Equilibrium Example 7 - Engineering Mechanics

TL;DR

A hanging electric bulb with a weight of 20 Newtons is pulled by a force, resulting in an angle of 70 degrees with the ceiling. Using Lami's theorem, the tension in the wire is found to be 10.15 Newtons, and the horizontal force is calculated to be 1.76 Newtons.

Transcript

let us solve the next question question number four what is given here an electric bulb of 20 newton weight is hanging from ceiling full stop its wire is pulled by a force acting at 20 degree to horizontal such that the wire makes an angle of 70 degree with the ceiling full stop find the magnitude of force and tension in the wire again they had giv... Read More

Key Insights

• ❓ Lami's theorem can be helpful in solving problems involving concurrent forces.
• 🔺 The angle between the force vector and the tension vector is important in Lami's theorem.
• 🏋️ The angle between the tension vector and the weight vector is also crucial for applying Lami's theorem.
• 🏋️ The tension in the wire can be obtained by using the weight and specific angles in the formula.
• 🏋️ The horizontal force can be calculated using the weight and angles in the relevant equation.
• 🧘 The initial position and angles of the wire and forces are essential in understanding the problem.
• 👨‍💼 The calculation involves trigonometric functions such as sine.

Questions & Answers

Q: How is the electric bulb positioned initially?

The bulb is initially positioned vertically, hanging from the ceiling.

Q: In what direction is the force pulling the wire?

The force is pulling the wire at a 20-degree angle to the horizontal direction.

Q: What angle does the wire make with the ceiling?

The wire makes a 70-degree angle with the ceiling.

Q: What is Lami's theorem used for in this problem?

Lami's theorem is used to calculate the tension in the wire and the horizontal force acting on the bulb.

Q: What formula is used to calculate the tension in the wire?

The formula used is Tension (T) = Weight (W) / (sin(angle between P and W) x sin(angle between T and W)).

Q: What is the value of the tension in the wire?

The tension in the wire is calculated to be 10.15 Newtons.

Q: How is the horizontal force (P) calculated?

The formula used to calculate the horizontal force is P = W / (sin(90) x sin(160)), resulting in a value of 1.76 Newtons.

Q: What are the final values obtained in the problem?

The tension in the wire is 10.15 Newtons, and the horizontal force is 1.76 Newtons.

Summary & Key Takeaways

• An electric bulb weighing 20 Newtons is hanging from the ceiling.

• The bulb is pulled by a force at a 20-degree angle to the horizontal, causing the wire to make a 70-degree angle with the ceiling.

• Using Lami's theorem, the tension in the wire is determined to be 10.15 Newtons, and the horizontal force is found to be 1.76 Newtons.