Four balls are dropped from a platform, 20 meters high. One ball is 5k, the other is 10kg, then 20kg, and 40kg. Which ball will experience the GREATEST change in kinetic energy, from platform to ground?
The potential energy loss and kinetic energy gain is M g H, where H is the platform height.
Since the elevation change is the same for all, the heaviest one has the most PE loss and KE gain.
To determine which ball will experience the greatest change in kinetic energy from the platform to the ground, we need to calculate the kinetic energy for each ball at both the platform and the ground and then compare the differences.
The formula for calculating kinetic energy is: KE = (1/2) * mass * velocity^2
Since all the balls are dropped from the same height, they will have the same gravitational potential energy at the platform (initial energy). This potential energy will be converted to kinetic energy as they fall to the ground.
First, we need to find the velocity of each ball upon hitting the ground using the formula: velocity = √(2 * acceleration * distance)
Given:
Height of the platform (distance) = 20 meters
Acceleration due to gravity (g) = 9.8 m/s^2
1. Ball with mass 5 kg:
velocity = √(2 * 9.8 * 20) ≈ 19.8 m/s
2. Ball with mass 10 kg:
velocity = √(2 * 9.8 * 20) ≈ 19.8 m/s
3. Ball with mass 20 kg:
velocity = √(2 * 9.8 * 20) ≈ 19.8 m/s
4. Ball with mass 40 kg:
velocity = √(2 * 9.8 * 20) ≈ 19.8 m/s
Now, let's calculate the kinetic energy at the platform (initial kinetic energy) and at the ground (final kinetic energy) for each ball using the formula mentioned earlier:
1. Ball with mass 5 kg:
Initial kinetic energy = (1/2) * 5 * 0^2 = 0 Joules
Final kinetic energy = (1/2) * 5 * 19.8^2 ≈ 484.05 Joules
2. Ball with mass 10 kg:
Initial kinetic energy = (1/2) * 10 * 0^2 = 0 Joules
Final kinetic energy = (1/2) * 10 * 19.8^2 ≈ 968.10 Joules
3. Ball with mass 20 kg:
Initial kinetic energy = (1/2) * 20 * 0^2 = 0 Joules
Final kinetic energy = (1/2) * 20 * 19.8^2 ≈ 1936.20 Joules
4. Ball with mass 40 kg:
Initial kinetic energy = (1/2) * 40 * 0^2 = 0 Joules
Final kinetic energy = (1/2) * 40 * 19.8^2 ≈ 3872.40 Joules
Now, let's calculate the change in kinetic energy for each ball by subtracting the initial kinetic energy from the final kinetic energy:
1. Ball with mass 5 kg:
Change in kinetic energy = Final kinetic energy - Initial kinetic energy ≈ 484.05 Joules - 0 Joules = 484.05 Joules
2. Ball with mass 10 kg:
Change in kinetic energy = Final kinetic energy - Initial kinetic energy ≈ 968.10 Joules - 0 Joules = 968.10 Joules
3. Ball with mass 20 kg:
Change in kinetic energy = Final kinetic energy - Initial kinetic energy ≈ 1936.20 Joules - 0 Joules = 1936.20 Joules
4. Ball with mass 40 kg:
Change in kinetic energy = Final kinetic energy - Initial kinetic energy ≈ 3872.40 Joules - 0 Joules = 3872.40 Joules
Therefore, the ball with a mass of 40 kg will experience the greatest change in kinetic energy from the platform to the ground, with a value of approximately 3872.40 Joules.