Force Calculator
☰

Force Calculator

Force in Physics

Force is a fundamental concept in physics, described as any interaction that, when unopposed, changes the motion of an object. It is a vector quantity, meaning it has both magnitude and direction.

Basic Formula for Force

The most commonly used formula for force is Newton's Second Law of Motion:

F = ma

Where:

  • F is the force applied (measured in Newtons, N)
  • m is the mass of the object (measured in kilograms, kg)
  • a is the acceleration of the object (measured in meters per second squared, m/s2)

Other Equivalent Formulas

Gravitational Force

F = G (m1 m2) / r2

Where:

  • G is the gravitational constant (6.67430 × 10-11 N m2 / kg2)
  • m1 and m2 are the masses of the two objects
  • r is the distance between the centers of the two masses

Frictional Force

Ff = μN

Where:

  • Ff is the frictional force
  • μ is the coefficient of friction
  • N is the normal force

Centripetal Force

Fc = mv2 / r

Where:

  • Fc is the centripetal force
  • m is the mass of the object
  • v is the velocity of the object
  • r is the radius of the circular path

Examples

Example 1: Using Newton's Second Law

A 5 kg object is subjected to an acceleration of 3 m/s2. Calculate the force applied.

F = ma
F = 5 kg × 3 m/s2
F = 15 N

Example 2: Gravitational Force between Two Masses

Calculate the gravitational force between two 10 kg masses separated by a distance of 2 meters.

F = G (m1 m2) / r2
F = (6.67430 × 10-11 N m2 / kg2) (10 kg × 10 kg) / (2 m)2
F = (6.67430 × 10-11) 100 / 4
F = (6.67430 × 10-11) × 25
F = 1.668575 × 10-9 N

Example 3: Frictional Force on a Flat Surface

A block with a mass of 10 kg is on a flat surface with a coefficient of friction μ of 0.5. Calculate the frictional force.

N = mg
N = 10 kg × 9.8 m/s2
N = 98 N

Ff = μN
Ff = 0.5 × 98 N
Ff = 49 N

Example 4: Centripetal Force for Circular Motion

A car of mass 1000 kg is moving at a speed of 20 m/s around a circular track of radius 50 meters. Calculate the centripetal force.

Fc = mv2 / r
Fc = 1000 kg × (20 m/s)2 / 50 m
Fc = 1000 × 400 / 50
Fc = 400000 / 50
Fc = 8000 N

Summary Table

Force Type Formula Example Result
Newton's Second Law F = ma F = 15 N
Gravitational Force F = G (m1 m2) / r2 F = 1.668575 × 10-9 N
Frictional Force Ff = μN Ff = 49 N
Centripetal Force Fc = mv2 / r Fc = 8000 N