Little BASICS

Before exploring Newton’s laws, we must revisit the following concepts.

1.      BALANCED AND UNBALANCED FORCES

There are two types of forces based upon the effect they produce on the object when it is applied to it.

1.    Balanced forces: It refers to forces that do not bring any change in the state of rest or uniform motion of the object.

a.    When the object is at rest: Say, as shown in the figure below, two persons are applying a force of 5N (read as 5 Newton) against each other on a box that is at rest. In such cases, since the forces are of equal magnitudes (size) and are acting opposite to each other, it does not produce any effect on the object because the forces acting on it get canceled out. In other words, the box remains at rest only though forces are acting on it. Such forces, which do not change the state of the object at rest are called balanced forces.

a.    When the object is moving with a uniform (same/constant) motion: Similarly, if the same amount of force is applied against each other on an object moving with a uniform speed, the forces will not produce any effect on the box. Such forces, which do not change the state of the object in motion are called balanced forces.

2. Unbalanced forces: It refers to forces that bring changes in the state of rest or uniform motion of the object.

a.    When the object is at rest: If two forces of different magnitudes are acting opposite to each other, as shown in the figure below, then the object moves in the direction of greater force.

In this case, the object moves in the direction of 8N (in the direction of greater force) with a total force of 3N.

a.    When the object is moving with a uniform motion: When unbalanced forces act on a moving object, it can change the direction, increase or decrease speed, or stop moving objects.

GENERALIZATION:

1.    Balanced forces do not bring change to the state of the object whether it is at resting or moving at a constant speed.

2.    Unbalanced forces being change to the state of the body at rest or moving with a uniform speed.

In general, it can bring about the following changes:

                                                  i.        make rest object move,

                                                ii.        change the shape of the object,

                                               iii.        change the direction of moving object,

                                               iv.        increase or decrease the speed of the moving object, and

                                                 v.        stop moving objects.

2.      INTERPRETATION OF THE SIMPLE EQUATIONS

There are numerous equations in physics. Generally, in physics, equations are used to meet the following three purposes:

 1. To represent the main information using symbols 

Let us take velocity for example. 

Definition: Speed is defined as the rate of change of distance.

2. To find the unit for the subject of the formula (refers to a single variable that everything else is equal to) 

In this case, speed is the subject of the formula. Usually, the subject of the formula lies on the left-hand side of the equation. 

Let us find out the unit for speed. To do that, we need to write the formula first.

Now, since we are looking out for unit for speed, our formula becomes like this:

Now we have to write the SI unit of distance and time. The SI unit for distance is metres (represented by small/lower-case letter, ‘m’) and for time is seconds (represented by small letter, ‘s’)

It is important to note that in physics, units are not written as fractions instead it is written as follows:

It is read as, metre per second.

1. Constructing the relationship between the quantities.

Generally, LHS of the equation depends on the RHS of the equation. That is, in the above case, we can conclude that speed depends upon distance and time. The left side of the equation is referred to as, ‘subject of the formula’.

The relation is such that, any change in the magnitude of variables on RHS will affect the magnitude of a variable in LHS of the equation.

1.    The subject of the formula will directly depend upon the variable holding the numerator     position in the RHS of the equation provided variable in the denominator remains constant.

That is, in our case, the subject of the formula is ‘speed’, the variable numerator position is ‘distance’ and constant variable in the denominator is ‘time’. The dependence will be such that, if the distance is increased, it is only intuitive that speed will have been naturally increased because time remains the same. The case will be opposite if the distance is decreased. 

In such a case, we say that speed is directly proportional to the distance (provided time is constant). 

This kind of direct dependence is represented as:

Where ∝ is the proportionality symbol.

The meaning stands the same, that is when the distance is increased speed will also be increased and vice-versa. 

The subject of the formula will depend inversely upon the variable holding the denominator position in the RHS of the equation provided the variable in the numerator remains constant.

That is, in our case, the subject of the formula is ‘speed’, the variable denominator position is ‘time’ and the constant variable is ‘distance’ which holds the numerator position. The dependence will be such that, if time is increased, speed will have been naturally decreased because distance remains the same. The case will be the opposite if the time is decreased.

In such a case, we sat that speed is inversely proportional to time (provided distance is constant).

This kind of direct dependence is represented as:

speed∝1/time

The meaning stands the same, that is when speed is increased time taken will also decrease and vice-versa (of course there are few things to consider here but in general, this is how we interpret the equation).