To calculate the energy lost by the ball as a result of the impact on the floor, we can use the principle of conservation of mechanical energy. The mechanical energy of the ball is the sum of its potential energy (PE) and kinetic energy (KE).
Initially, when the ball is at a height of 5m, its energy is in the form of potential energy. The potential energy can be calculated using the formula:
PE = mgh
where m is the mass of the ball (200g = 0.2 kg), g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the height (5m).
PE = 0.2 kg * 9.8 m/s² * 5m PE = 9.8 J
At the highest point of the ball's bounce, when it reaches a height of 3m, its energy is again in the form of potential energy. So, the potential energy at this point is:
PE = mgh PE = 0.2 kg * 9.8 m/s² * 3m PE = 5.88 J
The difference in potential energy before and after the bounce represents the energy lost by the ball:
Energy lost = Initial potential energy - Final potential energy Energy lost = 9.8 J - 5.88 J Energy lost = 3.92 J
Therefore, the ball loses 3.92 joules (J) of energy as a result of the impact on the floor.