To analyze the relationship between kinetic energy, velocity, and mass for the balls in the table, we can use the formula for kinetic energy:
\[ KE = \frac{1}{2}mv^2 \]
From the data provided, we can observe the following:
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Kinetic Energy vs. Mass: For balls with the same velocity, the kinetic energy increases as mass increases. For example, balls 1, 2, and 3 with a velocity of 3 m/s show different kinetic energies based on their masses.
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Kinetic Energy vs. Velocity: For balls with the same mass, kinetic energy increases with the square of the velocity. For example, ball 4 has a higher velocity (6 m/s) than ball 1 (3 m/s), which produces a significantly higher kinetic energy.
Based on this analysis, two potential pairs of graphs that can be supported by the data include:
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Kinetic Energy vs. Mass (at constant velocity): This graph would show a direct relationship, where kinetic energy increases as mass increases for a fixed velocity.
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Kinetic Energy vs. Velocity (at constant mass): This graph would show a parabolic curve since kinetic energy is proportional to the square of the velocity. For a fixed mass, an increase in velocity would lead to a much greater increase in kinetic energy.
In summary, the best-supported pairs of graphs would be:
- Kinetic Energy vs. Mass (linear relationship for constant velocity)
- Kinetic Energy vs. Velocity (parabolic relationship for constant mass)