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Newton's Second Law Calculator

Solve F = ma from any two values, with a force diagram and pitfalls

F=ma

Acceleration is proportional to the net force and inversely proportional to mass, along the direction of the net force.

Fill in any two of F, m and a; leave one blank to solve for it.

Net force F / NMass m / kgAcceleration a / m/s²

Mass unit

Acceleration a5 m/s²

On a frictionless horizontal surface the vertical forces cancel, so the net force is F.

WeightG = mg = 19.6 N

Normal forceN = G = 19.6 N

Net forceF合 = ma = 10 N

Steps

6 / 6

1Formula
$F=ma$
Newton's second law: net force equals mass times acceleration.
2Formula
$a=\frac{F}{m}$
Rearrange F = ma to isolate the unknown.
3Substitute
$a=\frac{10\ \mathrm{N}}{2\ \mathrm{kg}}$
Substitute the known values.
4Solve
$a=5\ \mathrm{m/s^2}$
Acceleration points along the net force.
5Check
$G=mg=2\times 9.8=19.6\ \mathrm{N}$
Weight follows: G = mg with g = 9.8 m/s².
6Note
$F_{\text{合}}=ma$
F is the net force: with several forces, add them as vectors first.

Concept

Newton's second law F = ma says the net force produces acceleration, along the force and inversely proportional to mass.

Mass measures inertia: the larger it is, the harder it is to change motion. Weight G = mg is the gravitational pull on that mass.

Going further

SI units: F = ma holds directly only with F in N, m in kg and a in m/s²; grams must be divided by 1000 first.
Apparent weight: In a lift accelerating upwards N = m(g + a) — apparently heavier; accelerating downwards N = m(g − a) — lighter; in free fall N = 0.
Connected bodies: For bodies moving together, treat the system as a whole to get the acceleration, then isolate one body to find internal forces.

Common mistakes

F in F = ma is the net force, not a single force — analyse the forces first.
Mass is a property of the body and does not change with location; weight G = mg does.
Use SI units: N, kg, m/s². Otherwise results are off by factors of 1000.
Acceleration follows the net force, not necessarily the velocity (they oppose when braking).

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