Equilibrium of a particle - Example : ExamSolutions

Summary

This tutorial focuses on solving a problem involving the equilibrium of a particle subjected to multiple forces. The speaker walks through the process of resolving forces in two perpendicular directions, both horizontally and vertically. By applying trigonometry and resolving components of the forces, the tutorial guides the audience through calculating the values of P and Q. The solution involves using trigonometric identities, rearranging equations, and performing calculations to find the unknown forces. The tutorial also emphasizes checking solutions and understanding the methodology behind resolving forces in equilibrium scenarios.

Takeaways

• 🔍 The problem involves finding the magnitudes of forces P and Q acting on a particle in equilibrium under multiple forces.
• 📏 To solve, forces are resolved into horizontal and vertical components, simplifying the analysis into two perpendicular directions.
• ↔️ Forces are resolved to the right first, considering the horizontal components and their effects.
• 🔢 The 9 Newton force acts entirely to the right, contributing positively to the horizontal resolution.
• 📐 The 7 Newton force is split into horizontal and vertical components, with only the horizontal component affecting the resolution.
• 📉 The component of the 7 Newton force to the right is calculated using the cosine of the 40° angle.
• ➗ Force P is perpendicular to the horizontal resolution direction and thus does not affect the horizontal balance.
• 🔄 Force Q is split into leftward and downward components, with only the leftward component affecting the horizontal resolution.
• 🔄 The resultant horizontal force is set to zero for equilibrium, leading to the calculation of Q.
• 📊 For the vertical resolution, P acts entirely upwards, contributing positively.
• 📐 The 7 Newton force's vertical component is calculated using the sine of the 40° angle.
• ➖ The vertical component of Q is calculated using the sine of the 20° angle, affecting the vertical balance negatively.
• 🔄 The resultant vertical force is also set to zero for equilibrium, leading to the calculation of P.

Q & A

What is the main topic of the tutorial?

The main topic of the tutorial is finding the forces P and Q acting on a particle in equilibrium under a system of forces.

What is the method used to resolve forces in this tutorial?

The method used is resolving forces in two mutually perpendicular directions, horizontally and vertically.

Why is it necessary to resolve forces into components?

Forces need to be resolved into components because only the components along the direction of interest affect the equilibrium of the particle.

What is the significance of the angle in resolving forces?

The angle is significant because it determines the direction of the force component relative to the direction being resolved.

What does the cosine function represent when resolving forces?

The cosine function represents the horizontal component of a force when resolving forces in a horizontal direction.

Why does the force P not affect the horizontal resolution in the tutorial?

Force P does not affect the horizontal resolution because it acts perpendicular to the horizontal direction being resolved.

How is the force Q resolved into components?

Force Q is resolved into components by considering the angle it makes with the direction being resolved, using the cosine of the angle for the horizontal component and the sine of the angle for the vertical component.

What is the resultant force acting on the particle in equilibrium?

The resultant force acting on the particle in equilibrium is zero, as the particle is not accelerating.

How is the value of Q calculated in the tutorial?

The value of Q is calculated by setting the sum of the horizontal components equal to zero and solving for Q.

What is the final value of Q given in the tutorial?

The final value of Q given in the tutorial is 15.3 Newtons to one decimal place.

How is the value of P calculated in the tutorial?

The value of P is calculated by setting the sum of the vertical components equal to zero and solving for P using the known value of Q.

What is the final value of P given in the tutorial?

The final value of P given in the tutorial is 0.7 Newtons to one decimal place.