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Lets assume, the block is 1kg which on earth applying 10N

According to Newton's Thrid Law,

For every action, there is an equal and opposite reaction.

Hence when the block is left on the table by itself, it is applying 10 N to the table and the table is exerting 10N to the block.

When one pushes down the block with a force of 10N

The Block total downwards force is 20N, thus the table too exert an equal, 20N opposite to the original force. Thus, the force applied by the table in the next instance increased.

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Q: When you push down on a block at rest on a table does the normal force exerted by the table on the block increase decrease or remain the same?
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