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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.

Обновлено Проверенные примеры: 6

Попробовать
Ускорение
m/s²
Ускорение: 2 m/s²
Значащих цифр: 6; До ближайшего, при равенстве — от нуля
Net force
3,000N
Масса
1,500kg
Weight
14,710N

A net force of 3,000 N on 1,500 kg gives an acceleration of 2 m/s² (0.2039 g).

Net force and acceleration

1,500 kgF = 3,000 Na = 2 m/s²
Как выполняется расчёт S

  1. Newton's second law

    a=Fm=3,0001,500=2 m/s2a = \frac{F}{m} = \frac{3{,}000}{1{,}500} = 2\ \mathrm{m/s^2}

  2. Weight on Earth for comparison

    W=mgn=(1,500)(9.80665)=14,710 NW = mg_n = (1{,}500)(9.80665) = 14{,}710\ \mathrm{N}

О калькуляторе: F = ma calculator: force, friction and inclined plane

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.

Примеры с решением

3000 N on a 1500 kg car

Problem
F = ma
Solve for
Ускорение
Net force F
3000 N
Mass m
1500 kg
Единица результатов
SI
Ускорение
2 m/s²

Источник проверки: Python 3.8: a = F/m = 3000/1500

Force to give 2 kg an acceleration of 1 g

Problem
F = ma
Solve for
Сила
Mass m
2 kg
Acceleration a
1 g
Единица результатов
SI
Net force
19.6133 N

Источник проверки: 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
Масса
Net force F
100 lbf
Acceleration a
1 g
Единица результатов
SI
Масса
45.3592 kg

Источник проверки: 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
Единица результатов
SI
Ускорение
3.20476 m/s²
Normal force
84.9281 N
Friction force
16.9856 N
Block
Slides down

Источник проверки: Python 3.8 math: N = mg cos30° = 84.92808…, f = 0.2N, a = g(sin30° − 0.2 cos30°) = 3.2047634

Вопросы

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.

Насколько точен «F = ma calculator: force, friction and inclined plane»?

Точность зависит от введённых данных и допущений метода. Десятичная арифметика использует 50 значащих цифр, но оценки, численные методы и исходные данные могут быть менее точными; округление на экране не устраняет эти ограничения. Решённые примеры, проверенные по независимым источникам: 6. Например, «3000 N on a 1500 kg car» проверяется по источнику Python 3.8: a = F/m = 3000/1500.

Откуда взята методика?

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

Об этом калькуляторе

F=ma;N=mgcos⁡θ,a=g(sin⁡θ−μkcos⁡θ) when tan⁡θ>μsF = ma;\qquad N = mg\cos\theta,\quad a = g(\sin\theta - \mu_k\cos\theta)\ \text{when } \tan\theta > \mu_s

Источники

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

Проверено по источникам

В калькулятор включены решённые примеры с ответами из независимых источников. Их количество: 6. Они входят в набор тестов, и вы также можете запустить их здесь.

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