an ball of mass initially at rest fragments into two masses each of 1 kg moving with speed 0.6c. find the mass of original body
To solve this problem, we can use the concept of conservation of momentum. According to this principle, the total momentum before and after the collision remains constant.
Let's denote the initial mass of the ball as M (unknown), and the velocity of each of the resulting masses as v (0.6c).
The momentum before the fragmentation is zero since the ball is at rest. The total momentum after the fragmentation can be calculated as follows:
Total momentum after = momentum of mass 1 + momentum of mass 2
The momentum of an object can be calculated by multiplying the mass by its velocity:
Momentum of mass 1 = mass of mass 1 * velocity of mass 1
= 1kg * (0.6c)
Momentum of mass 2 = mass of mass 2 * velocity of mass 2
= 1kg * (0.6c)
Since the total momentum before and after the fragmentation is conserved, we can equate them:
0 = 1 kg * (0.6c) + 1 kg * (0.6c)
0 = 2kg * (0.6c)
Now, we need to solve for M:
M = (2kg * (0.6c)) / 0.6c
The "c" term cancels out:
M = 2kg
Therefore, the mass of the original body (the ball) is 2 kg.