What Is Force?
Force is an interaction that, when unopposed, changes the motion of an object. Forces can cause a stationary object to start moving, a moving object to accelerate or decelerate, or an object to change direction. The SI unit is the newton (N), defined as the force needed to accelerate 1 kg by 1 m/s².
Forces are vectors: they have both magnitude and direction. Multiple forces acting on an object combine through vector addition to produce a net (resultant) force. An object is in equilibrium when the net force is zero.
F = ma (Newton’s Second Law)
The net force on an object equals its mass times its acceleration. This is the most fundamental equation in classical mechanics. It connects the cause (force) with the effect (acceleration) for a given mass.
W = mg (Weight Force)
Weight is the gravitational force on an object: mass times the local gravitational acceleration. On Earth, g ≈ 9.81 m/s². On the Moon, g ≈ 1.62 m/s², so objects weigh about one-sixth as much.
F = kx (Hooke’s Law)
The restoring force of an ideal spring is proportional to its displacement from equilibrium. The spring constant k (in N/m) characterises the stiffness. This law is valid only within the elastic limit.
F = μN (Friction Force)
Friction force depends on the coefficient of friction (μ) and the normal force (N). Static friction prevents motion (μₛ) and is typically larger than kinetic friction (μₖ), which acts during sliding.
F = mv²/r (Centripetal Force)
An object moving in a circle of radius r at speed v requires a centripetal (centre-seeking) force directed toward the centre. This force doesn’t do work — it only changes the direction of velocity.
How to Use the Calculator
- Select the force formula that matches your known quantities.
- Enter values and choose units.
- Click Calculate.
- Review the result, formula substitution, and interpretation.
Example Calculations
5 kg at 2 m/s\u00B2 (F = ma)
F = 5 × 2 = 10 N
70 kg on Earth (Weight)
W = 70 × 9.81 = 686.5 N ≈ 154.3 lbf
k = 200 N/m, x = 0.1 m (Spring)
F = 200 × 0.1 = 20 N
\u03BC = 0.3, N = 100 N (Friction)
F = 0.3 × 100 = 30 N
2 kg, 5 m/s, r = 10 m (Centripetal)
F = 2 × 25 / 10 = 5 N
Common Mistakes
- Confusing mass (kg) with weight (N).
- Forgetting that F = ma gives the net force, not an individual force.
- Assuming friction coefficient is always less than 1.
- Using the wrong normal force on an inclined surface.
- Ignoring that centripetal force is not a separate force but the net inward force.
Accuracy and Limitations
These formulas are for constant forces and point-mass approximations in classical mechanics. They do not account for air resistance, variable friction, elastic limits, relativistic speeds, or complex geometries. This tool is for education and estimation — always verify with authoritative engineering calculations for critical applications.
FAQ
What is force in physics?›
Force is an interaction that changes an object’s velocity. It has magnitude and direction (a vector). The SI unit is the newton (N) = kg·m/s².
What is Newton’s second law?›
F = ma states that the net force on an object equals its mass times its acceleration. It’s the core equation linking force, mass, and motion.
What is the difference between mass and weight?›
Mass (kg) is the amount of matter in an object and doesn’t change with location. Weight (N) is the gravitational force: W = mg. On the Moon, weight is about 1/6 of Earth weight.
What are the four fundamental forces?›
Gravity, electromagnetism, the strong nuclear force, and the weak nuclear force. All forces in everyday mechanics reduce to gravity and electromagnetism at the microscopic level.
Can friction coefficient be greater than 1?›
Yes. Rubber on rubber can have μ > 1. The coefficient is not a ratio of force to weight in the strict 0–1 sense; it’s determined experimentally.
What is centripetal vs centrifugal force?›
Centripetal force is the real inward force that keeps an object on a curved path. Centrifugal force is a fictitious force felt in a rotating reference frame.
Does Hooke’s law apply to all springs?›
Only within the elastic limit. Once a spring is stretched beyond that point, it deforms permanently and F = kx no longer holds.
How do I add forces as vectors?›
Use vector addition: break each force into x and y components, sum the components separately, then find the magnitude and direction of the resultant.
Sources
Author & technical reviewer
Manish Kumar
PhysicsCalcs tools are reviewed with an educational focus: clear formulas, transparent assumptions, and practical context for students and science learners.
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