The drawing shows box 1 resting on a table, with box 2 resting on top of box 1.

Question

The drawing shows box 1 resting on a table, with box 2 resting on top of box 1. A massless rope passes over a massless, frictionless pulley. One end of the rope is connected to box 2, and the other end is connected to box 3. The weights of the three boxes are W_1 = 55 N, W_2 = 35 N, and W_3 = 28 N. Determine the magnitude of the normal force that the table exerts on box 1. A mountain climber, in the process of crossing between two cliffs by a rope, pauses to rest. She weighs 535 N. As the drawing shows, she is closer to the left cliff than to the right cliff, with the result that the tensions in the left and right sides of the rope are not the same. Find the tensions in the rope to the left and to the right of the mountain climber.

Explanation / Answer

62)Let Tl and Tr be the tensions in left and right ropes respectively.

Considering the forces in Y direction:

Tl cos65 + Tr cos80 - 535 = 0

0.423 Tl + 0.174 Tr = 535 (1)

Forces along horizontal

Tl sin65 - Tr sin80 = 0

Tl = Tr sin80/sin65 = 1.09 Tr

putting this in (1)

0.423 x 1.09 Tr + 0.174 Tr = 535

Tr = 535/0.635 = 842.52 N

Tl = 1.09 x Tr = 1.09 x 842.52 = 918.35 N

Hence, Tl = 918.35 N and Tr = 842.52 N

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