To analyze the relationships described based on kinetic energy, it’s important to remember the equation for kinetic energy:
\[ KE = \frac{1}{2}mv^2 \]
Here, \( KE \) is the kinetic energy, \( m \) is the mass, and \( v \) is the velocity of the object.
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Direct relationship between kinetic energy and mass: This is accurate when velocity is constant. Since kinetic energy is directly proportional to mass (\( KE \propto m \) when \( v \) is constant), this means if the mass increases, the kinetic energy will also increase.
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Direct relationship between kinetic energy and velocity: Kinetic energy is also directly related to the square of the velocity. Therefore, if the velocity increases (while mass is constant), the kinetic energy will also increase.
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No relationship between velocity and mass: In this context, you can have any mass with any velocity, and they are independent variables. There’s no inherent relationship that connects the two directly unless specified.
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Direct relationship between kinetic energy and mass when velocity is constant: As mentioned earlier, if velocity does not change, then any increase in mass results in an increase in kinetic energy.
To summarize, based on the relationships outlined:
- Kinetic energy is directly related to mass when velocity is constant.
- Kinetic energy is directly related to the square of velocity when mass is constant.
- It's correct that there's no direct relationship between the velocity and mass independently of kinetic energy.
When graphing these relationships, the kinetic energy vs. mass graph (with constant velocity) would be a straight line, indicating a direct proportion. For kinetic energy vs. velocity (with constant mass), the graph would be a parabola reflecting the square relationship.
Therefore, when preparing graphs based on the data in your table, ensure they reflect these specific relationships correctly.
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