1. Draw a Diagram

Draw a simple diagram of the scaffold. Label the following:

* The scaffold itself (a horizontal line)

* The two cables supporting the scaffold (vertical lines at each end)

* The window washer (a small circle) located 1.5 meters from one end

2. Define the Forces

* Weight of the scaffold (W_s): This acts downwards at the center of the scaffold. W_s = m_s * g = 50 kg * 9.8 m/s² = 490 N

* Weight of the window washer (W_w): This acts downwards at the window washer's position. W_w = m_w * g = 80 kg * 9.8 m/s² = 784 N

* Tension in the left cable (T_l): This acts upwards at the left end of the scaffold.

* Tension in the right cable (T_r): This acts upwards at the right end of the scaffold.

3. Apply Equilibrium Conditions

Since the scaffold is in equilibrium (not moving), we can apply the following conditions:

* Sum of forces in the vertical direction = 0: T_l + T_r - W_s - W_w = 0

* Sum of moments about any point = 0: We'll choose the left end of the scaffold as our pivot point.

4. Calculate the Moments

* Moment of the scaffold's weight: This acts at the center of the scaffold (3.5 meters from the left end). Moment = W_s * 3.5 m = 490 N * 3.5 m = 1715 Nm (clockwise)

* Moment of the window washer's weight: This acts 1.5 meters from the left end. Moment = W_w * 1.5 m = 784 N * 1.5 m = 1176 Nm (clockwise)

* Moment of the tension in the right cable: This acts at the right end of the scaffold (7 meters from the left end). Moment = T_r * 7 m (counterclockwise)

5. Solve for the Tensions

* Moment equation: T_r * 7 m = 1715 Nm + 1176 Nm

* Solve for T_r: T_r = (1715 Nm + 1176 Nm) / 7 m = 413 N

* Force equation: T_l + 413 N - 490 N - 784 N = 0

* Solve for T_l: T_l = 490 N + 784 N - 413 N = 861 N

Therefore:

* The tension in the left cable (T_l) is 861 N.

* The tension in the right cable (T_r) is 413 N.