Question

a block placed on the table needs a force R.to be moved .if another identical block is placed on the first block the force required to move

Answer 1

Given:

A block is placed on the table needs force R to be moved.  Another identical block is placed on the first block.

To Find:

Force required to move the first block.

Solution:

A block is placed on the table.

Due to friction between block and table surface , there is restriction of motion of block.

The Force R is  sufficient to  just move the block or the block gets the tendency of motion.

Hence the friction acting on the block will be the limiting friction.

$F = \mu N$

1st case:

Normal reaction acting on the block due to table.

$N = mg \\hence\\F = \mu mg$

F = R = $\mu mg$

Case 2 :

Another identical block is placed on the first block

Normal force acting on block 1 due to ground;

Net force in vertical direction = 0

Free body diagram of block 1;

Normal reaction(N) due to table(upwards)

Normal reaction(P) due to block 2 (downwards)

weight mg(downwards)

$N = P + mg$

FBD of block 2.

normal reaction (P) upwards

weight mg (downwards)

P = mg

substitute P ;

$N = 2 mg\\F = \mu N \\F = \mu 2mg\\F = 2\mu mg\\F = 2 R$

Force required to move the block in case 2 is 2R.