Static Equilibrium of a Hanging Sign: Example Problem

📚 Quick Study Guide

• ⚖️ Static equilibrium means an object is not moving (translational equilibrium) and not rotating (rotational equilibrium).
• ➕ For translational equilibrium, the net force in both the x and y directions must be zero: $\sum F_x = 0$ and $\sum F_y = 0$.
• 📐 Identify all forces acting on the object (tension, weight, etc.).
• ✏️ Resolve forces into x and y components using trigonometry ($\sin(\theta)$, $\cos(\theta)$).
• 📝 Set up equations for $\sum F_x = 0$ and $\sum F_y = 0$.
• ➗ Solve the equations to find the unknown quantities (e.g., tension in a rope).
• 🌎 Weight is calculated as $W = mg$, where $m$ is mass and $g$ is the acceleration due to gravity (approximately $9.8 m/s^2$).

Practice Quiz

1. A sign with a weight of 50 N is hanging from two ropes. If the angle each rope makes with the horizontal is 30 degrees, what is the tension in each rope?
   1. 25 N
   2. 28.9 N
   3. 50 N
   4. 100 N
2. A 10 kg sign is suspended by two wires that make angles of 45 degrees with the horizontal. What is the tension in each wire?
   1. 49 N
   2. 69.3 N
   3. 98 N
   4. 138.6 N
3. A sign is hanging from a single rope at an angle. What happens to the tension in the rope as the angle increases towards 90 degrees?
   1. Tension decreases
   2. Tension increases
   3. Tension remains the same
   4. Tension becomes zero
4. A 20 N sign is hung with two ropes. One rope is horizontal, and the other is at an angle of 60 degrees with the horizontal. What is the tension in the horizontal rope?
   1. 11.5 N
   2. 20 N
   3. 34.6 N
   4. 40 N
5. What is the net force acting on a sign in static equilibrium?
   1. Equal to its weight
   2. Zero
   3. Depends on tension in ropes
   4. Cannot be determined
6. A sign with a mass of 5 kg is hung vertically from a single rope. What is the tension in the rope?
   1. 4.9 N
   2. 5 N
   3. 49 N
   4. 98 N
7. Two ropes are used to hang a sign. If one rope breaks, and the sign remains hanging from the other rope at an angle, is the sign still in static equilibrium?
   1. Yes
   2. No
   3. Only if the angle is zero
   4. Only if the sign is weightless