Forces and Introduction to Laws (Basic)

Balanced And Unbalanced Forces

In the study of motion, forces are central to understanding why objects move or remain stationary. A force, in physics, is an influence that can cause an object to change its velocity (accelerate) or deform.

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Forces are fundamentally vector quantities. This means that to fully describe a force, we need to specify both its magnitude (how strong it is) and its direction (in which way it is pushing or pulling). When multiple forces act on a single object simultaneously, their combined effect is determined by the net force. The net force is the vector sum of all the individual forces acting on the object.

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Consider an object being acted upon by several forces. If we add these forces together as vectors, the resulting vector is the net force. It is this net force that determines the overall effect on the object's motion.

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Balanced Forces

When the vector sum of all forces acting on an object is zero, the forces are said to be balanced. This means that the effects of all the individual forces cancel each other out. When only balanced forces act on an object:

• If the object is at rest, it will remain at rest.
• If the object is moving, it will continue to move with a constant velocity (constant speed in a straight line).

In other words, balanced forces do not produce acceleration ($ a=0 $). Balanced forces can, however, cause a change in the shape or size of an object (deformation). For example, if you press on a rubber ball from opposite sides with equal force, it will compress but remain in place. The forces are balanced, but the shape changes.

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Examples of Balanced Forces:

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Unbalanced Forces

When the vector sum of all forces acting on an object is not zero, the forces are said to be unbalanced. An unbalanced force acting on an object always causes a change in its state of motion. This change in motion is called acceleration ($ a \ne 0 $).

• If the object is at rest, an unbalanced force will cause it to start moving.
• If the object is moving, an unbalanced force will cause it to speed up, slow down, or change direction.

The effect of an unbalanced force is to produce an acceleration in the direction of the net force. The relationship between the unbalanced force, mass, and acceleration is described by Newton's Second Law of Motion ($ \vec{F}_{net} = m\vec{a} $), which we will study later.

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Examples of Unbalanced Forces:

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Here is a table summarising the key characteristics of balanced and unbalanced forces:

Feature	Balanced Forces	Unbalanced Forces
Net Force	Zero ($ \vec{F}_{net} = 0 $)	Non-zero ($ \vec{F}_{net} \ne 0 $)
Effect on object at rest	Remains at rest	Starts moving (accelerates)
Effect on object in uniform motion	Continues uniform motion (constant velocity)	Changes velocity (speeds up, slows down, or changes direction)
Effect on shape/size	Can cause deformation	Can cause deformation and motion change
Acceleration Produced	None ($ a=0 $)	Yes ($ a \ne 0 $)

First Law Of Motion

Newton's Laws of Motion are foundational to classical mechanics. They were formulated by Sir Isaac Newton and first published in his monumental work, Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy) in 1687. The First Law builds upon the ideas of Galileo Galilei regarding inertia.

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Statement of the Law of Inertia

Newton's First Law of Motion is often referred to as the Law of Inertia. It is stated as follows:

"Every body continues in its state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed upon it."

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In modern terminology, this can be rephrased as:

"An object will maintain a constant velocity (which may be zero) if and only if the net external force acting on it is zero."

A constant velocity means either the object is at rest ($ v=0 $) or moving at a constant speed ($ v = \text{constant} \ne 0 $) in a fixed direction.

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Explanation of the First Law

The First Law of Motion essentially defines the property of inertia and establishes the conditions under which an object's motion changes. It tells us that a change in motion (i.e., acceleration) is caused by a net external unbalanced force.

State of Rest or Uniform Motion:

The "state" of a body, as described by the law, refers to its velocity. If a body is at rest, its velocity is zero. If it is in uniform motion in a straight line, its velocity is constant and non-zero. The law says that a body naturally tends to stay in this state.

Unless Compelled to Change:

This part is crucial. The state of motion (velocity) changes only when an external force is applied, and specifically, when the net force is not zero. If the net force is zero (balanced forces), the state of motion does not change.

