MGU Physics · Preparatory Volume 1 · Part II — Motion and Forces
This chapter introduces force as a vector interaction, explains net force and inertia, develops Newton's three laws, and applies them to everyday mechanics, weight, action-reaction pairs, and common conceptual mistakes.
A force is a push or a pull exerted on an object by another object or by a field. Forces are interactions: they always involve two objects, and they always come in pairs, as described by Newton's third law. Forces are vector quantities: they have magnitude, direction, and a point of application.
The SI unit of force is the newton (N). One newton is defined as the force required to accelerate a 1 kg mass at 1 m/s².
This unit emerges directly from Newton's second law and ensures dimensional consistency throughout mechanics.
A force does not have to cause motion. A book resting on a table has gravity pulling it down and the table pushing it up. These forces are equal and opposite, so the book does not accelerate. The forces are real and significant; they just cancel. What matters for motion is the net force, the vector sum of all forces acting on an object.
| Force Type | Example | Origin |
|---|---|---|
| Gravitational | Weight of an object | Mass interacting with gravitational field |
| Normal | Table pushing up on book | Electromagnetic; compression of atomic bonds |
| Friction | Carpet slowing a sliding box | Electromagnetic; surface interaction |
| Tension | Rope pulling a crate | Electromagnetic; internal tension in rope |
| Applied | Hand pushing a door | Electromagnetic; contact between objects |
| Spring | Compressed spring pushing a cart | Electromagnetic; elastic deformation |
| Magnetic | Motor exerting force on wire | Magnetic field acting on current |
| Electric | Charged balloon attracting hair | Electric field acting on charge |
Forces are divided into two categories based on how they are transmitted between objects.
Contact forces require physical contact between the objects. They act only when surfaces touch. Examples include friction, normal force, tension, applied force, and air resistance. These forces vanish immediately when the objects separate.
Field forces, also called non-contact forces or action-at-a-distance forces, act between objects that are not in contact, through a field that permeates space. The field carries the force across the gap. Examples include gravity through a gravitational field, electric force through an electric field, and magnetic force through a magnetic field. Gravity acts between Earth and a falling apple even though they never touch; the gravitational field transmits the interaction.
Key Point: At the atomic level, all contact forces are fundamentally electromagnetic. When two surfaces touch, it is really the electrons in their atoms repelling each other. Gravity is the only truly distinct force at everyday scales. The four fundamental forces of nature — gravity, electromagnetism, strong nuclear, and weak nuclear — underlie every force encountered in this book.
The net force, sometimes called the resultant force, on an object is the vector sum of all forces acting on it. Because forces are vectors, they must be added using the component method from Chapter 4.
When the net force is zero, forces are balanced. A balanced object does not accelerate; it remains either at rest or moving with constant velocity. When the net force is non-zero, forces are unbalanced, and the object accelerates in the direction of the net force.
| Net Force | Forces | Effect on Motion |
|---|---|---|
| Zero | Balanced; equal and opposite | No acceleration; constant velocity or at rest |
| Non-zero, rightward | Unbalanced toward right | Accelerates to the right |
| Non-zero, downward | Unbalanced downward | Accelerates downward |
| Zero; two forces cancel | Balanced | No change in speed or direction |
Common Mistake: A moving object can have zero net force. Motion does not require a net force; only changes in motion do. A hockey puck sliding on frictionless ice has zero net force and continues moving at constant velocity forever. This is one of the most important conceptual distinctions in mechanics.
Newton's first law, the law of inertia, states that an object at rest stays at rest, and an object in uniform motion, meaning constant velocity, continues in uniform motion unless acted upon by a non-zero net external force.
The first law tells us two things. First, the natural state of an object with no net force is constant velocity, not rest. Rest is just the special case of constant velocity where the velocity happens to be zero. Second, forces are required to change velocity, not to maintain it.
Newton's first law overturned the older assumption that continued motion required continued force.
Before Newton, Aristotle's framework held that a continuous force was required to maintain motion and that objects naturally came to rest. Newton's first law overturned this: objects naturally maintain whatever motion they have. Friction is what brings earthly objects to rest; on a perfectly frictionless surface, they would slide forever.
Historical Note: Galileo effectively discovered the first law before Newton. Through inclined plane experiments, he showed that a ball rolling on a perfectly smooth horizontal surface would continue indefinitely. Newton generalized and formalized this idea into the first law and embedded it in a complete mathematical framework.
