# F = ma calculator: force, friction and inclined plane

> Solve Newton's second law F = ma for force, mass or acceleration, or find acceleration, normal force and friction for a block on an inclined plane.

النسخة التفاعلية: https://www.calcopenly.com/ar/science/force-friction-incline-calculator
الموضوع: حاسبات العلوم

Newton's second law says the net force on a body equals its mass times its acceleration, F = ma, so one newton gives 1 kg an acceleration of 1 m/s². Enter two of force, mass and acceleration to get the third. The inclined-plane mode splits the block's weight into mg sin θ down the slope and mg cos θ into it; the normal force balances the second part, and kinetic friction μk × N opposes the sliding.

The default, 3,000 N on a 1,500 kg car, gives 2 m/s², about 0.2 g. On the slope, a 10 kg block on a 30° incline with μk = 0.2 slides down at 3.20 m/s² against 16.99 N of friction.

Friction coefficients depend on both surfaces and their condition, so treat slope results as estimates. The block stays put while tan θ is at or below the static coefficient μs; leave μs blank and μk is used as that threshold.

## المدخلات

- **Problem** (الخيارات: F = ma, Inclined plane)
- **Solve for** (الخيارات: القوة, الكتلة, التسارع)
- **Net force F**
- **Mass m**
- **Acceleration a**
- **Block mass**
- **Incline angle**
- **Kinetic friction coefficient μk**: Approximate kinetic values from OpenStax University Physics Table 6.1
- **Static friction coefficient μs**: Leave blank to use μk as the threshold for starting to slide
- **Gravitational acceleration**
- **وحدة النتائج** (الخيارات: SI, US customary)

## النتائج

- التسارع (m/s²) — النتيجة الرئيسية
- Net force (N)
- الكتلة (kg)
- Block
- Normal force (N)
- Friction force (N)
- Weight component down the slope (N)
- Weight (N)
- Angle at which it starts to slide (°)

## الصيغة

$$
F = ma;\qquad N = mg\cos\theta,\quad a = g(\sin\theta - \mu_k\cos\theta)\ \text{when } \tan\theta > \mu_s
$$

## أمثلة محلولة

### 3000 N on a 1500 kg car

- Problem: F = ma
- Solve for: التسارع
- Net force F: 3000 N
- Mass m: 1500 kg
- وحدة النتائج: SI
- **التسارع: 2 m/s²**
- مصدر التحقق: ⁨Python 3.8: a = F/m = 3000/1500⁩

### Force to give 2 kg an acceleration of 1 g

- Problem: F = ma
- Solve for: القوة
- Mass m: 2 kg
- Acceleration a: 1 g
- وحدة النتائج: SI
- **Net force: 19.6133 N**
- مصدر التحقق: ⁨Python 3.8: 2 × 9.80665 = 19.6133⁩

### 100 lbf gives 1 g: mass is 100 lb (45.359237 kg)

- Problem: F = ma
- Solve for: الكتلة
- Net force F: 100 lbf
- Acceleration a: 1 g
- وحدة النتائج: SI
- **الكتلة: 45.3592 kg**
- مصدر التحقق: ⁨Definition of the pound-force (NIST SP 811 B.8): 1 lbf = 0.45359237 kg × 9.80665 m/s²⁩

### 10 kg block on a 30° slope, μk = 0.2

- Problem: Inclined plane
- Block mass: 10 kg
- Incline angle: 30 °
- Kinetic friction coefficient μk: 0.2
- وحدة النتائج: SI
- **التسارع: 3.20476 m/s²**
- **Normal force: 84.9281 N**
- **Friction force: 16.9856 N**
- **Block: Slides down**
- مصدر التحقق: ⁨Python 3.8 math: N = mg cos30° = 84.92808…, f = 0.2N, a = g(sin30° − 0.2 cos30°) = 3.2047634⁩

