# Kinetic and potential energy, work and power calculator

> Kinetic energy (½mv²), potential energy (mgh), spring energy, work (Fd cos θ) and power (W/t), solved for any variable, plus the speed after a drop.

Phiên bản tương tác: https://www.calcopenly.com/vi/science/work-energy-power-calculator
Chủ đề: Máy tính khoa học theo chủ đề

Six formulas cover the common mechanical-energy problems: kinetic energy ½mv², gravitational potential energy mgh, spring energy ½kx², work Fd cos θ, average power W ÷ t, and the speed after a frictionless drop, √(v₀² + 2gh). Pick one, choose the variable to solve for, and the others become inputs.

Energy comes out in joules, with the kilowatt-hour equivalent beside it from 1 Wh (3,600 J) up; 1 kWh = 3.6 MJ. The default, a 1,000 kg car at 20 m/s (72 km/h), carries 200,000 J, or 0.0556 kWh; at 40 m/s it would carry four times as much.

Potential energy is measured from whichever level you call h = 0, so only differences in height matter. The drop mode ignores friction and air resistance, which makes its speeds an upper limit for real falls.

## Dữ liệu đầu vào

- **Quantity** (lựa chọn: Kinetic energy ½mv², Gravitational potential energy mgh, Spring energy ½kx², Work W = Fd·cos θ, Power P = W/t, Speed at the bottom of a drop)
- **Solve for** (lựa chọn: Năng lượng, Khối lượng, Tốc độ)
- **Solve for** (lựa chọn: Năng lượng, Khối lượng, Chiều cao)
- **Solve for** (lựa chọn: Năng lượng, Spring constant, Extension)
- **Solve for** (lựa chọn: Work, Lực, Distance)
- **Solve for** (lựa chọn: Công suất, Work or energy, Thời gian)
- **Solve for** (lựa chọn: Speed at the bottom, Drop height)
- **Energy or work**
- **Khối lượng**
- **Tốc độ**
- **Chiều cao**
- **Spring constant k**
- **Extension or compression x**
- **Lực**
- **Distance moved**
- **Angle between force and motion**
- **Thời gian**
- **Công suất**
- **Speed at the top**
- **Speed at the bottom**
- **Gravitational acceleration**

## Kết quả

- Energy or work (J) — kết quả chính
- Công suất (W)
- Speed at the bottom (m/s)
- Khối lượng (kg)
- Tốc độ (m/s)
- Chiều cao (m)
- Spring constant (N/m)
- Extension (m)
- Lực (N)
- Distance (m)
- Thời gian (s)
- Energy or work (kWh)

## Công thức

$$
KE = \tfrac12 mv^2,\quad PE = mgh,\quad E_s = \tfrac12 kx^2,\quad W = Fd\cos\theta,\quad P = \frac{W}{t},\quad v_b = \sqrt{v_0^2 + 2gh}
$$

## Ví dụ có lời giải

### 1000 kg car at 20 m/s

- Quantity: Kinetic energy ½mv²
- Solve for: Năng lượng
- Khối lượng: 1000 kg
- Tốc độ: 20 m/s
- **Energy or work: 200,000 J**
- **Energy or work: 0.055556 kWh**
- Nguồn đối chiếu: Python 3.8 decimal: ½ × 1000 × 20² = 200000 J = 0.0555… kWh

### Speed of a 0.145 kg ball carrying 100 J

- Quantity: Kinetic energy ½mv²
- Solve for: Tốc độ
- Energy or work: 100 J
- Khối lượng: 0.145 kg
- **Tốc độ: 37.1391 m/s**
- Nguồn đối chiếu: Python 3.8 decimal: v = √(2E/m) = √(200/0.145) = 37.1390676…

### 50 kg lifted 10 m

- Quantity: Gravitational potential energy mgh
- Solve for: Năng lượng
- Khối lượng: 50 kg
- Chiều cao: 10 m
- **Energy or work: 4,903.33 J**
- Nguồn đối chiếu: Python 3.8 decimal: 50 × 9.80665 × 10

