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enter image description here If we assume g=10m/s^2 & negligible friction

The force needed to accelerate that box by 5m/s^2 would be 500N. This is a very basic one.

enter image description here The confusion came when an force of 250N (the force a 25kg mass/box would experience in a gravitational field) was exerted on the box, I then tought that the 250N would be cancelled out by the Normal force on the surface, thus the only mass would be the 75kg box and the required force to accelerate the box by 5m/s^2 is 375N.

My question is (for the 2nd diagram), should you calculate the force needed to 'push' the box as if there was a 25kg box resting above it or not? My intuition suggests that previous 375N would be the correct answer.

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If there is no friction between the two boxes as well as between the 75 kg box and the floor then you are correct. But unless there is friction between you and the floor you wouldn’t be able to push the box at all. Imagine trying to push the box if you were standing on ice.

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  • $\begingroup$ so for the second diagram the force needed to accelerate the object by 5m/s^2 is 375N, nonetheless the additional applied force on the top (250N or any value)? $\endgroup$ – KEVIN N May 26 at 8:12
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    $\begingroup$ @Kevin IOP Yes that’s correct $\endgroup$ – Bob D May 26 at 8:18
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Yes, you should calculate it as if there's a $25kg$ box on box A.

This is because all that box A experiences is a $250N$ force downwards. What actually causes that force is of no concern (as in Newton's laws, $F=ma$ tells us the acceleration of a body corresponding to the force experienced by it. What causes that force $F$ is of no concern.)

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