Inertia is the tendency of an object to resist changes in its state of motion. An object with more inertia is harder to accelerate: it takes more force to produce the same change in velocity.
Mass is the quantitative measure of inertia. The greater the mass, the greater the inertia, and the harder it is to accelerate the object. Mass is measured in kilograms and is an intrinsic property of matter. It does not depend on location, orientation, or the presence of other objects.
Mass is not the same as weight. Mass is inertia, or resistance to acceleration. Weight is the gravitational force on the mass. An astronaut in space has the same mass as on Earth but is nearly weightless. A 70 kg person has the same mass on the Moon as on Earth, but their weight on the Moon is about one-sixth their weight on Earth.
| Property | Mass | Weight |
|---|---|---|
| What it is | Measure of inertia; amount of matter | Gravitational force on the object |
| Symbol | \(m\) | \(W\) or \(F_g\) |
| SI Unit | kilogram (kg) | newton (N) |
| Scalar or vector? | Scalar | Vector; directed downward near Earth |
| Changes with location? | No; constant everywhere | Yes; depends on gravitational field |
| Relation | Defines inertia | \(W = mg\) |
Newton's second law, the law of acceleration, states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The acceleration is in the same direction as the net force.
This is the central equation of classical mechanics. It connects the kinematic quantity, acceleration, to the dynamic quantity, force, with mass as the proportionality constant.
Three important consequences follow immediately:
In one-dimensional problems, the vector equation reduces to signed scalars: positive force produces positive acceleration, and negative force produces negative acceleration, consistent with the sign convention chosen for the problem.
Bridge Note: Newton's second law links the description of motion from kinematics to the causes of motion in dynamics.
The second law \(\vec{F}=m\vec{a}\) encodes a proportional relationship: fix one quantity and the other two scale linearly. These relationships can be summarized graphically and numerically.
| Scenario | What Changes | Effect on Acceleration |
|---|---|---|
| Same mass, double force | \(F \times 2\) | \(a \times 2\); direct proportion |
| Same mass, halve force | \(F \div 2\) | \(a \div 2\) |
| Same force, double mass | \(m \times 2\) | \(a \div 2\); inverse proportion |
| Same force, halve mass | \(m \div 2\) | \(a \times 2\) |
| Double force and double mass | Both \(\times 2\) | \(a\) unchanged |
A net force of 15.0 N acts on a 3.0 kg box. The acceleration is:
The acceleration is in the direction of the force. If mass doubles to 6.0 kg with the same force, then:
If force doubles to 30.0 N with the original 3.0 kg mass, then:
Applying Newton's second law systematically requires the same discipline as applying kinematic equations: identify the system, identify all forces, find the net force, then solve for the unknown.
A 5.0 kg box is pushed right with 20.0 N and pulled left with 8.0 N. Find the acceleration.
What net force is needed to accelerate a 1200 kg car at 3.5 m/s²?
Newton's third law, the law of interaction, states that whenever object A exerts a force on object B, object B simultaneously exerts an equal and opposite force on object A.
Third-law force pairs always have these characteristics: they are equal in magnitude, opposite in direction, act simultaneously, are of the same type, and act on different objects. The third law is always true, without exception.
Common Mistake: Third-law pairs act on different objects. They cannot cancel each other for the purpose of Newton's second law because \(F=ma\) applies to one object at a time. Forces that cancel, or balance, are forces on the same object from different sources.
The term action-reaction pair is sometimes misunderstood to imply a time sequence: first an action, then a reaction. This is wrong. Newton's third-law forces are simultaneous. There is no primary action and secondary reaction; neither force causes the other. They are both part of the same interaction.
| Interaction | Force A Exerts on B | Force B Exerts on A |
|---|---|---|
| Book on table | Book pushes table down; normal force | Table pushes book up; normal force of equal magnitude |
| Rocket firing | Rocket pushes exhaust backward | Exhaust pushes rocket forward, producing thrust |
| Swimmer pushing wall | Swimmer pushes wall backward | Wall pushes swimmer forward |
| Earth-Moon gravity | Earth pulls Moon toward it | Moon pulls Earth toward it with the same magnitude |
| Bat hitting ball | Bat exerts force on ball | Ball exerts equal force on bat |
A rocket engine expels exhaust gas downward. By Newton's third law, the exhaust pushes the rocket upward with an equal force. The rocket does not push against air; it works in vacuum. The interaction is between the rocket body and the exhaust gas it ejects.
