Resultant Force Along a Straight Line

What you’ll learn

Combine forces with an explicit direction convention.

បូកកម្លាំងតាមបន្ទាត់តែមួយដោយកំណត់ទិសវិជ្ជមាន។

Meaning and use

A resultant is the vector sum of forces. In one dimension, choose a positive direction and add signed values. Zero resultant means no change in velocity in an inertial reference frame, not necessarily no motion. This lesson treats a straight-line model rather than forces at arbitrary angles.

កម្លាំងផ្គួបជាផលបូកវ៉ិចទ័រកម្លាំង។ ក្នុងមួយទិស ត្រូវកំណត់សញ្ញា ហើយបូកតាមទិស។ ផលបូកសូន្យមិនមានន័យថាវត្ថុត្រូវឈប់ទេ។

Formulas

Signed one-dimensional sum

\[F_{\mathrm{net}}=\sum_i F_i\]

Opposing directions

\[F_{\mathrm{net}}=F_{\mathrm{right}}-F_{\mathrm{left}}\]

Symbols and units

Symbol	Meaning	Unit or restriction
Fnet	Resultant force along the chosen axis	N
Fright, Fleft	Positive magnitudes in opposite directions	N

Conditions and limits

• The subtraction form assumes right has been chosen positive.
• Do not add unrelated perpendicular forces using this one-dimensional shortcut.
• កំណត់ទិសនៃចម្លើយ មិនត្រឹមតែលេខ។

Worked examples

Two opposing forces

A box has 12 N right and 5 N left.

1. Choose right positive.
2. Calculate \(F_{\mathrm{net}}=12-5=7\) N.

7 N right

ទិសដូចសញ្ញាវិជ្ជមានដែលបានជ្រើស។

A negative resultant

Forces are 4 N right and 10 N left.

1. Calculate \(4-10=-6\) N.
2. A negative value means left.

6 N left

លេខអវិជ្ជមានប្រាប់ថាទិសផ្ទុយពីទិសវិជ្ជមាន។

Common mistakes

Instead of	Use	Why
Opposing 12 N and 5 N give 17 N right.	They give 7 N right.	Opposing forces subtract in the signed model.
Zero resultant always means the object is stationary.	It can move at constant velocity.	Zero resultant concerns change in motion.

Practice

Solve these before revealing the worked solutions. Include units where relevant.

សាកល្បងដោះស្រាយមុនបើកមើលចម្លើយ។ សូមបង្ហាញជំហាន និងឯកតាដែលពាក់ព័ន្ធ។

1. Find resultant for 20 N right and 8 N left.
2. Find resultant for 6 N left and 6 N right.
3. Can the signed subtraction rule directly combine north and east forces?

Answers and steps

Show solutions / បង្ហាញដំណោះស្រាយ

1. 12 N right

   20 − 8 = 12.

2. 0 N

   The forces balance.

3. No.

   Those forces are not along one common line.

Quick recap

• Choose a positive direction.
• Add signed forces along one axis.
• Report magnitude and direction.