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Topic 5 of 20

Newton's Laws of Motion

Newton's three laws form the core of classical mechanics. They explain why objects move (or don't), how forces change motion, and why forces always come in pairs. Combined with free body diagrams, they provide a systematic method for analyzing any mechanical situation.

Key Concepts

Newton's First Law (Law of Inertia)

An object remains at rest or in uniform straight-line motion unless acted on by a net external force. Inertia is the resistance to changes in motion; it is proportional to mass.

Newton's Second Law

The net force on an object equals its mass times its acceleration:

\vec{F}_\text{net} = m\vec{a}

. This is a vector equation — apply it separately in each direction.

Newton's Third Law

For every force exerted by object A on object B, there is an equal and opposite force exerted by B on A. Action–reaction pairs act on different objects and never cancel each other.

Free Body Diagram (FBD)

A diagram of a single object showing all forces acting on it as labeled arrows. Drawing a correct FBD is the first step in every Newton's Law problem.

Weight and Normal Force

Weight

W = mg

is the gravitational pull of Earth on the object, directed downward. The normal force

N

is the contact force perpendicular to a surface, preventing penetration.

Inertial Reference Frame

A non-accelerating frame of reference in which Newton's laws hold. An elevator at constant speed is inertial; an accelerating elevator is not. Pseudo-forces appear in non-inertial frames.

Key Equations

Newton's Second Law

\vec{F}_\text{net} = m\vec{a} \quad \Longrightarrow \quad \sum F_x = ma_x, \quad \sum F_y = ma_y

Apply component-by-component. Choose a coordinate system aligned with the motion.

Weight

W = mg

Gravitational force on a mass m near Earth's surface. g ≈ 9.8 m/s² directed downward.

Newton's Third Law

\vec{F}_{A \to B} = -\vec{F}_{B \to A}

Equal magnitude, opposite direction. The pair always acts on two different objects.

Net force (multiple forces)

\vec{F}_\text{net} = \vec{F}_1 + \vec{F}_2 + \cdots = \sum_i \vec{F}_i

Vector sum of all external forces acting on the object.

Worked Example

Two Blocks on a Frictionless Surface

Problem

A 3 kg block and a 5 kg block are in contact on a frictionless surface. A force of 16 N pushes the system horizontally. Find the acceleration and the contact force between the blocks.

Solution

Treat the system as one object to find acceleration:

F = (m_1 + m_2)\,a \implies a = \frac{F}{m_1+m_2} = \frac{16}{3+5} = 2 \text{ m/s}^2

Isolate the 5 kg block. The only horizontal force on it is the contact force $F_c$ :

F_c = m_2 \, a = 5 \times 2 = 10 \text{ N}

Answer Acceleration = 2 m/s²; contact force = 10 N.

Practice

Exercises

7 problems

1 of 7

A net force of $20 \text{ N}$ acts on a $5 \text{ kg}$ box. What is its acceleration?

Your answer

m/s²

2 of 7

What net force is required to accelerate a $1200 \text{ kg}$ car at $3 \text{ m/s}^2$ ?

Your answer

3 of 7

A $70 \text{ kg}$ person stands on a scale in a stationary elevator ( $g = 9.8 \text{ m/s}^2$ ). What does the scale read?

Your answer

4 of 7

The same $70 \text{ kg}$ person is in an elevator accelerating upward at $2 \text{ m/s}^2$ ( $g = 9.8 \text{ m/s}^2$ ). What does the scale read?

Your answer

5 of 7

Two forces act on an object: $12 \text{ N}$ east and $5 \text{ N}$ north. What is the magnitude of the net force?

Your answer

6 of 7

A $4 \text{ kg}$ block is pushed by a $24 \text{ N}$ applied force but accelerates at only $4 \text{ m/s}^2$ . What is the friction force magnitude?

Your answer

7 of 7

A $0.15 \text{ kg}$ ball accelerates from rest to $40 \text{ m/s}$ in $0.06 \text{ s}$ . What average force was applied?

Your answer

Key Takeaways

Newton's First Law: no net force → no acceleration. An object moving at constant velocity is in equilibrium.
Newton's Second Law: $\vec{F}_\text{net} = m\vec{a}$ is a vector equation — solve it in components.
Newton's Third Law: action–reaction pairs are equal and opposite but act on different objects, so they never cancel.
Always draw a free body diagram before writing force equations.
Weight ( $mg$ ) and normal force ( $N$ ) are not a Newton's Third Law pair — they act on the same object.