# ch5 - 53 The free-body diagrams for part(a are shown below...

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53 . The free-body diagrams for part (a) are shown below. & F is the applied force and & f is the force exerted by block 1 on block 2. We note that & F is applied directly to block 1 and that block 2 exerts the force & f on block 1 (taking Newton’s third law into account). (a) Newton’s second law for block 1 is F f = m 1 a , where a is the acceleration. The second law for block 2 is f = m 2 a . Since the blocks move together they have the same acceleration and the same symbol is used in both equations. From the second equation we obtain the expression a = f / m 2 , which we substitute into the first equation to get F f = m 1 f / m 2 . Therefore, f Fm m m = + = + = 2 1 2 32 12 2 3 12 11 . . . . . . N kg kg kg N b gb g (b) If & F is applied to block 2 instead of block 1 (and in the opposite direction), the force of contact between the blocks is f Fm m m = + = + = 1 1 2 32 2 3 2 3 12 21 . . . . . . N kg kg kg N b gb g (c) We note that the acceleration of the blocks is the same in the two cases. In part (a), the force f is the only horizontal force on the block of mass m 2 and in part (b) f is the only

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