A Particle in a lab is fired through a particle accelerator. If its rest mass is 500 MeV, what is the mass when it is traveling at 0.8c?
can someone please help me on this im totally lost.
again, im really lost on this question. can someone explain to me how to do this?
To calculate the mass of a particle when it is moving at a certain velocity (in this case, 0.8 times the speed of light, or 0.8c), we can use the concept of relativistic mass. The relativistic mass of a particle is given by the equation:
m = γ * m₀
where m is the relativistic mass, γ (gamma) is the Lorentz factor, and m₀ is the rest mass of the particle.
The Lorentz factor is calculated using the formula:
γ = 1 / sqrt(1 - (v²/c²))
where v is the velocity of the particle and c is the speed of light.
In this case, the rest mass of the particle is 500 MeV. To convert from MeV to kg, we need to know the conversion factor. Let's assume it is approximately 1 MeV/c² = 1.783 × 10⁻³³ kg.
So, to find the mass of the particle when it is traveling at 0.8c, we can follow these steps:
Step 1: Calculate the Lorentz factor (γ) using the formula:
γ = 1 / sqrt(1 - (v²/c²))
γ = 1 / sqrt(1 - (0.8²/1²))
γ = 1 / sqrt(1 - 0.64)
γ = 1 / sqrt(0.36)
γ ≈ 1.25
Step 2: Calculate the relativistic mass (m) using the formula:
m = γ * m₀
m = 1.25 * 500 MeV * (1.783 × 10⁻³³ kg/MeV)
m ≈ 1.429 × 10⁻³⁰ kg (approximately)
Therefore, the mass of the particle when it is traveling at 0.8c is approximately 1.429 × 10⁻³⁰ kg.