Force Calculator

Newton's Second Law states that the force acting on an object equals its mass times its acceleration (F = ma). This means that for a constant mass, the acceleration is directly proportional to the net force. If you double the force, you double the acceleration. The law also implies that more massive objects require more force to achieve the same acceleration.

Mass is the amount of matter in an object, measured in kilograms (kg). It remains constant regardless of location. Weight is the force of gravity acting on that mass, measured in Newtons (N). Weight = mass × gravitational acceleration (W = mg). On Earth, g = 9.81 m/s². On the Moon (g = 1.62 m/s²), you'd weigh about 1/6 of your Earth weight, but your mass stays the same.

On an inclined plane, gravity splits into two components: parallel to the plane (causes sliding) and perpendicular (creates normal force). The parallel component is F_parallel = mg·sin(θ), where θ is the angle. The normal force is N = mg·cos(θ). If friction exists, friction force f = μ·N opposes motion. The net force down the plane is F_net = mg·sin(θ) - μ·mg·cos(θ).

Net force (resultant force) is the vector sum of all forces acting on an object. To calculate it, break each force into x and y components: Fx = F·cos(θ), Fy = F·sin(θ). Sum all x-components and all y-components separately. The net force magnitude is √((ΣFx)² + (ΣFy)²), and the direction is arctan(ΣFy/ΣFx).

The SI unit of force is the Newton (N), equal to 1 kg·m/s². Other common units include: kilonewtons (kN = 1000 N), pounds-force (lbf ≈ 4.45 N), kilograms-force (kgf = 9.81 N), and dynes (dyn = 0.00001 N). In everyday use, people often say 'kilograms' for weight, but scientifically that refers to kgf, not mass.

Friction is a force that opposes motion between surfaces in contact. Static friction (preventing motion) has maximum value f_s = μs·N. Kinetic friction (during motion) is f_k = μk·N. Typically μs > μk (it's harder to start moving than to keep moving). When calculating net force, subtract friction if the object is moving or about to move in the direction of applied force.

According to F = ma, acceleration a = F/m. For the same force, objects with larger mass have smaller acceleration (inertia). This is why it's easier to push an empty shopping cart than a full one. Inertia is an object's resistance to changes in motion, and it's directly related to mass.

Gravitational acceleration (g) varies by celestial body: Earth 9.81 m/s², Moon 1.62 m/s², Mars 3.72 m/s², Jupiter 24.79 m/s², Venus 8.87 m/s². This affects weight (W = mg) but not mass. A 70 kg person weighs 687 N on Earth, 113 N on the Moon, and 1735 N on Jupiter.