An explosion breaks an object into two pieces, one of which has 2 times the mass of the other. If 22500 J were released in the explosion, of which 21% is heat, how much kinetic energy did each piece acquire?
To find the kinetic energy acquired by each piece, we need to first determine the mass of each piece.
Let's assume the mass of one piece is 'm' and the mass of the other piece is '2m' (since one piece has 2 times the mass of the other).
Now, we know that the total energy released in the explosion is 22500 J, and 21% of that is heat. So, the remaining energy is converted into kinetic energy.
To find the kinetic energy acquired by each piece, we can calculate the kinetic energy using the equation:
Kinetic Energy = Total Energy - Heat Energy
The heat energy is given by:
Heat Energy = 0.21 * Total Energy
Therefore, the kinetic energy acquired by each piece can be calculated as:
Kinetic Energy of Piece 1 = (1 - 0.21) * Total Energy = 0.79 * Total Energy
Kinetic Energy of Piece 2 = (1 - 0.21) * Total Energy = 0.79 * Total Energy
Now, let's substitute the given values to find the kinetic energy acquired by each piece:
Kinetic Energy of Piece 1 = 0.79 * 22500 J = 17775 J
Kinetic Energy of Piece 2 = 0.79 * 22500 J = 17775 J
Therefore, each piece acquired kinetic energy of 17775 J.