To determine which statement is correct, we need to consider the formula for gravitational potential energy and kinetic energy:
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Gravitational Potential Energy (GPE): When the balls are on the table, they have gravitational potential energy given by the formula: \[ \text{GPE} = m \cdot g \cdot h \] where \( m \) is the mass of the ball, \( g \) is the acceleration due to gravity, and \( h \) is the height.
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Kinetic Energy (KE): When the balls fall, they convert their potential energy into kinetic energy, which is given by the formula: \[ \text{KE} = \frac{1}{2} m v^2 \] where \( v \) is the velocity of the ball when it hits the table.
If both balls are knocked over from the same height at the same time, the gravitational potential energy they initially have depends on their masses and the height they fall from. When they fall, this potential energy is transformed into kinetic energy just before they hit the table.
Since they are both falling from the same height:
- The potential energy of each ball will be proportional to its mass and the height.
- When they hit the table, they will both have the same height, so the potential energy converted to kinetic energy will depend on their respective masses.
Now, let's analyze the statements:
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"The red ball will generate more kinetic energy than the green ball because it has less mass." - This is incorrect. A ball with less mass will have less energy when falling from the same height.
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"The green ball will generate more kinetic energy because it has more mass." - This is correct if the green ball has a greater mass. More mass means more potential energy and consequently more kinetic energy when it hits the table.
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"They will both generate the same amount of kinetic energy because they are at the same height." - This is incorrect because the kinetic energy generated will depend on their masses, not just their height alone.
So, the correct statement is: "The green ball will generate more kinetic energy because it has more mass."