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Before Galileo and Newton, it was commonly believed, following Aristotle, that a force was required to *keep* an object in motion. Objects stopping was seen as their natural tendency. Galileo's experiments, however, suggested that objects stop moving due to friction, not because motion requires continuous force. Newton formalised this idea with the concept of inertia and his first law.

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The Role of Unbalanced Forces

The First Law implies that the presence of a non-zero net force is the sole cause of acceleration. If you observe an object accelerating, you can be certain that an unbalanced force is acting on it. Conversely, if an object is moving with constant velocity (or is at rest), the net force acting on it must be zero.

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Real-world Application and Friction:

In everyday life, we rarely see objects in motion continue moving forever at a constant velocity. A ball rolled on the ground eventually stops, a swing stops swinging, a car coasts to a halt if the engine is switched off. This is because forces like friction (between surfaces) and air resistance (or drag) are always present. These are external forces that oppose motion. When a ball rolls, friction acts opposite to its motion, creating an unbalanced force that causes it to decelerate and stop. To keep an object moving at a constant velocity against these resistive forces, an external force (like pushing or driving) must be applied that is equal in magnitude and opposite in direction to the total resistive force. In this situation, the net force is zero, and the object moves at a constant velocity.

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Examples illustrating the First Law:

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Inertia And Mass

The concept of inertia, which is central to Newton's First Law, is the inherent property of an object to resist changes in its state of motion. But how do we quantify this resistance? This is where the concept of mass comes in.

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Inertia

Inertia is not a physical quantity that can be measured directly with a unit like length or time. It is a property. It is the natural tendency of an object to oppose any attempt to change its velocity. This includes resisting being started from rest, resisting being stopped if in motion, or resisting a change in direction if moving.

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Think about pushing different objects:

• It's easier to push a toy car than a real car.
• It's easier to change the direction of a tennis ball than a cricket ball thrown with the same speed.
• It's harder to stop a heavy boulder rolling down a hill than a small stone.

These examples illustrate that some objects have 'more' inertia than others. What determines how much inertia an object has? This leads us to mass.

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Mass

Mass is a fundamental property of an object that quantifies the amount of matter it contains. It is a scalar quantity, meaning it only has magnitude. The standard international (SI) unit for mass is the kilogram (kg).

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Mass is the quantitative measure of inertia. The greater the mass of an object, the greater is its inertia. This means that an object with a large mass is more difficult to accelerate (start moving, stop, or change direction) than an object with a small mass, when subjected to the same unbalanced force.

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Newton's Second Law of Motion ($ F = ma $) provides the direct relationship between net force ($ F $), mass ($ m $), and acceleration ($ a $). Rearranging this formula to $ m = F/a $, we can see that for a given net force, the acceleration produced is inversely proportional to the mass. If you apply the same force to two different objects, the one that accelerates less has more mass (and thus more inertia).

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Distinction between Mass and Weight

It is important to distinguish between mass and weight.

• Mass is an intrinsic property of an object; it is the amount of matter it contains and is a measure of its inertia. Mass is constant regardless of where the object is (on Earth, on the Moon, or in space).
• Weight is the force of gravity acting on an object. It is a vector quantity. Weight depends on both the mass of the object and the strength of the gravitational field it is in. Weight is calculated using the formula $ W = mg $, where $ m $ is the mass and $ g $ is the acceleration due to gravity. Since $ g $ varies slightly across the Earth's surface and is different on other celestial bodies, weight is not constant like mass.

For example, a person with a mass of 60 kg has a weight of approximately $ 60 \times 9.8 = 588 $ Newtons (N) on the Earth's surface. On the Moon, where the gravitational acceleration is about $ 1/6 $th of Earth's, their weight would be only about $ 588 / 6 \approx 98 $ N, but their mass would still be 60 kg.

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Examples Linking Inertia and Mass:

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