Calculating Tensions in a Scaffold with a Worker: An Applied Example of Static Equilibrium

When analyzing the stability of a scaffold with a worker, understanding the principles of static equilibrium is crucial. This article explores how to calculate the tensions in two ropes supporting a scaffold with a worker standing on it. The scaffold and the worker both exert forces, and by applying the principles of static equilibrium, we can solve for the tensions in the ropes.

Problem Description

A window washer is standing on a scaffold that is supported by a vertical rope at each end. The scaffold weighs 200 N and is 3.00 m long. The worker weighs 700 N and is standing 1.00 m from one end. The task is to find the tension in each rope.

Step 1: Define the System

T1 tension in the rope at one end where the worker is closest. T2 tension in the rope at the other end.

Step 2: Set Up the Equilibrium Equations

Sum of Vertical Forces

The vertical forces must balance each other out for the system to be in equilibrium.

T1 T2 Ws Ww

T1 T2 200 N 700 N 900 N

Sum of Torques

Torques must also be zero for equilibrium, taken about the end where T1 is applied.

-The torque due to the scaffold's weight acts at its center (1.5 m from either end).

-The torque due to the worker acts at 1.00 m from the end where T1 is applied.

The equation is given by:

T2 * 3.00 m - 200 N * 1.5 m - 700 N * 1.00 m 0

Solve for T2:

T2 * 3.00 200 * 1.5 700 * 1.00

T2 * 3.00 300 N 700 N 1000 N

T2 1000 N / 3.00 m ≈ 333.33 N

Step 3: Solve for T1

Substitute T2 into the vertical forces equation:

T1 333.33 N 900 N

T1 900 N - 333.33 N ≈ 566.67 N

Final Results

T1 ≈ 566.67 N T2 ≈ 333.33 N

Thus, the tensions in the ropes are approximately: - T1 ≈ 566.67 N - T2 ≈ 333.33 N

Real-World Application

The principles discussed in this example can be applied to real-world scenarios involving various types of scaffolds and workers. By accurately calculating the tensions in the supporting ropes, it ensures the stability and safety of the scaffold.

Conclusion

Understanding static equilibrium is key to ensuring the safety and stability of scaffolds in construction. This example demonstrates how to apply the principles of static equilibrium to calculate the tensions in the ropes supporting a scaffold. Such calculations are essential for any professional working in construction or involved in the safe operation of scaffolding.