To analyze the statements, let's consider the relationship between force, mass, and acceleration as described by Newton's second law of motion, which states \( F = ma \) (force equals mass times acceleration).
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Statement A: The log will require less force to move than the ball.
- This statement is false. The log is heavier than the ball, so it will generally require a greater force to overcome its inertia and move it.
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Statement B: It will be harder to move the ball a long distance.
- This statement is not inherently true or false without more context. The ease of moving an object long distances depends on various factors, including friction, surface conditions, and more. However, heavier objects generally have more inertia, so it could be argued that moving the log long distances may be harder than moving the ball.
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Statement C: If an equal force is applied to both objects, the ball will move farther.
- This statement is true. Given that \( F = ma \), if the same force is applied to both the 5 kg ball and the 40 kg log, the acceleration of the ball will be greater (since \( a = F/m \)). This will mean that over time, the ball will likely cover more distance than the log under the same force.
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Statement D: If an equal force is applied to both objects, the log will move faster.
- This statement is false. The acceleration of both objects under equal force will depend inversely on their masses. Since the log has much greater mass, it will accelerate more slowly than the ball when both are subjected to the same force.
Thus, the statement that is true among the given options is C: If an equal force is applied to both objects, the ball will move farther.
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