# Unbalanced Force

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When two or more external forces acting on a body produce a net resultant force, i.e, the vector sum of forces is not zero, the forces are unbalanced.

## Newton’s Second Law of Motion

Newton’s Second Law of Motion says that the resultant force acting on a body produces a net acceleration and causes the body to accelerate in the direction of the resultant force.

• If the net resultant force is in the direction of the motion, the body will accelerate (positive acceleration).
• If the net resultant force is against the direction of motion, the body will decelerate (negative acceleration).

For a body of constant mass, Newton’s Second Law of Motion can be expressed as:

$$F = ma\tag{1}$$

, where

F = force
m = mass
a = acceleration

Since mass (m) is scalar quantity, the direction of acceleration (a) is thus in the same direction as the applied force (F).

To calculate the acceleration of a body, one should use Equation 1, with $F$ being the net resultant force exerted on the body.

Note:

All forces observed in nature can be explained in terms of four basic interactions that occur between elementary particles:

• Gravitational force
• Electromagnetic force
• Strong nuclear force
• Weak nuclear force

## Worked Examples

### A box of mass 20 kg is pushed with a force of 50 N. What is the acceleration of the box? Neglect the effects of friction.

From Newton’s Second Law,

\begin{aligned} F &= ma \\ a &= \frac{F}{m} \\ &= \frac{50}{20} \\ &= 2.5 \text{ m s}^{-2} \end{aligned}

### A car of mass 1000 kg accelerates from rest to $20 \text{ m s}^{-1}$ in 5 s. Calculate the driving force of the engine. (Neglect the effects of friction)

Let’s calculate the acceleration first.

\begin{aligned} a &= \frac{v-u}{t} \\ &= \frac{20-0}{5} \\ &= 4 \text{ m s}^{-2} \end{aligned}

From Newton’s Second Law,

\begin{aligned} F &= ma \\ &= 1000 \times 4 \\ &= 4000 \text{ N} \end{aligned}

## Additional notes on the four fundamental forces stated above:

(Not Important. Just for fun. 🙂 )

• The four forces are thought to be split off from one super-force.
• The Universe is thought to be created from a big bang. (The beginning of time and space)
• The Universe is very hot at the beginning and the particles in the Universe have a lot of energy.
• As time went by, the Universe cools.
• With the drop in the particles’ energy, the super-force split into the familiar four forces as observed today.