Two blocks are sliding to the right across a horizontal surface, as the drawing

Question

Two blocks are sliding to the right across a horizontal surface, as the drawing shows.

In Case A the mass of each block is 3.4 kg. In Case B the mass of block 1 (the block behind) is 6.8 kg, and the mass of block 2 is 3.4 kg. No frictional force acts on block 1 in either Case A or Case B. However, a kinetic frictional force of 6.7 N does act on block 2 in both cases and opposes the motion. For both Case A and Case B determine (a) the magnitude of the forces with which the blocks push against each other and (b) the magnitude of the acceleration of the blocks.

Explanation / Answer

a)   Case A

Here, a = F/3.4

Also, a = (6.7 - F)/3.4

=>   (6.7 - F)/3.4 = F/3.4

=> F = 3.35 N

Thus, the magnitude of the forces with which the blocks push against each other =   3.35 N

Case B

Here, a = F/6.8

Also, a = (6.7 - F)/3.4

=>   (6.7 - F)/3.4 = F/6.8

=> F = 4.46 N

Thus, the magnitude of the forces with which the blocks push against each other =  4.46 N

b) Case A

the magnitude of the acceleration = 3.35/3.4 = 0.985 m/s2

Case B

the magnitude of the acceleration = 4.46/6.8 = 0.656 m/s2

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