A body of mass m breaks up into 2 parts of rest mass m1 and m2 with velocity v1 and v2 ,what will be the energies of m1 and m2 in terms of m,m1,m2 and c,the velocity of light.
To find the energies of m1 and m2, we can use the equation for relativistic energy:
E = γmc^2
where E is the energy, m is the rest mass, c is the velocity of light, and γ is the Lorentz factor given by:
γ = 1 / √(1 - (v/c)^2)
Given that the body of mass m breaks up into two parts with velocities v1 and v2, we can calculate the energies of m1 and m2 separately.
For m1:
E1 = γ1m1c^2
To calculate γ1, we need to find the velocity v1 in terms of c:
v1 = (m - m2) * v / m1
γ1 = 1 / √(1 - (v1/c)^2)
Substituting the value of v1 in γ1, we have:
γ1 = 1 / √(1 - ((m - m2) * v / (m1 * c))^2)
Now we can calculate E1:
E1 = γ1m1c^2
Similarly, for m2:
γ2 = 1 / √(1 - (v2/c)^2)
E2 = γ2m2c^2
Therefore, the energies of m1 and m2 are given by the equations:
E1 = (m1 * c^2) / √(1 - ((m - m2) * v / (m1 * c))^2)
E2 = (m2 * c^2) / √(1 - (v2/c)^2)
These equations will give the energies of m1 and m2 in terms of m, m1, m2, and c.