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Class 9 Science Chapter 6: How Forces Affect Motion — Notes, Examples & Practice

Why does a passenger lurch forward when a bus brakes? Why does a gun recoil? Why do cricketers pull their hands back while catching? Newton's three laws of motion answer all of these. This chapter explains forces, inertia, momentum and the conservation of momentum, with a simple routine for solving force problems: draw the object, mark the forces, choose a positive direction.

1Force and balanced forces

A force is a push or a pull. It can start or stop motion, change speed, change direction, or change shape. Its SI unit is the newton (N), and it is a vector — direction matters.

When several forces act, what matters is the net (resultant) force. If the forces cancel, they are balanced: the net force is zero and the object's motion does not change (it stays at rest or keeps moving uniformly). A book on a table has its weight balanced by the table's upward push.

If the forces do not cancel, they are unbalanced, and the object's velocity changes — it speeds up, slows down or turns. Friction is a force that opposes sliding between surfaces; it is why a ball rolling on grass eventually stops.

Key points & definitions
  • Net force = 0 → balanced → no change in velocity.
  • Net force ≠ 0 → unbalanced → acceleration.
  • Friction opposes relative motion between surfaces.
Worked example 1

Two children push a box: one with 30 N to the right, the other with 20 N to the left. Friction is negligible. Find the net force.

  1. Take right as positive: 30+(−20)=1030 + (-20) = 10 N.
  2. The net force is 10 N to the right, so the box accelerates to the right.

Answer: 10 N to the right (unbalanced).

Common mistakes
  • Thinking a moving object must have a net force on it — a body moving at constant velocity has zero net force.

2Inertia and the first law

Newton's first law: an object stays at rest, or keeps moving with uniform velocity in a straight line, unless an unbalanced external force acts on it.

This tendency to resist a change in the state of rest or motion is called inertia. Mass is the measure of inertia: a loaded truck is much harder to start or stop than a bicycle.

Everyday inertia: passengers jerk forward when a bus brakes (their bodies keep moving); dust leaves a carpet when it is beaten (the carpet moves, the dust stays); a coin on a card over a glass drops into the glass when the card is flicked away. Seat belts protect us by supplying the force that stops our bodies.

Key points & definitions
  • First law = law of inertia.
  • Greater mass ⇒ greater inertia.
Common mistakes
  • Saying an object 'needs a force to keep moving' — it needs a force only to change its motion (e.g. to overcome friction).

3Momentum and the second law

Momentum p=mvp = mv (mass × velocity) measures the 'quantity of motion'. Its unit is kg m/s and it is a vector. A slow truck and a fast bullet can both have large momentum.

Newton's second law: the rate of change of momentum of an object is proportional to the net force on it, and happens in the direction of the force. For constant mass this becomes F=maF = ma, which defines the newton: 1 N gives a 1 kg mass an acceleration of 1 m/s².

Rearranged, F=ΔptF = \dfrac{\Delta p}{t}: the same change in momentum produces a smaller force if it happens over a longer time. That is why cricketers pull their hands back while catching, why airbags and seat belts stretch, and why high-jumpers land on soft mattresses.

Key points & definitions
  • p=mvp = mv
  • F=ma=m(v−u)tF = ma = \dfrac{m(v - u)}{t}
  • F=ΔptF = \dfrac{\Delta p}{t} — longer time ⇒ smaller force.
  • Weight W=mgW = mg (g≈9.8g \approx 9.8 m/s²)
Worked example 1

A 1200 kg car accelerates from 10 m/s to 25 m/s in 5 s. Find the force needed (ignoring friction) and the change in momentum.

  1. a=25−105=3a = \dfrac{25 - 10}{5} = 3 m/s².
  2. F=1200×3=3600F = 1200 \times 3 = 3600 N.
  3. Δp=1200×(25−10)=18000\Delta p = 1200 \times (25 - 10) = 18000 kg m/s (check: F×t=3600×5F \times t = 3600 \times 5 ✓).

Answer: 3600 N; 18,000 kg m/s.

Worked example 2

A 0.15 kg cricket ball moving at 20 m/s is stopped by a fielder. Find the average force if it stops in 0.05 s, and in 0.2 s (hands pulled back).

  1. Δp=0.15×20=3\Delta p = 0.15 \times 20 = 3 kg m/s.
  2. In 0.05 s: F=30.05=60F = \dfrac{3}{0.05} = 60 N.
  3. In 0.2 s: F=30.2=15F = \dfrac{3}{0.2} = 15 N.

Answer: 60 N vs 15 N — pulling the hands back cuts the force to a quarter.

Common mistakes
  • Confusing mass (kg) and weight (N).
  • Using F=maF = ma with aa in km/h per second.

4The third law

Newton's third law: whenever one object exerts a force on another, the second exerts an equal and opposite force on the first. Forces always come in action–reaction pairs.

The two forces act on different objects, so they never cancel each other. When you walk, your foot pushes the ground backward and the ground pushes you forward. A rocket pushes hot gases down; the gases push the rocket up.

Equal forces do not mean equal effects: when a gun fires, the force on the bullet and the gun are equal, but the much heavier gun gets a much smaller acceleration (a=F/ma = F/m).

Key points & definitions
  • FAB=−FBAF_{AB} = -F_{BA} — equal size, opposite direction, different bodies.
  • Action and reaction act at the same time.
Worked example 1

A horse pulls a cart. By the third law, the cart pulls the horse back equally. How can they move?

  1. The two pulls act on different bodies, so they do not cancel.
  2. The horse moves forward because the ground pushes it forward (reaction to the horse pushing the ground back) more strongly than the cart pulls it back.
  3. The cart moves because the horse's pull on it exceeds the friction on the cart.

