Class 9 · Science · NCERT Exploration
Chapter 6: How Forces Affect Motion
Complete Study Notes Newton’s Three Laws, Friction & Momentum Exam-Ready Format
1. The Concept of Force
A force can: (i) make an object move from rest, (ii) change the speed or direction of a moving object, and (iii) change the shape of an object (e.g., kicking a ball, striking a ball with a bat, squeezing a lemon).
Force is a Vector Quantity
Like position, displacement, velocity, and acceleration, force needs both magnitude and direction to be fully specified (e.g., friction acts opposite to motion; gravity acts downward; buoyant force acts upward). SI unit: newton (N) — written with a small “n” as a word, but capital “N” as a symbol.
Exam Tip
Common slip: writing “Newton” for the unit name or “n” for the symbol. Correct: unit name = newton (lowercase), symbol = N (uppercase) — this rule applies to any unit named after a person (e.g., kelvin/K, pascal/Pa).
1.1 Measuring the Magnitude of a Force
A spring balance measures the force with which you pull on the spring inside it — it can measure weight (gravitational force) or force in general.
Threads of Curiosity — Scale of Forces
Everyday smallest perceivable forces: order of millinewtons ($10^{-3}$ N, e.g., a light touch). Scientists can measure forces as small as yoctonewtons ($10^{-24}$ N) in specialised experiments.
2. Balanced and Unbalanced Forces
Usually, more than one force acts on an object simultaneously (e.g., pushing a box: applied force + friction; a floating ball: gravity + buoyant force).
Balanced Forces
Equal in magnitude, opposite in direction → net force = 0. Object’s motion does not change (e.g., tug-of-war with equal pulling teams — rope doesn’t move).
Unbalanced Forces
Net force ≠ 0 → causes a change in the object’s state of motion. The object moves/accelerates in the direction of the larger force.
2.1 Calculating Net Force
6 N
10 N
Same direction → Net force = sum of magnitudes, along that direction. Opposite directions → Net force = difference of magnitudes, along the larger force’s direction.
Solved Example 6.1 — Net Force on a Block
Two forces, 10 N and 6 N, act on a block. Find the net force in each case:
(a) Both acting right: $F_{net} = 10 + 6 = 16\ \text{N}$, towards the right.
(b) 10 N right, 6 N left: $F_{net} = 10 – 6 = 4\ \text{N}$, towards the right (direction of larger force).
(c) 6 N right, 10 N left: $F_{net} = 10 – 6 = 4\ \text{N}$, towards the left.
(a) Both acting right: $F_{net} = 10 + 6 = 16\ \text{N}$, towards the right.
(b) 10 N right, 6 N left: $F_{net} = 10 – 6 = 4\ \text{N}$, towards the right (direction of larger force).
(c) 6 N right, 10 N left: $F_{net} = 10 – 6 = 4\ \text{N}$, towards the left.
Exam Tip
Key line for definitions: forces equal in magnitude and opposite in direction are called balanced forces; the rope in tug-of-war “does not move if forces are balanced, but moves if forces are unbalanced” — a favourite fill-in-the-blank/reasoning line.
Beyond the Basics
Forces that act at an angle to each other (not parallel/opposite), and equal-and-opposite forces applied to two ends of an extended object (causing rotation — e.g., turning a handlebar or a tap), are studied in higher grades.
3. The Force of Friction
Friction is the force that opposes relative motion (or attempted motion) between two surfaces in contact. It always acts opposite to the direction of motion.
Note — Multiple Forces, One Net Effect
Multiple forces may act on an object (applied force, friction, gravity/weight, normal force), but its motion depends only on the net force. Weight (downward) and normal force (upward, perpendicular to surface) are balanced for an object on a horizontal surface — they don’t affect horizontal motion.
3.1 Activities 6.1 & 6.2 — Friction Depends on Surface Nature
Key Experimental Finding
A stack of coins launched by a stretched rubber band travels different distances on different surfaces (wooden table < laminated table < polished marble/tile) even though launched with the same force each time.
Conclusion: smoother surfaces → smaller force of friction → object decelerates more slowly → travels farther before stopping. A spring balance pulling a block confirms this directly: a smaller spring-balance reading (force needed to just start motion) = smaller friction on that surface.
Exam Tip — “What If” Reasoning
If friction disappeared entirely: once set in motion, objects would continue moving forever at constant velocity (per Newton’s First Law) — nothing would ever naturally come to rest by sliding to a stop. This is a classic HOTS/thought-experiment question.
4. Newton’s First Law of Motion (Law of Inertia)
Statement
An object at rest remains at rest, and an object in motion continues to move with a constant velocity, unless a net force acts upon it.
If net force = 0 → acceleration = 0 → object cannot begin to move or change its velocity.
