Final answer:
The tensions in the ropes supporting a window washer on a plank can be determined by applying principles of static equilibrium. The smaller tension (T1) is calculated to be 313.94 N, while the larger tension (T2) is found to be 588.06 N.
Step-by-step explanation:
The question involves calculating the tension in each rope that supports a window washer on a plank. The system can be analyzed using principles of static equilibrium where the sum of forces and the sum of moments (torques) around any point must be zero. The plank weighs 205 N and the worker weighs 697 N. We can take moments around one end of the plank to find the tension in the rope closest to the worker, which we'll call T1, and use the sum of forces in the vertical direction to find the tension in the other rope, T2.
Let's set up the moments equation around the end of the plank farthest from the worker:
\( T1 * 3.40 m = 205 N * (3.40/2) m + 697 N * 1.03 m \)
Next, solve for T1:
\( T1 = \frac{205 N * 1.7 m + 697 N * 1.03 m}{3.40 m} \)
\( T1 = \frac{348.5 N + 718.91 N}{3.40 m} \)
\( T1 = \frac{1067.41 N}{3.40 m} \)
\( T1 = 313.94 N \)
Now we can find T2 by subtracting T1 from the total weight:
\( T2 = Total Weight - T1 \)
\( T2 = (205 N + 697 N) - 313.94 N \)
\( T2 = 902 N - 313.94 N \)
\( T2 = 588.06 N \)
Therefore, the smaller tension T1 is 313.94 N and the larger tension T2 is 588.06 N.