Question

A climber helps his friend up an icy slope. His friend is hauling a box of supplies. If the mass of the friend is 90 kg and the mass of the supplies is 22 kg, what are the tensions in the ropes AB and CD? Assume that the slope is smooth. That is, only normal forces are exerted on the man and the box by the slope.

Answer 1

Isolate the box. The weight vector is

W₂ = (22)(9.81)j = -215.8j (N).

The angle between the normal force and the positive x axis is (90° - 60°) = 30°.

The normal force is N_B = |N_B|(0.866i - 0.5j).

The angle between the rope CD and the positive x axis is (180° - 75° = 105°); the tension is:

Isolate the friend. The weight is

W = -(90)(9.81) = -882.9j (N).

The angle between the normal force and the positive x axis is (90° - 40°) = 50°. The normal force is:

NF = |N_F|(0.6428i + 0.7660j).

The angle between the lower rope and the x axis is -75°; the tension is

T₂ = |T₂|(0.2588i + 0.9659j)

The angle between the tension in the upper rope and the positive x axis is (180° - 20° )= 160°, the tension is

T₁ = |T₁|(0.9397i + 0.3420j).

The equilibrium conditions are