Kinetic Energy

What you’ll learn

Relate motion energy to mass and squared speed.

ភ្ជាប់ថាមពលស៊ីនេទិចទៅម៉ាស និងការ៉េល្បឿន។

Meaning and use

For ordinary nonrelativistic translational motion, kinetic energy is one half mass times speed squared. Squaring the speed makes its effect nonlinear: doubling speed quadruples this energy for fixed mass. The value depends on the reference frame used to measure speed.

ថាមពលស៊ីនេទិចនៃចលនាបម្លាស់ទីស្មើពាក់កណ្ដាលម៉ាសគុណការ៉េល្បឿន។ បើល្បឿនកើនពីរដង ថាមពលកើនបួនដង ពេលម៉ាសថេរ។

Formulas

Translational kinetic energy

\[E_k=\frac12mv^2\]

Rearrangement for nonnegative speed

\[v=\sqrt{\frac{2E_k}{m}}\]

Symbols and units

Symbol	Meaning	Unit or restriction
Ek	Translational kinetic energy	J
m	Positive mass	kg
v	Speed in the stated reference frame	m/s

Conditions and limits

• Use ordinary speeds far below the speed of light.
• The formula concerns translational energy; rotation can add other kinetic energy.
• ល្បឿនជា m/s មុនលើកការ៉េ។

Worked examples

Energy of motion

A 2 kg object moves at 3 m/s.

1. Square speed: \(3^2=9\).
2. Calculate \(E_k=\frac12\times2\times9=9\) J.

9 J

ត្រូវលើកការ៉េល្បឿន មិនមែនម៉ាសទេ។

A speed change

The same 2 kg object speeds up to 6 m/s.

1. Calculate \(E_k=\frac12\times2\times36=36\) J.
2. Compare \(36/9=4\).

36 J, four times the earlier energy

ល្បឿនពីរដងធ្វើឱ្យថាមពលបួនដង។

Common mistakes

Instead of	Use	Why
Ek = mv/2.	Ek = mv²/2.	The speed must be squared.
Doubling speed doubles kinetic energy.	It quadruples kinetic energy for fixed mass.	The speed dependence is quadratic.

Practice

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

សាកល្បងដោះស្រាយមុនបើកមើលចម្លើយ។ សូមបង្ហាញជំហាន និងឯកតាដែលពាក់ព័ន្ធ។

1. Find kinetic energy for 4 kg at 5 m/s.
2. Find speed for Ek = 18 J and m = 4 kg.
3. If mass doubles at fixed speed, what happens to Ek?

Answers and steps

Show solutions / បង្ហាញដំណោះស្រាយ

1. 50 J

   One half × 4 × 25 = 50.

2. 3 m/s

   √(2 × 18/4) = √9.

3. It doubles.

   Ek is directly proportional to mass.

Quick recap

• Square the speed before multiplying.
• Use kg and m/s for joules.
• Distinguish mass scaling from speed scaling.