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# ch05-p053 - f m 2 g F N 1 F N 2(c The acceleration of the...

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53 (a) The free-body diagrams are shown to the right. ± F is the applied force and ± f is the force of block 1 on block 2. Note that ± F is applied only to block 1 and that block 2 exerts the force ± f on block 1. Newton’s third law has thereby been taken into account. 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 .S i n c e the blocks move together they have the same acceleration and the same symbol is used in both equations. Use the second equation to obtain an expression for a : a = f/m 2 . Substitute into the first equation to get F f = m 1 f/m 2 . Solve for f : f = Fm 2 m 1 + m 2 = (3 . 2 N)(1 . 2kg) 2 . 3kg+1 . 2kg =1 . 1N . (b) If ± F is applied to block 2 instead of block 1, the force of contact is f = Fm 1 m 1 + m 2 = (3 . 2 N)(2 . 3kg) 2 . 3kg+1 . 2kg =2 . 1N . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .......... .......... F f m 1 g F N 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Unformatted text preview: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................... . . . . . . . . . . . . . . . . . . . f m 2 g F N 1 F N 2 (c) The acceleration of the blocks is the same in the two cases. Since the contact force f is the only horizontal force on one of the blocks it must be just right to give that block the same acceleration as the block to which ± F is applied. In the second case the contact force accelerates a more massive block than in the first, so it must be larger....
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