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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.

업데이트 검증한 예제: 6

시도하기
가속도
m/s²
가속도: 2 m/s²
유효 자릿수: 6; 가장 가까운 값, 중간값은 0에서 먼 쪽으로
Net force
3,000N
질량
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
계산 방법 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}

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

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.

계산 예제

3000 N on a 1500 kg car

Problem
F = ma
Solve for
가속도
Net force F
3000 N
Mass m
1500 kg
결과 단위
SI
가속도
2 m/s²

검증 출처: Python 3.8: a = F/m = 3000/1500

Force to give 2 kg an acceleration of 1 g

Problem
F = ma
Solve for
힘
Mass m
2 kg
Acceleration a
1 g
결과 단위
SI
Net force
19.6133 N

검증 출처: 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
질량
Net force F
100 lbf
Acceleration a
1 g
결과 단위
SI
질량
45.3592 kg

검증 출처: 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
결과 단위
SI
가속도
3.20476 m/s²
Normal force
84.9281 N
Friction force
16.9856 N
Block
Slides down

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

자주 묻는 질문

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.

“F = ma calculator: force, friction and inclined plane”의 정확도는 어느 정도인가요?

정확도는 입력값과 계산 방법의 가정에 따라 달라집니다. 십진 연산은 유효숫자 50자리를 사용하지만, 추정값·수치해석 방법·원본 데이터의 정밀도는 더 낮을 수 있습니다. 표시값을 반올림해도 이러한 한계는 사라지지 않습니다. 독립적인 출처의 풀이와 대조한 계산 예시: 6. 예를 들어 “3000 N on a 1500 kg car”은 Python 3.8: a = F/m = 3000/1500와 대조해 확인합니다.

이 계산 방법의 출처는 무엇인가요?

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

이 계산기 소개

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

출처

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

출처와 대조하여 검증

이 계산기에는 독립적인 출처에서 답을 얻은 계산 예제가 6개 있습니다. 테스트 모음에서 실행되며 여기에서도 실행할 수 있습니다.

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