A vendor hangs an 8.0 kg sign in front of …

Physics Questions
Short Answer
Step by Step Solution
Physics Questions

A vendor hangs an 8.0 kg sign in front of his shop with a cable held away from the building by a lightweight pole. The pole is free to pivot about the end where it touches the wall, as shown in (Figure 1).

Short Answer

The scenario involves a vendor suspending an 8.0 kg sign with a cable supported by a pole angled at 60 degrees. By applying equilibrium equations for both vertical and horizontal forces, the tension in the cable is calculated to be approximately 156.96 Newtons.

Step-by-Step Solution

Step 1: Understand the Setup

In this scenario, a vendor is suspending an 8.0 kg sign with a cable supported by a pole that pivots against a wall. The key to solving for the tension in the cable is recognizing the role of the angle. The pole makes an angle of 60 degrees with the cable and leans away from the wall, affecting the tension’s components.

Step 2: Establish Equations for Equilibrium

To find the tension in the cable, we must apply the conditions for equilibrium, identifying vertical and horizontal forces. The equations are established as:

  • Vertical equilibrium: Tsin(60°) – Fsin(150°) – W = 0
  • Horizontal equilibrium: Tcos(60°) + Fcos(150°) = 0

In these equations, T represents the tension, F is the force from the pole, and W is the weight of the sign (78.48 N).

Step 3: Solve for Tension

By substituting the horizontal equilibrium equation into the vertical one, we eliminate the force F to solve for T. Following through the calculations leads to:

  • Substituting yields: 0.866T – (-0.5)(0.5T – 0.866F) – 78.48 = 0
  • Simplifying results in T ‚Äöaa 156.96 N

This means the tension in the cable is approximately 156.96 Newtons, confirming the solution for the given setup.

Related Concepts

Setup

The arrangement of the components in a physics problem, including the objects involved and their relative positions or orientations within a given scenario.

Equilibrium

A state in which the sum of the forces acting on an object is zero, resulting in no acceleration; conditions must be satisfied for both vertical and horizontal forces.

Tension

The pulling force transmitted along a cable or string, which acts in opposite directions along the length of the cable and is essential in determining the forces acting on suspended objects.

Table Of Contents
  1. A vendor hangs an 8.0 kg sign in front of his shop with a cable held away from the building by a lightweight pole. The pole is free to pivot about the end where it touches the wall, as shown in (Figure 1).

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