⚡ CLASS 9 SCIENCE · CHAPTER 6 · PART 2 of 2
How Forces Affect Motion
Newton’s Second Law, Third Law, Forces on a System of Objects — with derivations, real-life applications, and fully solved numerical problems.
📖 Exploration · Grade 9
🧪 5 Activities
📝 8 Solved Examples
Quick Navigation
6.5 Newton’s Second Law
6.6 Newton’s Third Law
6.7 System of Objects
Revise, Reflect, Refine
Final Quiz
At a Glance
6.5
Newton’s Second Law of Motion
A force can set an object in motion, bring it to rest, or change its velocity — i.e., a force produces acceleration. But what is the relationship between net force and acceleration?
🤔 Think as a Scientist — Hypothesis 1
A gentle push on a ball gives a small acceleration; a strong push gives a larger acceleration. Hypothesis: for the same object, a larger force results in larger acceleration.
Activity 6.3: Let Us Experiment (Demonstration)
🛒
Cart & Pulley System — Testing Force vs Acceleration
- Build a cart using a cardboard box with 2 pencils as axles and 4 wheels. Attach a thread to the front.
- Set up a pulley (pipe) at the table edge; pass the thread over it and attach a paper cup to the end.
- Place objects in the cup — as released, the cup’s weight pulls the cart with a constant force.
- Record a slow-motion video; measure time T₁ for the cart to travel a fixed distance.
- Double the mass in the cup (i.e., double the force) and repeat to get time T₂.
Analysis: Using s = ½aT² for both cases (u = 0): a₁/a₂ = T₂²/T₁². When force was doubled for the same cart mass, acceleration increased.
📘 Conclusion
The acceleration of an object of fixed mass increases as the net force applied on it increases.
🤔 Think as a Scientist — Hypothesis 2
With the same force, lighter objects are easier to set in motion than heavier ones. Second hypothesis: for the same force, a smaller mass has a larger acceleration.
Activity 6.4: Let Us Experiment (Demonstration)
⚖️
Testing Mass vs Acceleration
- Repeat Activity 6.3, but keep the cup’s mass constant; instead double the mass of the cart by adding objects.
- Measure the cart’s mass with a weighing scale.
- Repeat the timing steps and find the ratio of accelerations.
Conclusion: For the same force, when cart mass was doubled, acceleration decreased. So acceleration is inversely related to mass.
NEWTON’S SECOND LAW OF MOTION
When a net force acts on an object, the object accelerates in the direction of the net force. The magnitude of the acceleration is proportional to the magnitude of the net force and is inversely proportional to the mass of the object.
a = F / m or F = ma
a = acceleration, F = net force, m = mass
📘 Definition — The Newton
If m = 1 kg and a = 1 m s⁻², then F = 1 kg × 1 m s⁻² = 1 N. One newton is the force that produces an acceleration of 1 m s⁻² on an object of mass 1 kg.
🧵 Threads of Curiosity
How much does a force of 1 N feel? If you hold a 100 g mass in your palm, the upward force your palm applies is around 1 N.
Gravitational Force & Acceleration due to Gravity
The acceleration during free fall towards Earth is called acceleration due to gravitational force (g), unit m s⁻². Using F = ma, the gravitational force on a mass m is:
F = mg
g = 9.8 m s⁻² (taken as 10 m s⁻² for quick estimation)
📌 Note
The acceleration due to gravitational force by the Earth (g) does not depend on the mass of the object.
🧵 Threads of Curiosity — Why Measurements Don’t Match Exactly
In Activity 6.3, doubling the force should double the acceleration — but you may find the increase slightly less than a factor of two. In Activity 6.4, doubling mass should halve acceleration, but the value may differ slightly. Apart from measurement errors, friction between the cart’s wheels and surface causes such differences.
🚀 Ready to Go Beyond — Momentum Form
The more complete form of Newton’s second law is expressed in terms of momentum (mass × velocity, same direction as velocity). The law states: the rate of change of momentum is proportional to the net force, in the direction the force acts. This form applies even when mass is not constant.
Real-Life Applications of Newton’s Second Law
🌍 Bridging Science and Society — Cricket Catch & Airbags
While catching a fast ball, a fielder pulls their hands backward with the ball, increasing the time over which velocity reduces to zero. This reduces acceleration, requiring less force and minimising injury.
