Correct Answer to Question 13

Figure (a) shows a diagram of the situation. We consider each block as a separate system and draw a free-body diagram for each (Figures (b) and (c)). The tension in the cord is the same at both ends of the cord since the cord and pulley are ideal. We choose the +x-axis to the right and the +y-axis up. The accelerations of the blocks are equal in magnitude if the cord length is fixed.

The block on the horizontal surface is acted on by three forces: tension in the string, gravity, and the normal force. Block 1 slides along the table surface, so there cannot be a vertical component of acceleration; the normal force must be equal in magnitude to the weight: N+W=0. With the two vertical forces canceling, the only remaining force is horizontal: the pull of the cord. The net force is equal to the tension in the string; the acceleration of the block is towards the pulley (in the +x direction). This is true regardless of whether Block 1 is sliding to the left or to the right.

Only vertical forces act on block 2. Two forces act on the hanging block: the tension pulling upward and gravity pulling downward. The accelerations of the two blocks must have the same magnitude. The acceleration of block 2 is in the ­y-direction (downward). Since the net force on Block 2 must also be downward, T < mg.

Correct answer: B

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