Galileo Galilei
Through thought experiments, argued (17th century) that if a body moves on a horizontal plane with all impediments (friction) removed, it will continue moving indefinitely — challenging the old belief that force is needed to sustain motion.
Isaac Newton
Introduced the term inertia — the tendency of objects to resist a change in their state of rest or uniform motion. Framed the First Law using this idea; presented all three laws of motion in 1687 (Principia).
Exam Tip — Position-Time & Velocity-Time Graphs (No Net Force)
At rest: position-time graph = horizontal line at a fixed position; velocity-time graph = horizontal line at $v=0$.
Constant velocity: position-time graph = straight sloped line; velocity-time graph = horizontal line at some non-zero $v$.
This is one of the most frequently asked graph-sketching questions in this chapter.
Constant velocity: position-time graph = straight sloped line; velocity-time graph = horizontal line at some non-zero $v$.
This is one of the most frequently asked graph-sketching questions in this chapter.
Solved Example 6.2
A person pushes a moving box forward with a force exactly equal to friction. Will the box stop or keep moving?
Answer: The two forces are equal and opposite → balanced → net force = 0 → by Newton’s First Law, the box continues moving with constant velocity (it does NOT stop, and does NOT speed up).
Answer: The two forces are equal and opposite → balanced → net force = 0 → by Newton’s First Law, the box continues moving with constant velocity (it does NOT stop, and does NOT speed up).
5. Newton’s Second Law of Motion
A force produces acceleration. Experiments (pulling a cart with varying weights via a pulley system) show:
- For a fixed mass, acceleration increases as net force increases (larger force → larger acceleration)
- For a fixed force, acceleration decreases as mass increases (larger mass → smaller acceleration)
Statement
When a net force acts on an object, the object accelerates in the direction of the net force. The magnitude of acceleration is directly proportional to net force and inversely proportional to mass.
Newton’s Second Law
$$a = \frac{F}{m} \qquad \text{or} \qquad F = ma$$
Definition of the Newton (N)
If $m = 1\ \text{kg}$ and $a = 1\ \text{m s}^{-2}$: $F = 1\ \text{kg} \times 1\ \text{m s}^{-2} = 1\ \text{kg m s}^{-2} = 1\ \text{N}$
One newton is the force that produces an acceleration of $1\ \text{m s}^{-2}$ on a mass of $1\ \text{kg}$.
One newton is the force that produces an acceleration of $1\ \text{m s}^{-2}$ on a mass of $1\ \text{kg}$.
Gravitational Force / Weight
$$F = mg \qquad g \approx 9.8\ \text{m s}^{-2}\ (\text{take}\ 10\ \text{m s}^{-2}\ \text{for quick estimates})$$
$g$ does NOT depend on the mass of the object.
Threads of Curiosity — Real vs. Ideal
In real experiments, doubling force doesn’t exactly double acceleration (and vice versa for mass) due to measurement errors and friction between the cart’s wheels and the surface — a good explanation to cite for “why did your experimental ratio not match theory” type questions.
Beyond the Basics — Momentum Form
Momentum = mass × velocity (direction same as velocity). The more complete Second Law: the rate of change of momentum of an object is proportional to the net force and occurs in the direction of the net force. This form applies even when mass is not constant.
5.1 Newton’s Second Law in Everyday Life
- Catching a fast ball: pulling hands back while catching increases the time over which velocity drops to zero → reduces acceleration → reduces force on hands (less injury)
- Airbags: increase the time of impact during a collision → reduce deceleration → reduce force on the passenger
- Cracking a coconut: very short stopping time on hitting the ground → very large force → shell breaks
Quick Recall: Longer stopping/impact time → smaller force (catching, airbags, landing mats). Shorter stopping time → larger force (coconut cracking, bullet penetration).
Solved Numericals — Newton’s Second Law
Example 6.4 — Weightlifter’s Force
Barbell: 10 kg on each side + 10 kg bar = 30 kg total.
$$F = mg = 30 \times 9.8 = 294\ \text{N (downward, due to gravity)}$$ To hold it steady, the weightlifter applies an equal and opposite force of 294 N upward.
$$F = mg = 30 \times 9.8 = 294\ \text{N (downward, due to gravity)}$$ To hold it steady, the weightlifter applies an equal and opposite force of 294 N upward.
Example 6.5 — Pushing a Block Against Friction
Block mass = 25 kg; max friction = 50 N.
(i) Applied force = 50 N → balances friction exactly → net force = 0 → block stays stationary.
