Question

A window washer is standing on a plank supported by a vertical rope at each end. The plank weighs 191 N and is 3.10 m long. What is the tension in each rope when the 697 N worker stands 1.18 m from one end?

1) Smaller tension
2) Larger tension

Answer 1

The tension in the rope closer to the worker (T1) is smaller than the tension in the rope farther from the worker (T2).

The correct option is 1.

Step-by-step explanation:

To solve this problem, you can use the principles of torque and equilibrium. When the plank is in equilibrium, the sum of the torques and forces acting on it must be zero.

Let's denote the tension in the rope closer to the worker as T_1 and the tension in the rope farther from the worker as T_2.

1. Calculate the torque due to the plank's weight about the point where the worker stands:

Torque_plank = Weight_plank x Distance_worker

Torque_plank = 191 N x 1.18 m

2. Calculate the torque due to the worker's weight about the same point:

Torque_worker = Weight_worker x Distance_worker

Torque_worker = 697 N x 1.18 m

3. In equilibrium, the torques must balance:

Torque_plank = Torque_worker

4. Express the tensions in terms of the distances from the center (half of the plank's length):

T_1 = Torque_worker / Distance_center

T_2 = Torque_plank / Distance_center

Now, you can compare T_1 and T_2 to determine which one is larger or smaller.

Given the information, the correct answer is:

1) Smaller tension (The tension in the rope closer to the worker is smaller than the tension in the rope farther from the worker.)