The weight of an object is the gravitational force exerted on it by a nearby massive body, usually Earth. Weight is a force, a vector pointing toward Earth's center, and is measured in newtons, not kilograms.
On Earth's surface, \(g = 9.81\,\text{m/s}^2\). On the Moon, \(g_{\text{Moon}} \approx 1.62\,\text{m/s}^2\). On Mars, \(g_{\text{Mars}} \approx 3.71\,\text{m/s}^2\). An astronaut with mass 70.0 kg has weight 687 N on Earth, 113 N on the Moon, and 260 N on Mars, but the same mass everywhere.
The third-law pair of weight, Earth pulling an object down, is the object pulling Earth upward with the same force. Earth's enormous mass means this force produces negligible acceleration of Earth, so we do not notice it.
A student has mass 60.0 kg. Her weight is:
In everyday speech, people say they "weigh 60 kg." In physics, that is mass, not weight. Weight is always a force measured in newtons.
Common Mistake: Never express weight in kilograms. Weight is a force, measured in newtons. The confusion between mass and weight is one of the most persistent errors in introductory physics.
Newton's laws operate in every physical situation, though we rarely think about them explicitly in daily life. The following scenarios can be analyzed in terms of forces and net force.
| Situation | Net Force | Motion Result |
|---|---|---|
| Car at constant highway speed | Zero; drive force equals friction plus drag | Constant velocity; first law |
| Ball in free fall | Gravity only, downward | Constant downward acceleration equal to \(g\) |
| Elevator accelerating upward | Normal force greater than weight | Upward acceleration; you feel heavier |
| Elevator in constant-speed ascent | Normal force equals weight | Zero net force; you feel normal weight |
| Book resting on table | Weight down equals normal force up | Zero acceleration; at rest |
| Skydiver at terminal velocity | Gravity equals drag, or air resistance | Zero net force; constant velocity downward |
No. Objects maintain their velocity without any net force, as stated by the first law. Friction is what slows most real objects; in the absence of friction, they would continue indefinitely. A hockey puck on ice, a spacecraft in deep space, and a marble in a frictionless tube all demonstrate this.
Acceleration depends on net force divided by mass. A very large force on a very massive object may produce less acceleration than a small force on a tiny object.
Both forces in a Newton's third-law pair are equally real, simultaneous, and equal in magnitude. Neither causes the other; they are both aspects of a single interaction.
This is correct only when speaking about the net force. Students sometimes think there must be a specific "accelerating force" acting in the direction of motion. A single unbalanced force produces acceleration; no separate mover force is needed.
In a vacuum, all objects fall with the same acceleration \(g\), regardless of mass. Galileo demonstrated this, and it follows directly from \(F=mg\) and \(a=F/m=g\), which is independent of mass. Air resistance is what causes feathers to fall slower than hammers. On the Moon, where there is no air, they fall together.
Newton's laws provide an extraordinarily accurate description of the physical world for the vast majority of situations encountered in engineering and everyday life. However, they have well-defined limits.
Within their domain of validity — objects of everyday size, moving at speeds much less than light, in moderate gravitational fields — Newton's laws are exquisitely accurate. GPS satellites, bridge engineering, spacecraft trajectory planning, and crash-safety design all rely on Newtonian mechanics to extraordinary precision.
Bridge Note: Newtonian mechanics remains the practical foundation for most everyday and engineering-scale motion, even though deeper theories are required outside its domain.
Forces are vector interactions that cause changes in motion. Newton's three laws provide the complete causal framework of classical mechanics.
| I can... | Section |
|---|---|
| Define force and state its SI unit. | 10.1 |
| Distinguish contact forces from field forces with examples. | 10.2 |
| Calculate net force from multiple forces using vector addition. | 10.3 |
| State Newton's first law and identify situations where it applies. | 10.4 |
| Explain the difference between mass and weight with numerical examples. | 10.5, 10.11 |
| Apply \(F_{\text{net}} = ma\) to find acceleration, force, or mass. | 10.6, 10.8 |
| State Newton's third law and identify action-reaction pairs. | 10.9, 10.10 |
| Calculate weight using \(W=mg\). | 10.11 |
| Identify and correct five common misconceptions about force and motion. | 10.13 |
| State the conditions under which Newton's laws break down. | 10.14 |