Mechanical Work by a Parallel Force

What you’ll learn

Calculate work when force and displacement are aligned.

គណនាកម្មន្តពេលកម្លាំងស្របនឹងបម្លាស់ទី។

Meaning and use

Mechanical work transfers energy when a force acts through displacement. For a constant force parallel to the displacement in the same direction, work is force times distance. A perpendicular force does no work on that displacement; an opposing force does negative work. The simple positive formula must not be applied blindly to any force.

កម្មន្តជាការផ្ទេរថាមពលដោយកម្លាំងតាមបម្លាស់ទី។ W=Fd វិជ្ជមានពេលកម្លាំងថេរស្របនិងទិសដូចគ្នា។ កម្លាំងកែងមិនធ្វើកម្មន្តតាមបម្លាស់ទីនោះទេ។

Formulas

Constant aligned force

\[W=Fd\]

Opposing aligned force

\[W=-Fd\]

Symbols and units

Symbol	Meaning	Unit or restriction
W	Mechanical work	joule (J)
F	Constant force magnitude	N
d	Displacement distance along the force line	m

Conditions and limits

• Use W = Fd only for a constant force aligned with the displacement.
• Forces at other angles need the component along the displacement.
• ក្នុងមេរៀននេះ W ជានិមិត្តសញ្ញាកម្មន្ត; ឯកតាវ៉ាត់ក៏សរសេរ W ប៉ុន្តែន័យខុសគ្នា។

Worked examples

A push

A constant 20 N force pushes a box 3 m in the same direction.

1. Use \(W=Fd\).
2. Calculate \(20\times3=60\) J.

60 J

កម្លាំង និងបម្លាស់ទីស្របគ្នា ដូច្នេះប្រើផលគុណបាន។

Work against motion

A 5 N resistive force acts opposite a 4 m displacement.

1. Use a negative sign for the opposite direction.
2. Calculate \(W=-5\times4=-20\) J.

−20 J

សញ្ញាអវិជ្ជមានបង្ហាញកម្លាំងយកថាមពលពីចលនានោះ។

Common mistakes

Instead of	Use	Why
A force always does work if it acts for a long time.	Work also requires displacement along the force component.	Time alone does not determine mechanical work.
An opposing force does positive Fd.	Its work is negative in this signed convention.	Direction matters.

Practice

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

សាកល្បងដោះស្រាយមុនបើកមើលចម្លើយ។ សូមបង្ហាញជំហាន និងឯកតាដែលពាក់ព័ន្ធ។

1. Find work for 12 N pushing 5 m in the same direction.
2. A person holds a stationary bag. What work does the upward holding force do on the bag’s zero displacement?
3. Find work by 3 N resistance over 2 m.

Answers and steps

Show solutions / បង្ហាញដំណោះស្រាយ

1. 60 J

   12 × 5 = 60.

2. 0 J

   Mechanical displacement is zero, even though the person can become tired.

3. −6 J

   The force is opposite the displacement.

Quick recap

• Check force direction and displacement.
• Use joules for work.
• Opposing forces can do negative work.