(ii) Applied force = 55 N → $F_{net} = 55 – 50 = 5\ \text{N}$ $$a = \frac{F}{m} = \frac{5}{25} = 0.2\ \text{m s}^{-2}$$ $$s = ut + \frac{1}{2}at^2 = (0)(2) + \frac{1}{2}(0.2)(2)^2 = 0.4\ \text{m (forward)}$$
(i) Applied force = 50 N → balances friction exactly → net force = 0 → block stays stationary.
(ii) Applied force = 55 N → $F_{net} = 55 – 50 = 5\ \text{N}$ $$a = \frac{F}{m} = \frac{5}{25} = 0.2\ \text{m s}^{-2}$$ $$s = ut + \frac{1}{2}at^2 = (0)(2) + \frac{1}{2}(0.2)(2)^2 = 0.4\ \text{m (forward)}$$
Example 6.6 — Force from a Velocity-Time Graph
Sports car, mass 1500 kg. Graph: 0–5 s (0 → 10 m/s), 5–10 s (constant 10 m/s), 10–15 s (10 → 0 m/s).
0–5 s: $a = \frac{v-u}{t} = \frac{10-0}{5} = 2\ \text{m s}^{-2}$; $F = ma = 1500 \times 2 = 3000\ \text{N}$ (towards east)
5–10 s: constant velocity → $a = 0$ → $F = 0$ N
10–15 s: $a = \frac{0-10}{5} = -2\ \text{m s}^{-2}$; $F = 1500 \times (-2) = -3000\ \text{N}$ (negative sign → force acts towards west, opposite to motion)
0–5 s: $a = \frac{v-u}{t} = \frac{10-0}{5} = 2\ \text{m s}^{-2}$; $F = ma = 1500 \times 2 = 3000\ \text{N}$ (towards east)
5–10 s: constant velocity → $a = 0$ → $F = 0$ N
10–15 s: $a = \frac{0-10}{5} = -2\ \text{m s}^{-2}$; $F = 1500 \times (-2) = -3000\ \text{N}$ (negative sign → force acts towards west, opposite to motion)
6. Newton’s Third Law of Motion
Statement
Whenever one object exerts a force on a second object, the second object simultaneously exerts an equal and opposite force on the first object.
Exam Tip — Critical Distinction
Action-reaction force pairs act on two different objects — so they never cancel each other (they cannot “balance” since they act on different bodies). This is distinct from balanced forces (which act on the same object).
6.1 Everyday Applications
Paddle → water
Water → paddle & canoe
Canoeing: paddle pushes water backward; water pushes paddle (and canoe) forward with equal force. Pushing harder → larger forward force → higher canoe velocity.
- Walking/running: feet push the ground backward; the ground pushes feet forward (via friction) — here friction helps motion rather than opposing it
- Climbing a tree: legs push the trunk down; friction pushes the person up — harder on smooth (low-friction) trunks
- Rocket launch: engine expels gas downward; gas exerts equal-opposite force on rocket upward; when this exceeds the rocket’s weight, it lifts off
- Chandrayaan-3’s Vikram lander: fired its engine in the direction of motion (forward) to produce a backward reaction force, slowing it down for a soft lunar landing
Exam Tip — Grooves & Treads
Grooves on footwear soles and treads on vehicle tyres increase friction between the surfaces — necessary for the reaction force (via friction) that pushes us/vehicles forward. This is why it’s hard to walk on wet polished floors/ice, and risky to drive on wet/snowy roads (friction, hence reaction force, is too low).
6.2 Newton’s Third Law Applies to All Force Types
Not just contact forces — also applies to non-contact forces: two magnets repel/attract each other equally; two charged balloons apply equal electrostatic forces; the Earth and a fruit apply equal gravitational forces on each other.
Note — Equal Forces, Unequal Accelerations
Forces in a third-law pair are always equal in magnitude, but they generally do NOT produce equal accelerations, because $a = F/m$ — if the masses of the two objects differ, their accelerations differ too.
Example 6.7 — Why Doesn’t the Earth Move Towards the Fruit?
The Earth and a falling fruit exert equal and opposite gravitational forces on each other. But the Earth’s mass is astronomically larger than the fruit’s, so $a_{Earth} = F/m_{Earth}$ is extremely tiny — undetectably small — while the fruit visibly accelerates towards Earth.
Example 6.8 — Gun Recoil
0.1 kg bullet fired from a 5 kg gun; force = 2 N.
By Newton’s Third Law, recoil force on gun = 2 N (equal, opposite). $$a_{gun} = \frac{2\ \text{N}}{5\ \text{kg}} = 0.4\ \text{m s}^{-2} \qquad a_{bullet} = \frac{2\ \text{N}}{0.1\ \text{kg}} = 20\ \text{m s}^{-2}$$ Equal forces, but very different accelerations because the masses differ hugely.
