How To Calculate Force

The word force appears in practically every imaginable aspect of daily life, from sports to weather to military conflicts. But fundamentally, force is a concept rooted in physics, where is has a very specific and critical meaning. The standard unit of force is the newton (N), equal to kg ⋅ m/s².

Force is one of two quantities of physics that affect the motion of an object, the other being mass. The description of the motion of objects in space is called kinematics, which takes into account position, velocity and acceleration; including force and mass in the study of motion introduces the concept of dynamics.

Before learning about specific forces and how to do calculations involving this quantity, it is helpful to review the three basic laws of motion conceived by Isaac Newton:

1. Every object in a state of constant motion (including rest) will remain in that state unless acted on by external force.
2. Force is the product of mass and acceleration.
3. For every force, there exists a force opposite in direction and equal in magnitude.

Newton's second law is the one of greatest interest if you want to calculate force, or determine mass or acceleration if given information about the force and one of the other two quantities. Acceleration is a change in velocity.

You can think of a force as something that pushes or pulls; while helpful as a metaphor, however, this does not do much to advance your real-world understanding. Instead, a list that shows the range of natural forces is a better tool for becoming familiar with the forces you will use in your physics calculations.

Weight is a mysterious force that acts on all objects with mass and results from gravity, which at Earth's surface has a value of 9.8 meters per second squared (9.8 m/s²). Tension, elasticity, friction and the so-called normal force are forces that act on solids; buoyancy, lift, thrust and drag are forces uniquely associated with fluids (liquids and gases).

The electrostatic and magnetic forces are associated with charged particles. Also, nature includes four fundamental forces that give rise to all other forces. One of these is gravity, which is by far the weakest fundamental force; the others are electromagnetism and the strong and weak nuclear interactions in atoms.

The standard form of the force formula across physics states that the net external force on an object is the product of its mass and its acceleration:

\(\textbf{F} = m\textbf{a}\)

Here, force and acceleration are vector quantities, meaning that they have both a value (magnitude, represented by a number) and a direction in space associated with them. Mass is a scalar quantity, meaning it is described fully in terms of its magnitude.

A compact car with a mass of 1,000 kg is accelerating due north at 5 m/s². What is the force produced by this acceleration?

F = (1,000 kg)(5 m/s²) = 5,000 N.

The car eventually reaches a velocity of 40 m/s (about 90 miles per hour) and levels off at this speed. What is the external force on the car now?

This is a trick question of sorts. While a speeding car has plenty of momentum, if the car is not experiencing acceleration, both sides of the force equation are zero, and there is no net external force acting on the system, in this case consisting solely of the car. The physical quantity of greatest interest here, momentum, is the product of mass and velocity v (compare this to the force equation).