---
title: "Find F1 and F2 for equilibrium"
subject: "Applied Mechanics"
chapter: 2
key: "semester_1/applied_mechanics:unknown-forces-f1-f2-equilibrium"
source: https://www.bctengineer.com/q/semester_1/applied_mechanics/unknown-forces-f1-f2-equilibrium
site: BCT Engineering
---

# Find F1 and F2 for equilibrium

Applied Mechanics · Chapter 2: Basic Concept in Statics and Static Equilibrium

- Asked in: 2069 Chaitra, 4 marks
- Video: [Find the Values of F1 and F2 | Resolution of Vector Forces | Equilibrium of Forces](https://www.youtube.com/watch?v=G4njuMWsOzw) — Kelvin Academy
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/applied_mechanics/unknown-forces-f1-f2-equilibrium
- Whole chapter: https://www.bctengineer.com/md/semester_1/applied_mechanics/chapter-2

## Question

Determine the value of F1 and F2 if the forces shown in figure below are in equilibrium. [Figure: concurrent forces at O: 20 kN to the left, F2 to the right, 75 kN downward, F1 upward at 40° to the horizontal.]

## Short answer

From ΣFy=0: F1 sin40° = 75 kN ⇒ F1 = 116.68 kN. From ΣFx=0: F2 + F1 cos40° − 20 = 0 ⇒ F2 = −69.38 kN, meaning F2 acts to the left.

## Answer

**Reading of the figure:** concurrent forces at O: 20 kN to the left, 75 kN downward, F₂ along the x axis (drawn to the right), and F₁ pointing up and to the right at 40° to the horizontal.

For equilibrium ΣFx = 0 and ΣFy = 0.

#### ΣFy = 0
F₁ sin 40° − 75 = 0
F₁ = 75 / 0.6428 = **116.68 kN**

#### ΣFx = 0 (right positive)
F₂ + F₁ cos 40° − 20 = 0
F₂ = 20 − 116.68 × 0.7660 = 20 − 89.38 = **−69.38 kN**

The negative sign means F₂ really acts to the **left**, opposite to the direction drawn in the figure.

**Answer: F₁ = 116.68 kN (up-right at 40°), F₂ = 69.38 kN directed to the left.**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. From SFy = 0, F1 =
   A. 75 kN
   B. 75 / cos 40°
   C. 75 sin 40°
   D. 75 / sin 40° = 116.68 kN
   Answer: D. F1 sin 40° = 75. (Key point: F1)

2. The SFx = 0 equation is:
   A. F2 + F1 cos 40° - 20 = 0
   B. F2 + F1 sin 40° = 20
   C. F2 = 20 + F1 cos 40°
   D. F2 - F1 cos 40° - 20 = 0
   Answer: A. F1's horizontal component and F2 act right; 20 kN left. (Key point: F2 equation)

3. F2 = -69.38 kN means:
   A. The solution is wrong
   B. It acts to the right
   C. It acts to the left, opposite to the drawn direction
   D. The forces are not in equilibrium
   Answer: C. A negative result reverses the assumed sense. (Key point: Negative sign)

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