Question

A particle has a momentum equal to \(m c .\) Calculate its speed.

Short answer

The speed of the particle is equal to \(c\).

Step-by-step solution

Understand the problem

The momentum of a particle is given as \(p = m c\), where \(c\) could represent a constant or some speed of light. With the momentum formula \(p = m v\), equating both expressions will provide the speed of the particle. This step is important as it gives the direction of how to get from the given information to the needed information - the speed.

Equate both equations

Setting the two given formulas equal to each other gives us \(m v = m c\). This step involves the basic concept that if two quantities are each equal to a third quantity, then they are equal to each other.

Solve for speed

Solving the equation for speed gives \(v = c\). This step involves dividing both sides of the equation by \(m\) to isolate \(v\). As both equations had \(m\), this cancels out and we are left with the speed of particle equals \(c\).

Key concepts

Speed of Light

The speed of light, often denoted as \( c \), is one of the most fundamental constants in nature. It describes how fast light travels in a vacuum, and it is approximately \( 299,792,458 \) meters per second. Understanding this constant is essential since it serves as a baseline in many physics equations, including Einstein’s equation \( E = mc^2 \).

When dealing with problems that involve momentum and speed, the speed of light appears frequently, especially in scenarios involving particles moving extremely fast, close to the speed of light. In the context of particles, if a particle's momentum is described as \( m c \), simplifying equations might reveal that its speed is precisely \( c \).

• It acts as a limit for the maximum speed at which information and matter can travel.
• In many equations, \( c \) is used as a comparative measure to better understand the relative speed of particles.

Particles

In physics, a particle is a small localized object with physical or chemical properties such as mass and charge. These particles can be elementary, such as electrons and protons, or composite, like atoms or molecules. Depending on their type and the context in which they're studied, their behavior can vary significantly.

Particles are crucial when discussing momentum, as they help us visualize how objects with mass move and interact. For example, in high-speed physics scenarios, understanding a particle's momentum enables us to determine its speed. When a problem states a particle's momentum equals \( m c \), it usually implies a high-speed condition, often approaching relativistic speeds where classical physics might need adjustments.

• Particles can vary in size from subatomic particles to larger composite forms.
• Their behavior is governed by principles of classical mechanics and quantum mechanics.
• High-energy particles often require consideration of relativistic effects.

Momentum Formula

Momentum is a measure of the motion of an object and is calculated using the formula \( p = mv \), where \( p \) represents momentum, \( m \) is the mass, and \( v \) is the velocity of the object. This fundamental concept in physics describes how mass and velocity collectively contribute to an object’s motion.

In problems involving high-speed scenarios, such as particles moving at speeds near the speed of light, adjustments or reinterpretations of this equation might be necessary. When given the equation \( p = mc \), where a particle's momentum is equated to its mass times the speed of light, this implies the particle is moving at the speed of light. This serves as a clear expression that the velocity \( v \) equates to \( c \).

• Momentum depends directly on both mass and velocity.
• It is a vector quantity, meaning it has both magnitude and direction.
• Understanding the relationship between mass, velocity, and momentum is crucial in solving physics problems.