Similarly, airbags in vehicles inflate quickly during a collision. The passenger’s head/chest push into the soft cushion over a longer time, reducing acceleration and force — lowering injury risk, especially combined with seat belts.
Cracking a coconut: A coconut hit hard against the ground stops in a very short time. To change its velocity so quickly, the ground must exert a very large force — this breaks the shell.
📝 Example 6.4 — Weightlifter’s Force
A weightlifter holds a barbell with 10 kg fixed on each side; bar itself is 10 kg. How much force does she apply to keep it steady?
Total mass = 30 kg. Gravitational force F = mg = 30 × 9.8 = 294 N (downward). To keep it steady, she applies an equal force 294 N upward.
📝 Example 6.5 — Pushing a Block Against Friction
A 25 kg block has max friction of 50 N opposing motion. Find displacement in 2 s if pushed with (i) 50 N and (ii) 55 N.
(i) Applied force = friction → balanced → net force = 0 → block remains stationary.
(ii) Net force = 55 − 50 = 5 N. a = F/m = 5/25 = 0.2 m s⁻².
s = ut + ½at² = 0 + ½ × 0.2 × (2)² = 0.4 m in the forward direction.
📝 Example 6.6 — Sports Car Velocity-Time Graph
A 1500 kg sports car’s velocity-time graph: rises 0→10 m/s over 0–5 s, constant 10 m/s from 5–10 s, falls 10→0 m/s over 10–15 s. Find the force in each interval.
0–5 s: a = (10−0)/5 = 2 m s⁻². F = 1500 × 2 = 3000 N (towards east).
5–10 s: constant velocity → a = 0 → F = 0 N (no force acting).
10–15 s: a = (0−10)/5 = −2 m s⁻². F = 1500 × (−2) = −3000 N, i.e., 3000 N towards west (opposing motion).
⏸️ Pause and Ponder
- A 100 g toy car moves at a constant velocity of 0.5 m s⁻¹. What is the net force acting on it?
- Two children of different masses sit on identical swings. For identical initial acceleration, for which child would you need a larger force? Explain why.
- How are glass items packed for transportation using bubble wrap or hay protected from damage?
Q1. A 4 kg object experiences a net force of 12 N. What is its acceleration?
48 m s⁻²
8 m s⁻²
3 m s⁻²
1/3 m s⁻²
Q2. As per Newton’s second law, acceleration is directly proportional to:
Net force
Mass
Time
Distance
Q3. In Activity 6.4, when the mass of the cart was doubled (force kept the same), the acceleration:
Doubled
Decreased (halved)
Remained the same
Became zero
Q4. A weightlifter holds a 30 kg barbell steady. What upward force must she apply? (take g = 9.8 m s⁻²)
30 N
98 N
3 N
294 N
6.6
Newton’s Third Law of Motion
At least two objects must interact for a force to come into play. When you kick a ball, you also feel a force from the ball on your foot. How are both objects affected?
Activity 6.5: Let Us Explore
🪑
Chair with Wheels & a Heavy Table
- Sit on a wheeled chair with legs raised. Push a heavy table away with both hands.
- Observe: does your chair move in the opposite direction?
- Now try pulling the table towards you. Which direction does the chair move now?
Conclusion: Each time you applied a force on the table, the table applied an equal and opposite force on you.
🌍 Bridging Science and Society — Walking, Cycling & Friction
To move forward on a bicycle without pedalling, you push the ground backward with your feet — the ground pushes you (and the bicycle) forward. This is exactly how walking/running works too: your feet push the ground backward, and the ground’s friction pushes you forward.
If there were no friction, your foot would slip backward while pushing the ground, and you’d fall. This is why grooves on footwear soles and treads on tyres increase friction — and why it’s hard to walk on wet polished floors or ice, or risky to drive on wet/snowy roads.
Activity 6.6: Let Us Verify
🔗
Two Spring Balances Connected Together
- Take two identical spring balances; connect them by their hooks, placed horizontally on a table.
- Fix the free end of one to an immovable object or hold it with your hand.
- Pull the free end of the other with your other hand; predict the readings on both scales.
- Repeat with varying force magnitudes — compare your predictions with observations.
Conclusion: The readings of both spring balances are always the same — the forces they apply on each other in opposite directions are equal in magnitude.
