운동 에너지 공식 (KE = ½mv²): 무료 계산기 & 예제
계산 kinetic 에너지 with KE = ½mv², convert km/h safely, and rearrange for 질량 or 속력. Verify with a free kinetic 에너지 calculator.
What 운동 에너지 Means
운동 에너지 is the 에너지 an object has because it is moving. In school mechanics, the usual 공식 is KE = ½ m v². 질량 입력s once; 속력 입력s squared, so doubling the 속력 roughly quadruples the kinetic 에너지 when 질량 stays fixed.
That squared 속력 is why home일 answers swing so much when 속도 단위 are wrong. 변환 to metres per second and kilograms before you multiply, then report joules.
If you already have 질량 and 속력 and only need a 확인ed number, open the free kinetic 에너지 calculator first, then return here for unit traps and 일ed examples.
The 공식 KE = ½mv²
For a single particle or rigid body treated as a point 질량:
Rotational kinetic 에너지 ½ I ω² belongs to a different model. Use the linear form unless the question clearly asks for spinning 에너지 about an axis.
단위 That Keep Marks Safe
SI defaults for most 일sheets:
예제 trap: a car at 72 km/h is 20 m/s, not 72 m/s. Leaving km/h in the 공식 inflates KE by more than an order of magnitude because of the square.
풀이 예제
예제 1: 2.0 kg at 3.0 m/s
KE = ½ (2.0)(3.0)² = ½ (2.0)(9.0) = 9.0 J. Rough 확인: ½ × 2 × 9 = 9.
예제 2: find 속력 from 50 J
A 4.0 kg object has KE = 50 J. v = √(2 × 50 / 4.0) = √(25) = 5.0 m/s. 확인: ½ (4)(25) = 50 J.
예제 3: km/h conversion
A 0.50 kg ball moves at 36 km/h. First v = 36 / 3.6 = 10 m/s. KE = ½ (0.50)(10)² = 25 J. Skipping the conversion would wrongly use 36².
운동 에너지 vs 위치 에너지
운동 에너지 depends on motion (속력). Gravitational potential 에너지 near Earth depends on height: PE = m g h. A falling object converts PE into KE if other losses are ignored — but you still compute each 공식 with its own variables.
For height-based 에너지, see how to 계산 potential 에너지 and the matching PE calculator.
흔한 실수
Sanity 확인: everyday walking 속력s for a few kilograms of 질량 usually give tens of joules, not megajoules.
확인 With the 무료 계산기
The kinetic 에너지 calculator applies KE = ½mv² with visible steps so you can verify home일 rearrangements.
운동 에너지 calculator — KE, 질량, or 속력.
위치 에너지 calculator — PE = mgh.
속도 calculator — find v for 에너지 problems.
일 calculator — connect 힘 and 에너지 transfer.
학습 KE = ½mv² with clean SI 단위, then confirm every answer on the calculator.