### Static friction holds (μs = 0.7 > tan 30°)

- Problem: Inclined plane
- Block mass: 10 kg
- Incline angle: 30 °
- Kinetic friction coefficient μk: 0.5
- Static friction coefficient μs: 0.7
- وحدة النتائج: SI
- **التسارع: 0 m/s²**
- **Friction force: 49.0333 N**
- **Block: Stays at rest**
- **Angle at which it starts to slide: 34.99 °**
- مصدر التحقق: ⁨Python 3.8 math: tan30° = 0.577 < 0.7, friction = mg sin30° = 49.03325 N; atan(0.7) = 34.992°⁩

### Frictionless slope

- Problem: Inclined plane
- Block mass: 5 kg
- Incline angle: 45 °
- Kinetic friction coefficient μk: 0
- وحدة النتائج: SI
- **التسارع: 6.93435 m/s²**
- **Friction force: 0 N**
- مصدر التحقق: ⁨Python 3.8 math: a = g sin45° = 6.9343487⁩

## الأسئلة

### What is one newton of force?

One newton is the force that gives a 1 kg mass an acceleration of 1 m/s², so 1 N = 1 kg·m/s² in the SI. A 1 kg mass weighs 9.80665 N under standard gravity, and one pound-force is exactly 4.4482216152605 N (NIST SP 811). A 100 lbf push that accelerates an object at 1 g therefore means a mass of 100 lb, or 45.36 kg.

### How do you calculate the friction force?

Friction equals the coefficient of friction times the normal force, f = μN. On level ground N = mg, so a 10 kg crate with μk = 0.2 needs a 19.61 N push to keep sliding at constant speed. Static friction is a limit, not a fixed value: it matches the applied force up to μs × N, and the object starts to move once that limit is passed.

### At what angle does an object start to slide down a slope?

It starts to slide once the slope angle exceeds arctan μs, the point where the pull down the slope, mg sin θ, overtakes the most static friction can supply, μs mg cos θ. With μs = 0.7 that angle is 34.99°; with μs = 0.2 it is 11.31°. Tilting a surface until an object slips and reading the angle is a standard way to measure μs.

### What are typical coefficients of friction?

OpenStax University Physics Table 6.1 gives approximate values, static then kinetic: rubber on dry concrete 1.0 and 0.7, wood on wood 0.5 and 0.3, ice on ice 0.1 and 0.03. Real values shift with surface finish, moisture and temperature, so a measured coefficient beats a table value. The kinetic coefficient is lower than the static one for each of these pairs.

### Does a heavier block slide down a slope faster?

No. Mass cancels in a = g(sin θ − μk cos θ), because both the pull down the slope and the friction are proportional to the weight. A 5 kg block and a 50 kg block on a frictionless 45° slope both accelerate at 6.93 m/s². Differences seen in practice come from air resistance and from friction coefficients that change with load or speed.

### ما مدى دقة «⁨F = ma calculator: force, friction and inclined plane⁩»؟

تعتمد الدقة على مدخلاتك وافتراضات الطريقة. يستخدم الحساب العشري 50 رقمًا معنويًا، لكن التقديرات والأساليب العددية وبيانات المصدر قد تكون أقل دقة؛ تقريب القيم المعروضة لا يزيل هذه الحدود. أمثلة محلولة جرى التحقق منها بمصادر مستقلة: 6. مثلًا، يجري التحقق من «⁨3000 N on a 1500 kg car⁩» بالرجوع إلى ⁨Python 3.8: a = F/m = 3000/1500⁩.

### ما مصدر هذه الطريقة؟

OpenStax University Physics Volume 1, §5.3 Newton's second law and §6.2 Friction; HyperPhysics — Inclined plane with friction.

## المصادر

- [OpenStax University Physics Volume 1, §5.3 Newton's second law and §6.2 Friction](https://openstax.org/books/university-physics-volume-1/pages/6-2-friction)
- [HyperPhysics — Inclined plane with friction](http://hyperphysics.phy-astr.gsu.edu/hbase/Mechanics/incline.html)