NEWTON’S THIRD LAW OF MOTION
Whenever one object is exerting a force on a second object, the second object is simultaneously exerting an equal and opposite force on the first object.
📌 Note
The forces always occur in pairs, but these two forces act on two different objects — so they never cancel each other out.
Climbing a tree: A person’s legs push down against the trunk; friction between trunk and legs pushes the person upward by an equal force. This is why it’s harder to climb smooth tree trunks (less friction).
Rowing a canoe: The paddle pushes water backward; water pushes the paddle (and canoe) forward with an equal force. These act on different objects (paddle vs water), so they don’t cancel. Pushing harder → larger forward force → faster canoe.
🧵 Threads of Curiosity
Apart from paddling force, factors like drag, water currents, mass of the canoe, and rowing style also affect canoe speed.
Activity 6.7: Let Us Understand — Rocket Motion
🎈
Balloon, Straw & Thread
- Inflate a balloon; tie its neck with thread. Stick a drinking straw on the balloon with adhesive tape, one end pointing toward the neck.
- Pass a long thread through the straw; tie both ends to nails on two walls, keeping it taut.
- Remove the thread tied to the neck — observe which direction the balloon and straw move.
Conclusion: The balloon material pushes air molecules out as it shrinks. The escaping air exerts an equal and opposite force on the balloon, causing it to move opposite to the direction the air rushes out.
A rocket works similarly: its engine produces gas and expels it downward, which exerts an equal and opposite force on the rocket upward. Since this upward force exceeds the rocket’s weight, the net force is upward, and the rocket lifts off.
If a rocket’s engine fires in the direction of motion (in space), exhaust gases push it in the opposite direction, slowing it down. This is how the Vikram lander of Chandrayaan-3 slowed down for a soft landing near the Moon’s south pole.
📌 Note — Important Distinction
The pair of equal-and-opposite forces (Newton’s third law) acts on two different objects, so they do not balance each other. If two equal-and-opposite forces act on the same object, then they balance each other.
Newton’s third law applies to all forces — contact or non-contact — encountered in everyday mechanical situations: two bar magnets repelling/attracting equally, two similarly charged balloons repelling, or the Earth and a fruit applying equal gravitational forces on each other.
📝 Example 6.7 — Why Doesn’t the Earth Move Towards the Fruit?
The Earth and a falling fruit apply equal and opposite gravitational forces on each other. Then why does the fruit move towards Earth, but Earth doesn’t seem to move towards the fruit?
Though forces are equal, Earth’s mass is so much larger than the fruit’s. Since a = F/m, Earth’s acceleration is extremely small — too small to be noticed.
📝 Example 6.8 — Bullet & Gun Recoil
A 0.1 kg bullet fires from a 5 kg gun with a force of 2 N; the gun recoils. Find the initial accelerations of both.
Recoil force on gun (Newton’s 3rd law) = 2 N.
Gun’s acceleration = 2 N / 5 kg = 0.4 m s⁻².
Bullet’s acceleration = 2 N / 0.1 kg = 20 m s⁻².
Even though forces are equal, accelerations differ greatly because of different masses.
📌 Note
Even though forces acting on two interacting objects are always equal in magnitude, they do not, in general, produce equal acceleration — because the masses of the objects may be different.
⏸️ Pause and Ponder
- Why does a fireperson sometimes struggle when holding the pipe issuing water?
- Suppose a spacecraft is moving where gravitational force is negligible. Suggest how it can change its velocity.
Q1. Two objects of different masses experience equal and opposite forces during a collision (Newton’s third law). Which statement is correct?
Both objects get equal acceleration
The lighter object gets larger acceleration
The heavier object gets larger acceleration
Neither object accelerates
Q2. Newton’s third law force pairs always act on:
The same object, so they cancel out
No object at all
Two different objects, so they never cancel out
Only contact forces, never non-contact forces
Q3. In Activity 6.7 (balloon and straw), the balloon moves opposite to the direction in which air rushes out. This is best explained by:
Newton’s third law
Newton’s first law
The law of gravitation
Friction
Q4. While climbing a coconut tree, a person’s legs push down against the trunk. What pushes the person upward?