### Spring k = 200 N/m compressed 10 cm

- Quantity: Spring energy ½kx²
- Solve for: Năng lượng
- Spring constant k: 200 N/m
- Extension or compression x: 10 cm
- **Energy or work: 1 J**
- Nguồn đối chiếu: Python 3.8 decimal: ½ × 200 × 0.1² = 1 J

### 100 N at 60° over 5 m

- Quantity: Work W = Fd·cos θ
- Solve for: Work
- Lực: 100 N
- Distance moved: 5 m
- Angle between force and motion: 60 °
- **Energy or work: 250 J**
- Nguồn đối chiếu: Python 3.8 math: 100 × 5 × cos60° = 250 J

### Force perpendicular to motion does no work

- Quantity: Work W = Fd·cos θ
- Solve for: Work
- Lực: 100 N
- Distance moved: 5 m
- Angle between force and motion: 90 °
- **Energy or work: 0 J**
- Nguồn đối chiếu: W = Fd cos 90° = 0 (OpenStax UP1 §7.1)

## Câu hỏi

### What is the formula for kinetic energy?

Kinetic energy is KE = ½mv²; with mass in kilograms and speed in metres per second the result is in joules. Because speed is squared, doubling it quadruples the energy: a 1,000 kg car has 200 kJ at 20 m/s and 800 kJ at 40 m/s. Rearranged for speed, v = √(2KE ÷ m), so a 0.145 kg ball carrying 100 J moves at 37.1 m/s.

### What is the difference between work and power?

Work is energy transferred by a force, W = Fd cos θ, measured in joules; power is how fast that transfer happens, P = W ÷ t, measured in watts, where 1 W = 1 J/s. Lifting 50 kg through 10 m takes 4,903 J however it is done; doing it in 5 s needs 981 W, and spreading it over 60 s needs 81.7 W.

### How many joules are in a kilowatt-hour or a kilocalorie?

One kilowatt-hour is 3,600,000 J, because it is 1,000 W sustained for 3,600 s. One kilocalorie, the food Calorie, is 4,184 J, using the thermochemical calorie of exactly 4.184 J listed in NIST SP 811. The 200,000 J carried by a 1,000 kg car at 20 m/s is therefore 0.0556 kWh, or about 47.8 kcal.

### How fast does an object hit the ground when dropped?

Without air resistance the impact speed is v = √(2gh), whatever the mass. A drop from 20 m ends at 19.81 m/s (71.3 km/h); a drop from 5 m ends at 9.90 m/s. Speed grows with the square root of height, so four times the height only doubles the speed. Air drag makes real speeds lower, most of all for light objects and long falls.

### How much energy does a spring store?

A spring stores E = ½kx², where k is the spring constant in N/m and x the extension or compression in metres. A 200 N/m spring compressed by 10 cm stores 1 J; compressed by 20 cm it stores 4 J. The formula holds only within the elastic range, where Hooke's law F = kx applies and the spring returns to its original length.

### “Kinetic and potential energy, work and power calculator” chính xác đến mức nào?

Độ chính xác phụ thuộc vào dữ liệu nhập và giả định của phương pháp. Phép tính thập phân dùng 50 chữ số có nghĩa, nhưng ước lượng, phương pháp số và dữ liệu nguồn có thể kém chính xác hơn; làm tròn khi hiển thị không loại bỏ các giới hạn đó. Ví dụ có lời giải đã đối chiếu với nguồn độc lập: 8. Ví dụ, “1000 kg car at 20 m/s” được kiểm tra bằng Python 3.8 decimal: ½ × 1000 × 20² = 200000 J = 0.0555… kWh.

### Phương pháp này lấy từ đâu?

OpenStax University Physics Volume 1, ch. 7 Work and kinetic energy; ch. 8 Potential energy and conservation of energy; HyperPhysics — Work, energy and power.

## Nguồn

- [OpenStax University Physics Volume 1, ch. 7 Work and kinetic energy; ch. 8 Potential energy and conservation of energy](https://openstax.org/books/university-physics-volume-1/pages/7-introduction)
- [HyperPhysics — Work, energy and power](http://hyperphysics.phy-astr.gsu.edu/hbase/work.html)