Force Formula

In physics, force is defined as any push or pull acting on an object. The formula to calculate force is derived from Newton’s Second Law of Motion, which states:

Force (F) = Mass (m) × Acceleration (a)

This means that the force applied to an object depends on two things:

1. The mass of the object (in kilograms)
2. The acceleration it experiences (in meters per second squared)

Definition

Force is an interaction between two or more objects that can cause a change in motion, shape, or direction. In simple terms, force is what makes an object move, stop, speed up, slow down, or change direction.

The standard unit of force in the International System of Units (SI) is the Newton (N).

What is a Newton?

One Newton (N) is the amount of force needed to accelerate a 1-kilogram object by 1 meter per second squared (1 m/s²).

To relate it with common units:

1 Newton ≈ 0.22 pounds (lbs)

So, if someone weighs 100 lbs, their equivalent force due to Earth’s gravity (also called gravitational force, Fg) is: 100 lbs × 4.45= 445 Newtons

That means a girl who weighs 100 lbs exerts a gravitational force of about 445 N on the ground.

Newton’s First Law

The First Law of Motion by Newton says that every object persists to be in uniform motion in a straight line or in the state of rest unless an external force acts on it.

Newton’s Second Law

The second law of motion by Newton says that the force is equal to the change in momentum per change in the time. For a constant mass, force equals the mass times acceleration, i.e. F = m x a.

A vector equation is the modern statement of newton’s second law:

$\vec{F}$ = $\frac{\vec{dp}}{dt}$

Where:

$\vec{p}$ = momentum and $\\vec{p}$ = mv

If the time interval for the applied force increases, as a result, the value of the force applied decreases.

From newton’s second law of motion:

$\vec{F}$ ∝ $\frac{\vec{dp}}{dt}$
${\vec{F}}$ = K × $\frac{{\vec{dp}}}{dt}$ = ${\vec{kma}}$

For simplicity, the constant of proportionality (k) is decided to be 1, therefore:

$\vec{F} = \vec{ma}$

Newton’s Third Law

Every time a body exerts a force on another body, the latter simultaneously exerts an equal and opposite force on the first one. In vector form, if $F_{1,2}$ is the force of the body 1 on the body 2 and $F_{2,1}$ that of that of body 2 on body 1, then:

$F_{1,2} = -F_{2,1}$

In a system composed of object 1 and object 2, the net force on the system due to their mutual interactions is 0:

$F_{1,2}$ + $F_{2,1}$ = 0

Solved Examples on Force Formula

Example 1. A constant force acting on a body of mass 3.0 kg changes its speed from 2.0 m/s to 3.5m/s in 25 s. The direction of the motion of the body does not changes. What is the magnitude and what is the direction of the force?

Solution

Mass of the body, m = 3 kg
Initial speed of body, u = 2 m/s
Final speed of body, v = 3.5 m/s
Time, t = 25 s

Using the first equation of motion, the acceleration (a) produced in the body can be calculated as:

v = u+at

a = $\\frac{v-u}{t}$

= (3.5−2)/25 = 0.06m/s²

F = ma

= 3 × 0.06 = 0.18 N

Since the application of the force does not change the direction of the body, the net force acting on the body goes in the direction of its motion.

Example 2. A stream of water flowing horizontally with a speed $15ms^{-1}$ of gushes out of a tube of cross-sectional area $10^{_{-2}}m^{^{2}}$, and hits a vertical wall nearby. What is the force exerts on the wall by the water’s impact, assuming it does not rebound?

Solution

Speed of water stream, v = 15 m/s
The cross-sectional area of the tube, A = 10 m
The volume of water that comes out through the pipe per second,
V = A x v = 15 x 10 m /s
Density of water, = 10 kg/m
Mass of water that flows out in the pipe per second = density V = 150 kg/s
The water hits the wall and doesn’t rebound. Therefore, the force that the water exerts on the wall is given by

Newton’s second law of motion as:
F = Rate of change of momentum = P / t.
= mv / t
= 150 x 15 = 2250 N