Gravity
Normal force from the ground
Air resistance
Friction between the trunk and legs (Newton’s 3rd law reaction)
6.7
Forces Acting on a System of Objects
Can Newton’s laws be applied to two or more connected objects? Consider two boxes (masses m₁, m₂) on a frictionless surface, connected by a string. A force F pulls Box 1 to the right; Box 1 pulls Box 2 via the string (tension T); by Newton’s third law, Box 2 pulls Box 1 back with equal tension T.
📘 The System Approach
Instead of analysing each box separately, treat both boxes + string as a single system. Internal forces (tension T, acting on both boxes) need not be considered — only external forces (force F) matter.
a = F / (m₁ + m₂)
Acceleration of the connected system, treated as mass (m₁+m₂)
The system of two boxes accelerates just like a single object of mass (m₁ + m₂). Analysing the boxes individually gives the same result — but treating connected objects as a system simplifies the analysis significantly.
🚀 Ready to Go Beyond
In addition to F, external forces on the system also include gravitational force (m₁g + m₂g) downward, balanced by the normal force (N₁ + N₂) from the ground.
🧵 Threads of Curiosity
While walking, your arms and legs move in a complex manner. Yet your overall motion can be studied by treating your body as a single object. Science often becomes simpler when we stop looking at parts and start looking at the whole.
Q1. Two boxes (m₁ and m₂) connected by a string are pulled by an external force F on a frictionless surface. The system’s acceleration is:
F × (m₁ + m₂)
F / m₁ only
F / m₂ only
F / (m₁ + m₂)
Q2. In a system of two connected boxes, the tension in the connecting string is treated as:
An external force on the system
An internal force, which can be ignored when analysing the whole system
Not a real force
Equal to the gravitational force
Q3. Why is it simpler to treat connected objects (like two boxes joined by a string) as a single system?
Internal forces cancel out, so only external forces need to be considered
It gives a completely different (more accurate) answer
Friction is automatically zero
Mass becomes irrelevant
📝
Revise, Reflect, Refine — Chapter-End Questions
1.Using a horizontal force F, a table is moved across the floor at a constant velocity. How much is the frictional force exerted by the floor on the table?
Since the table moves at constant velocity, net force = 0 (Newton’s 1st law). So the frictional force is equal in magnitude to F, acting opposite to the direction of motion.
2.For a ball on a frictionless surface: (i) no net force → velocity remains same/increase/decrease? (ii) force in direction of motion → velocity remains same/increase/decrease? (iii) force opposite to motion → velocity remains same/increase/decrease?
(i) Remain the same (Newton’s 1st law). (ii) Increase (force adds to motion). (iii) Decrease (force opposes motion).
3.Blocks P (4 N and 5 N opposite forces) and Q (moving at constant velocity) on a smooth surface — which experiences a net force?
P experiences a net force (5 − 4 = 1 N, unbalanced). Q moves at constant velocity on a smooth (frictionless) surface, meaning no net force acts on it. Answer: (i) P experiences a net force and Q does not.
4.100 oarsmen row a snake boat; 95 row backward (to propel forward) but 5 mistakenly row the opposite way. Each applies 200 N. What is the net force on the boat?
Forward force = 95 × 200 = 19000 N. Opposing force = 5 × 200 = 1000 N. Net force = 19000 − 1000 = 18000 N in the forward direction.
5.When a net force acts on an object, the object accelerates: (i)-(iv) options about direction and proportionality.
(iv) in the direction of force, with acceleration proportional to the force acting on the object (as per F = ma).
6.Position-time graphs for objects A (straight inclined line), B (horizontal), C (curved/exponential), D (straight inclined, decreasing) — on which object does a net force act?
A: straight line → constant velocity → no net force. B: horizontal → at rest → no net force. D: straight line → constant velocity → no net force. C: curved (changing slope) → changing velocity → acceleration → net force acts. Answer: (iii) Object C.
7.A sailor jumps out from a small boat to the shore. As the sailor jumps forward, will the boat move? If yes, in which direction and why?
Yes, the boat moves backward (away from the shore). By Newton’s 3rd law, as the sailor pushes the boat backward with their feet to jump forward, the boat exerts an equal and opposite force on the sailor — pushing the sailor forward and the boat backward.
8.During a high jump, a landing mat or sand bed is placed for the athlete. Explain why.
The soft mat/sand increases the time over which the athlete’s velocity reduces to zero on landing. By F = ma, a longer time means smaller deceleration, hence a smaller force on the athlete’s body — reducing injury risk.
