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Force and Laws of Motion

Chapter: Force and Laws of Motion

In our everyday life, we observe that some effort is required to put a stationary object into motion or to stop a moving object. We generally experience this as a muscular effort and say that we must push or hit or pull an object to change its state of motion. The concept of force is based on this push, hit or pull. Let us now ponder about ‘force’. 

What is force?

Actually, no one has seen, tasted or ever felt force. Nevertheless, we always see or feel the effect of force. It can be explained by describing what happens when force is applied to an object. Pushing, throwing, hitting and Pulling of objects are all, ways of bringing objects in motion. They move because we make force to act on them.

Balanced and Unbalanced Forces

Let us assume a wooden block placed on a horizontal table. Two strings X and Y are tied to the two opposite faces of the block. We observe that the block begins to move to the right if we apply force by pulling the string X. In the same way, if we pull the string Y, the block moves to the left side. However, if the block is pulled from both the sides with equal amount of forces, the block will not move any side. These forces are called balanced forces and they do not change the state of rest or of motion of an object. Let us take an example of a situation in which two opposite forces of different magnitudes pull the block. We find that the block would begin to move in the direction of the application of a greater force. Thus it can be concluded that the two forces are not balanced and this unbalanced force acts in the direction of the movement of the block. Hence we can conclude that the unbalanced force acting on an object brings it in motion.

First Law of Motion

Galileo performed some experiments on motion of objects on an inclined plane and he postulated that the objects move with a constant speed when there is no force acting on them. He made a marble roll down on an inclined plane and observed that its velocity increases as shown in the figure (a) below. Also he observed that the marble falls under gravity force which is unbalanced as it rolls down and it gains a definite amount of velocity by the time it reaches the bottom of the inclined plane. As shown in Figure (b), its velocity decreases as the marble climbs up.

Let us observe the above figure (c). It shows a marble which is resting on a plane. It is frictionless and also is inclined on both sides. Galileo argued that when the marble is released from left side of the plane, it would roll down the slope of the inclined plane and go up on the opposite side of the plane to the same height from where it was released. In addition, it is observed that the marble will try to climb the same distance it has covered as it rolls down when the inclinations of the planes on both sides are equal. If the angle of inclination of the right-side plane is slowly decreased, then the marble would travel more distances till it reaches the original height. If the right-side plane is made horizontal (that is, the slope becomes zero), the marble would continue to travel forever trying to reach the same height from where it was released. Newton made further study on Galileo’s ideas on force and motion and presented three fundamental laws that rule the motion of objects. These three laws are known as Newton’s laws of motion. The First law of motion is stated as:

"An object remains in a state of rest or of uniform motion in a straight line unless compelled to change that state by an applied force."

We can say that all objects have a resistance for change in their state of motion. The tendency of undisturbed objects to stay at rest or to keep moving with the same velocity is called inertia. So the first law of motion is also known as the law of inertia.

Inertia and Mass

Inertia is defined as the resistance of any physical object to any change in its state of motion, including changes to its speed and direction. It is a tendency of an object to keep moving in a straight line at a constant velocity. The principle of inertia is termed to be one of the fundamental principles of physics which are used to describe the motion of objects and their effects due to applied forces.

Mass is defined as the property of a physical body which determines the body's resistance to being accelerated by a force and the strength of its mutual gravitational attraction with other bodies. The SI unit of mass is the kilogram (kg). Mass is different from weight, even though we generally calculate any object's mass by measuring its weight. A man standing on the Moon would weigh less than he would on Earth because of the lower gravity, but he would have the same mass.

Second Law of Motion

The first law of motion indicates that when an unbalanced external force acts on an object, its velocity drastically changes and the object is said to get acceleration. Let us focus on how the acceleration of an object depends on the force applied to it and how force can be measured. Let us see some examples from our everyday life. Have you ever watched a table tennis game? The ball does not hurt the player though it hits him during the game. But in cricket, if a fast moving ball hits a player, he gets badly hurt.

This implies that the effect/impact produced by any object depends on its mass and velocity. Similarly, if an object is to be accelerated, we know that a greater force is required to give a greater velocity. There appears to be some sort of importance that cumulates the object’s mass and its velocity. This property called momentum and was introduced by Newton. 

The momentum, p of an object is defined as the product of its mass, m and velocity, v. That is,   p = mv

Momentum is said to have both direction and magnitude. Its direction is the same as that of velocity, v. The SI unit of momentum is kilogram-meter per second (kg m/s).

The second law of motion states that:

"The rate of change of momentum of an object is proportional to the applied unbalanced force in the direction of force."

F α (p2 – p1 )/t  


 F = k (p2 – p1 )/t  

             = kma                       

If k=1 then,                              F = ma

Third Law of Motion

The third law of motion states that when one object exerts a force on another object, the second object instantaneously exerts a force back on the first. I.e. to every action there is always an equal and opposite reaction. These two forces are always equal in magnitude but opposite in direction. These forces act on different objects but never on the same object.

Suppose you are standing at rest and start walking on a road, you must start accelerating, and this requires a force according to the second law of motion. What is this force? Is it the muscular effort you exert on the road? Is it in the direction we start to move? No, but you actually push the road below backwards. We notice that the road exerts an equal and opposite reaction force on your feet to make you move forward. Also we can see that even though the action and reaction forces are always equal in magnitude; these forces may not produce accelerations of equal magnitudes. This is because each force acts on a different object that may have a different mass.

Conservation of Momentum

The law of momentum conservation can be stated as follows:

"In absence of an external force the total momentum of a system remains constant."

For example in a collision occurring between object 1 and object 2 in an isolated system, the total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision. That is, the momentum lost by object 1 is equal to the momentum gained by object 2.