Question

# Two blocks connected by a rope of negligible mass are being dragged by a horizontal force (Fig. above). Suppose , and the coefficient of kinetic friction between each block and the surface is . (a) Draw a free-body diagram for each block. Determine (b) the acceleration of the system and (c)Β the tension in the rope.

Hard

## Solution

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## Because the cord has constant length, both blocks move the same number of centimeters in each second and so move with the same acceleration. To find just this acceleration, we could model the system as a particle under a net force. That method would not help to finding the tension,so we treat the two blocks as separate accelerating particles. (a) Below figure shows the free-body diagrams for the two blocks. The tension force exerted by block on block is the same size as the tension force exerted by object on object . The tension in a light string is a constant along its length, and tells how strongly the string pulls on objects at both ends. (b) We use the free-body diagrams to apply Newtonβs second law. For or ........... [1] And also Β Β Β  or Also, the definition of the coefficient of friction gives Β Β Β  For ...................................... [2] Also from the component, orΒ  And againΒ  Substituting from equation [1] into [2], we get Β Β Β  or Solvind for Β Β Β  (c) From equation [1] Β Β Β

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