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 4.4 kg. In Case B the mass of block 1 (the block behind) is 8.8 kg, and the mass of block 2 is 4.4 kg. No frictional force acts on block 1 in either Case A or Case B. However, a kinetic frictional force of 8.6 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

Case A
Let the common accelerations of the blocks be 'a'. Let F1 be the force which block1 applies on block 2 and F2 be the force which block 2 applies on block1. The directions of F1 and F2 are opposite but there magnitudes which are always considered as positive and equal to say F. By Newtons second law of motion
The block1 decelerates by acceleration, a given by
a = F/4.4 and also by a = (8.6 - F)/4.4. Equating the two we get
F =8.6 - For 2F = 8.6 or F = 4.3 N, and a = 4.3/4.4 = 0.977 m/s^2

Case B
Similarly, we have
8.8*a = F and 4.4*a = 8.6 - F
adding them together, we get 13.2*a = 8.6 or a = 0.6515 m/s^2 and F =8.8 *a = 5.73 N

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