By Newton’s Third Law, recoil force on gun = 2 N (equal, opposite). $$a_{gun} = \frac{2\ \text{N}}{5\ \text{kg}} = 0.4\ \text{m s}^{-2} \qquad a_{bullet} = \frac{2\ \text{N}}{0.1\ \text{kg}} = 20\ \text{m s}^{-2}$$ Equal forces, but very different accelerations because the masses differ hugely.
7. Forces on a System of Objects
For two objects connected by a string (e.g., two boxes, masses $m_1$ and $m_2$, pulled by external force $F$), treat them as a single system: internal forces (tension $T$) cancel out within the system; only the external force $F$ matters.
Acceleration of a Connected System
$$a = \frac{F}{\text{mass of system}} = \frac{F}{m_1 + m_2}$$
Exam Tip
The system also has external gravitational force $(m_1+m_2)g$ downward, balanced by normal force $(N_1+N_2)$ upward from the ground — these don’t affect horizontal acceleration. This “treat connected objects as one system” trick massively simplifies numerical problems on connected bodies/systems.
8. Quick Summary Table — All Three Laws
| Law | Statement (essence) | Key formula | Real-life cue |
|---|---|---|---|
| First (Inertia) | No change in motion without net force | $F_{net}=0 \Rightarrow a=0$ | Object slides to rest only due to friction |
| Second | Net force produces acceleration, proportional to F, inverse to m | $F=ma$ | Catching a ball softly (increase time, reduce force) |
| Third | Every action has an equal & opposite reaction (on a different body) | $F_{12} = -F_{21}$ | Rowing a canoe, rocket launch, walking |
9. Exam Question Bank
A. MCQ / Assertion–Reason (1 mark each)
- A table moved at constant velocity by force $F$ across a floor — frictional force = $F$ (equal and opposite, since velocity is constant → net force = 0).[1]
- Two identical spring balances connected and pulled from both ends show the same reading — confirms Newton’s Third Law experimentally.[1]
B. Short Answer (2–3 marks)
- Why does a canoe move forward when the canoeist pushes water backward with the paddle? Why does it move faster with a harder push?[3]
- Explain why airbags reduce injury in a car crash, using Newton’s Second Law.[3]
- Distinguish between balanced and unbalanced forces with one example each.[2]
- Why do treads on tyres and grooves on shoe soles help us move rather than slip?[2]
C. Numerical Problems
- A bullet of mass 50 g moving at 100 m/s penetrates 50 cm into a wooden block and stops. Estimate the stopping force (assume constant deceleration).[3]
- A footballer kicks a 0.4 kg ball to a speed of 108 km/h with a force of 800 N. Find the time of contact between foot and ball.[3]
- An object of mass 2 kg moving at constant 10 m/s enters a rough patch where friction (7 N) plus an additional opposing force (3 N) act. Find the distance travelled before it stops.[3]
- A 0.1 kg bullet is fired from a 5 kg gun with a force of 2 N. Find the initial accelerations of the bullet and the gun.[3]
D. Long Answer / HOTS (4–5 marks)
- A tractor pulls a harrow of mass $m_1$ with force $F$ giving acceleration $a_1$, and separately pulls a trolley of mass $m_2$ with the same force $F$ giving acceleration $a_2$. If the tractor now pulls both together (trolley + harrow) with the same force $F$, derive the resulting acceleration in terms of $a_1$ and $a_2$.[5]
- Explain, using Newton’s third law, why a bar magnet brought near a compass causes the compass needle to move but the bar magnet appears stationary — even though the forces are equal and opposite.[4]
- A sailor jumps forward from a small boat onto the shore. Explain, using Newton’s laws, whether the boat moves, and in which direction.[3]
- Explain why a landing mat or sand bed is used in a high jump event, linking your answer to the concept of impact time and force.[3]
At a Glance — Chapter Summary
- Force is a vector — needs magnitude AND direction; SI unit = newton (N); measured using a spring balance.
- Balanced forces → net force = 0 → no change in motion. Unbalanced forces → net force ≠ 0 → causes acceleration.
- Friction opposes relative motion; depends on the nature of the surfaces in contact.
- Newton’s First Law: An object at rest stays at rest, an object in motion continues with constant velocity, unless acted on by a net force (Law of Inertia).
- Newton’s Second Law: $F = ma$ — acceleration ∝ net force, inversely ∝ mass. $F=mg$ gives weight ($g \approx 9.8\ \text{m s}^{-2}$).
- Newton’s Third Law: Every action has an equal and opposite reaction, acting on a different object — hence these paired forces never balance each other.
- Connected objects can be treated as a single system: $a = F/(m_1+m_2)$ using only external forces.
- Real-life applications: catching a ball, airbags, rocket propulsion, walking/rowing (friction/reaction helps motion), tyre treads and shoe grooves.