A 360kg mine at rest explodes into 3 pieces x,y and z.piece x has a mass of 12kg and it moves with 90m/s .piece x has a mass off 18kg and moves with 62m/s .piece z has a mass of 6kg with unknown velocity. Calculate the unknown velocity of the 6kg piece.
any information on the directions?
No
No, no direction
To calculate the unknown velocity of the 6kg piece (piece z), we will make use of the principle of conservation of momentum.
The principle of conservation of momentum states that the total linear momentum of an isolated system remains constant before and after the explosion. In this case, the total linear momentum of the system before the explosion (when the mine was at rest) is zero. After the explosion, the total linear momentum should still be zero.
Let's denote the velocity of piece z as vz.
Before the explosion:
The total linear momentum is given by the formula:
Total momentum before = mass of x * velocity of x + mass of y * velocity of y + mass of z * velocity of z
Since the mine is at rest, the total linear momentum before the explosion is zero.
0 = (mass of x * velocity of x) + (mass of y * velocity of y) + (mass of z * velocity of z)
Substituting the given values:
0 = (12kg * 90m/s) + (18kg * 62m/s) + (6kg * vz)
Simplifying the equation:
0 = 1080 + 1116 + 6vz
0 = 2196 + 6vz
Rearranging the equation to isolate vz:
6vz = -2196
vz = -2196/6
vz = -366 m/s
Therefore, the unknown velocity of the 6kg piece (piece z) is -366 m/s.
Note: The negative sign indicates the direction of the velocity, which means piece z is moving in the opposite direction to pieces x and y.