Question

In: Physics

Particle A moves along an axis in the laboratory with velocity V = 0.3c. Particle b...

Particle A moves along an axis in the laboratory with velocity V = 0.3c. Particle b moves with velocity of V = .9c along the direction of motion of particle A.

What kinetic energy does the particle b measure for the particle A?

Solutions

Expert Solution

Solution:

Using the Lorentz velocity transformation in lab frame,

First, find the velocity of A observed by B,

Using the relative velocity of object moving same directions,

vbx = vax - vb/[1 - vaxvb/c2]

Now Substitue vax = 0.3c and vb = 0.9c

vbx = 0.3c - 0.9c /[1 - (0.3*0.9)/c2]

= - 0.6c/[1-0.27]

= - 0.822c.

We go the velocity of A as measured by B,

Now, just calcualte the kinetic energy,

K.E = 1/2mvbx2

[Note: As mass of the particle is not mentioned in the question.]

Please comment the mass for kinetic energy.

I hope you understood the problem, If yes rate me!! or else comment for a better solution.


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