Question Does it take more force to accelerate a moving object? An example would be a long truck that has a safe in the back. As the truck starts accelerating from 0 to 60 MPH, the safe is moved from the back to the front at a constant speed in relation to the truck. Would it take more force to accelerate the truck if the safe were moving? If it does not effect the acceleration of the truck, where does the potential energy of the safe go since for every action there is an equal and opposite reaction?
Answer No, acceleration is independent of velocity. This is a basic consequence of Newton's laws of motion and consistent with relativity. In your example, however, you're moving the safe. If the safe is in a constant state of motion relative to the truck, then it would take the same force to accelerate the truck as if the safe were sitting still...assuming you accelerated the safe to a constant state of motion before you started accelerating the truck. If the safe is accelerating during the truck's acceleration, then it will affect things. Your example doesn't really deal with potential energy. It does deal with kinetic energy, since the same force will have to be applied to the safe over a longer distance if it is moving vs. if it is at rest relative to the truck.
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