The scenario you described is indeed possible, even with the conditions you specified. Let's break down the key points:
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Equal Masses: Both objects have the same mass, \( m \).
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Both in Motion: Both objects are moving, indicating they have some kinetic energy.
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Different Kinetic Energies: One object has greater kinetic energy than the other.
The kinetic energy (\( KE \)) of an object is given by the formula: \[ KE = \frac{1}{2}mv^2 \] where \( v \) is the velocity of the object.
For two objects with equal mass, if one object has a greater kinetic energy, it must have a greater velocity. Therefore, they must have different velocities.
Now, regarding the statement about volume: The volume of an object does not directly affect the kinetic energy in the context of classical mechanics. Kinetic energy is purely dependent on mass and the square of the velocity. However, it’s possible that the object with greater volume could have the same mass as the other object because volume does not determine mass; it’s the density of the object that does.
Thus, the object with greater volume can still have the same mass if it has a lower density. Hence, if one object is less dense but has a larger volume (and still has equal mass), it doesn't inhibit the condition where one object moves faster (and thus has a greater kinetic energy) while both have equal mass.
In conclusion, the difference in volumes can coexist with them having equal mass. The object with the greater kinetic energy must be moving faster compared to the other object, despite any differences in physical dimensions like volume.