Question

A body of mass 8 kg is traveling at 2m/s with no external force acting at a certain instant an internal explosion occurs, splitting the body into two chunks of 4 kg mass each. The explosion gives the chunks an additional 16J of kinetic energy. Neither chunk leaves the line of original motion. Determine the speed and direction of motion of each of the chunks after the explosion.1. What is the larger velocity?2. What is the smaller velocity?

Answer 1

Step-by-step explanation:

The given data is as follows.

Original kinetic energy =
`(1)/(2)mv^(2)` = 16 J

Energy imparted due to explosion = 16 J

Total energy = 32 J

Therefore, expression for total energy will be as follows.

Total K.E =
`(1)/(2)m_(1)v^(2)_(1) + (1)/(2)m_(2)v^(2)_(2)`

32 J =
`2v^(2)_(1) + 2v^(2)_(2)`

16 J =
`v^(2)_(1) + v^(2)_(2)`

Now, according to the conservation of linear momentum the expression is as follows.

mv =
`m_(1)v_(1) + m_(2)v_(2)`

`8 * 2 = 4v_(1) + 4v_(2)`

16 =
`(v^(2)_(1) + v^(2)_(2))^(2)`

that is,
`v_(1)v_(2)` = 0

Therefore, it means one of the chunk stops at rest and the velocity of another chunk is 4 m/s in the same direction.

Therefore, we can conclude that the larger velocity is 4 m/s and the smaller velocity is 0 m/s.