Question

An object disintegrates into two fragments. one fragment has a mass of 2.00 mev/c2 and a speed of 0.5c in the positive x direction. the other fragment has a mass of 1.00 mev/c² and a speed of 0.8c in the positive y direction

what was the speed of the original object?

Answer 1

By applying conservation of momentum and conservation of energy, we set up equations involving the masses and velocities of the fragments, solving to find the speed of the original object.

In this scenario, we can use the principles of conservation of momentum and conservation of energy to determine the speed of the original object before disintegration. Let's denote the original object's mass as M and its speed as v.

1. Conservation of Momentum:

The total momentum of the system before disintegration is equal to the total momentum after disintegration. The momentum of each fragment is given by the product of its mass and velocity.

`\[ Mv = m_1v_(1x) + m_2v_(2y) \]`

where:

• 
  `\(m_1\)` and
  `\(v_(1x)\)` are the mass and velocity of the first fragment,

• 
  `\(m_2\)` and
  `\(v_(2y)\)` are the mass and velocity of the second fragment.

2. Conservation of Energy:

The total energy of the system before disintegration is equal to the total energy after disintegration. The relativistic kinetic energy (KE) for each fragment is given by:

`\[ KE = (\gamma - 1)mc^2 \]`

where
`\(\gamma\)` is the Lorentz factor, and (c) is the speed of light.

The total kinetic energy before disintegration is equal to the sum of the kinetic energies of the fragments after disintegration.

`\[ KE_{\text{total}} = KE_1 + KE_2 \]`

This involves calculating the Lorentz factor for each fragment.

Once we have these equations, we can solve them simultaneously to find the speed v of the original object before disintegration.