Answer: Look at the forces on each body separately.

Trick / memory aid

Name both bodies every time: 'force of A on B' and 'force of B on A'.

Common mistakes
  • Saying weight and the normal force on a book are an action–reaction pair — they act on the same book; they are balanced forces, not a third-law pair.

5Conservation of momentum

When two objects interact (collide, push apart) with no external force on them, the forces they exert on each other are equal and opposite and act for the same time, so the momentum one gains equals the momentum the other loses.

Therefore the total momentum of an isolated system stays constant: m1u1+m2u2=m1v1+m2v2m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2.

This explains the recoil of a gun (total momentum before firing is 0, so the gun moves backward), the motion of rockets, and the result of collisions between vehicles or balls.

Key points & definitions
  • m1u1+m2u2=m1v1+m2v2m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2
  • Recoil: 0=mbvb+mgvg⇒vg=−mbvbmg0 = m_b v_b + m_g v_g \Rightarrow v_g = -\dfrac{m_b v_b}{m_g}
Worked example 1

A 4 kg gun fires a 20 g bullet at 300 m/s. Find the recoil velocity of the gun.

  1. Before firing, total momentum =0= 0.
  2. 0=0.02×300+4v⇒4v=−6⇒v=−1.50 = 0.02 \times 300 + 4 v \Rightarrow 4v = -6 \Rightarrow v = -1.5 m/s.

Answer: 1.5 m/s backward.

Worked example 2

A 1000 kg car at 20 m/s hits a stationary 1500 kg car, and they move together. Find their common velocity.

  1. Before: 1000×20+0=200001000 \times 20 + 0 = 20000 kg m/s.
  2. After: (1000+1500)v=20000⇒v=8(1000 + 1500)v = 20000 \Rightarrow v = 8 m/s.

Answer: 8 m/s in the original direction.

Common mistakes
  • Forgetting the minus sign for motion in the opposite direction.
  • Not converting grams to kilograms.

Important questions

Try each question on paper first, then tap it to check the answer.

Basic Recall and direct use

State Newton's first law and why it is called the law of inertia.Answer
A body continues at rest or in uniform straight-line motion unless an unbalanced force acts on it. It describes inertia — the tendency of bodies to resist changes in motion.
Find the momentum of a 50 kg girl running at 4 m/s.Answer
p=50×4=200p = 50 \times 4 = 200 kg m/s.
What force gives a 5 kg mass an acceleration of 2 m/s²?Answer
F=5×2=10F = 5 \times 2 = 10 N.

Medium Two or three steps

Why do passengers fall backward when a bus suddenly starts?Answer
Their feet move with the bus, but the upper body, due to inertia of rest, tends to stay where it is, so they lean backward.
A force of 20 N acts on a 4 kg body at rest for 3 s. Find its final velocity and distance moved.Answer
a=5a = 5 m/s². v=0+5×3=15v = 0 + 5 \times 3 = 15 m/s. s=12×5×9=22.5s = \dfrac{1}{2} \times 5 \times 9 = 22.5 m.
Explain, using momentum, why karate experts can break slabs with a fast hand strike.Answer
The hand's large momentum is reduced to zero in a very short time, so the force (Δp/t\Delta p/t) on the slab is very large.

Advanced Reasoning and HOTS

A 60 kg boy jumps from a 140 kg boat at rest, horizontally at 3 m/s. Find the boat's velocity. Why is it easier to jump from the ground?Answer
0=60×3+140v⇒v=−180140≈−1.290 = 60 \times 3 + 140v \Rightarrow v = -\dfrac{180}{140} \approx -1.29 m/s (opposite direction). From the ground the 'recoiling' body is the whole Earth, whose huge mass means it hardly moves, so all your push goes into your own motion.
Two balls of masses 2 kg and 1 kg move towards each other at 3 m/s and 4 m/s. After collision the 2 kg ball moves back at 1 m/s. Find the velocity of the 1 kg ball.Answer
Take the 2 kg ball's initial direction as positive: before =2(3)+1(−4)=2= 2(3) + 1(-4) = 2. After: 2(−1)+1(v)=2⇒v=42(-1) + 1(v) = 2 \Rightarrow v = 4 m/s in the positive direction (it bounces back).

Self-check quiz

Five quick questions. Tap an option to see if you are right.

Mass is a measure of
The SI unit of momentum is
Action and reaction forces
A 2 kg body accelerates at 3 m/s². The net force is
Airbags reduce injury mainly because they

FAQ

If action equals reaction, why don't forces always cancel?

Because the two forces act on different objects. To decide whether an object accelerates, add only the forces acting on that object.

What is the difference between mass and weight?

Mass (kg) is the amount of matter and measures inertia; it is the same everywhere. Weight (N) is the gravitational force on the mass, W=mgW = mg, and changes with location (about one-sixth on the Moon).

Which numericals are most common?

F=maF = ma with the equations of motion, change of momentum and average force, and conservation of momentum (recoil and objects sticking together).

Book references

  • NCERT Exploration, Chapter 6: How Forces Affect MotionRead the chapter and do every exercise set first.
  • Science for Class 9 (Physics, Chemistry, Biology) — Lakhmir Singh & Manjit Kaur (S. Chand)Extra numericals and short answers; chapter order follows the old syllabus, so match by topic.
  • S. Chand's Science for Class 9 — S. ChandUseful extra reading and practice; match by topic.
  • Exemplar Problems in Science, Class IX — NCERTConcept-testing MCQs and short answers (written for the old book).

These notes, examples and questions are written by PrepRung in our own words to help you study the NCERT Exploration book. NCERT and CBSE are not affiliated with PrepRung. Always study from your textbook too.