it accelerates to higher velocities, its relativistic mass, which depends on both its rest mass and speed, increases.


• Energy Injection: According to relativity, injecting energy into a particle, such as using electric fields, adds to its total energy and thus increases its mass.

This principle helps us understand why option D (injecting energy using electric fields) in the exercise is correct. When energy is added to a particle, its mass grows due to this energy-mass equivalence. Therefore, using electric fields to inject energy will result in an increase in particle mass.

particle physics

Particle physics is the branch of physics that studies the fundamental particles of the universe and their interactions. It delves into the components of atoms, such as protons, neutrons, and electrons, and even smaller particles like quarks and leptons.
Understanding particle physics is crucial for evaluating the given exercise options. Let's break it down:

• Particle Acceleration: In accelerators, particles are often accelerated to high speeds using electric fields. The additional energy from these fields increases the particle's relativistic mass, illustrating the correct answer to the exercise.


• Collider Experiments: In facilities like the Large Hadron Collider, particles are accelerated to near light speeds to study collisions. These collisions produce new particles and demonstrate mass-energy equivalence.

To summarize, particle physics provides the framework to understand how particles behave at high energies and reinforces why injecting energy using electric fields (Option D) results in an increase in particle mass.

energy and mass relationship

The relationship between energy and mass is a cornerstone of modern physics, famously encapsulated by Albert Einstein's equation, \( E = mc^2 \). This equation states that energy (E) and mass (m) are interchangeable; one can be converted into the other, with \( c \) being the speed of light.
This principle is fundamental to understanding how particles behave when energy is introduced. Here’s a closer look:

• Energy Injection: When a particle is injected with energy, its total energy increases. According to relativity, this increase in energy translates to an increase in mass.


• Practical Examples: In accelerators, particles are often given energy using electric fields. This results in a noticeable increase in their mass, confirming that energy and mass are two sides of the same coin.

Therefore, when the exercise highlights that injecting energy using electric fields increases particle mass (Option D), it directly ties back to this fundamental relationship. By understanding \( E = mc^2 \), we grasp that injecting energy inherently leads to an increase in mass, validating the solution provided.