9.A loaded hand cart collides with an identical empty hand cart. During collision, which statement is correct about the forces exerted?
(iv) The loaded cart and the empty cart both exert an equal magnitude of force on each other — as per Newton’s 3rd law, forces between two interacting objects are always equal and opposite, regardless of mass. (Their resulting accelerations differ, but the forces are equal.)
10.An acceleration-mass graph shows acceleration decreasing as mass increases (inverse relationship, force constant). Plot the force-mass graph.
Since a = F/m and the graph shows a × m = constant (= F), the force is constant regardless of mass. The force-mass graph would be a horizontal straight line — force does not change with mass since F is fixed in this experiment (only acceleration changes due to mass).
11.A 10 kg object’s velocity-time graph rises from 10 m/s to 30 m/s between t = 4 s and t = 8 s (straight line). Calculate the force.
a = (30 − 10)/(8 − 4) = 20/4 = 5 m s⁻². F = ma = 10 × 5 = 50 N.
12.A 50 g bullet at 100 m s⁻¹ enters a wooden block and stops after penetrating 50 cm. Estimate the stopping force.
m = 0.05 kg, u = 100 m s⁻¹, v = 0, s = 0.5 m.
Using v² = u² + 2as: 0 = (100)² + 2a(0.5) → a = −10000 m s⁻².
F = ma = 0.05 × 10000 = 500 N (stopping/retarding force).
13.A footballer kicks a 0.4 kg ball to 108 km h⁻¹ with an estimated force of 800 N. Find the contact time.
108 km h⁻¹ = 30 m s⁻¹. a = F/m = 800/0.4 = 2000 m s⁻².
Using v = u + at: 30 = 0 + 2000 × t → t = 30/2000 = 0.015 s.
14.A 2 kg object at constant velocity 10 m s⁻¹ hits a rough patch with friction 7 N, plus an additional 3 N opposing force is applied. Find the distance travelled before stopping.
Total opposing force = 7 + 3 = 10 N. a = F/m = 10/2 = 5 m s⁻² (deceleration).
Using v² = u² − 2as: 0 = (10)² − 2(5)s → s = 100/10 = 10 m.
15.A tractor with force F gives a harrow (mass m₁) acceleration a₁, and a trolley (mass m₂) acceleration a₂. If both are pulled together with the same F, find the resulting acceleration in terms of a₁ and a₂.
F = m₁a₁ = m₂a₂, so m₁ = F/a₁ and m₂ = F/a₂.
Combined: a = F/(m₁+m₂) = F / (F/a₁ + F/a₂) = 1 / (1/a₁ + 1/a₂) = a₁a₂/(a₁+a₂).
16.A bar magnet near a compass: both exert equal and opposite forces, but the compass needle moves while the bar magnet doesn’t. Explain why.
Although the forces are equal in magnitude, the compass needle has a very small mass compared to the bar magnet (which is usually held in hand or much heavier). Since a = F/m, the needle gets a noticeable acceleration and moves, while the bar magnet’s acceleration is too small to observe.
🏆 Part 2 Final Quiz
15 questions covering Newton’s Second Law, Third Law & System of Objects
1. Newton’s second law states that acceleration is:
Proportional to mass, inversely proportional to force
Proportional to net force, inversely proportional to mass
Independent of both force and mass
Inversely proportional to both force and mass
2. One newton is defined as the force that produces an acceleration of:
1 m s⁻² on a 1 kg object
1 m s⁻² on a 10 kg object
10 m s⁻² on a 1 kg object
1 m s⁻¹ on a 1 kg object
3. A 5 kg object accelerates at 4 m s⁻². What is the net force acting on it?
1.25 N
9 N
20 N
45 N
4. The acceleration due to gravity (g) near the Earth’s surface is approximately:
1 m s⁻²
98 m s⁻²
100 m s⁻²
9.8 m s⁻²
5. Airbags in cars reduce injury by:
Increasing the force on the passenger
Increasing the time of impact, reducing acceleration and force
Decreasing the time of impact
Stopping the car instantly
6. Newton’s third law states that for every action, there is:
A smaller and opposite reaction
An equal reaction in the same direction
An equal and opposite reaction
No reaction at all
7. Newton’s third law force pairs act on:
Two different objects
The same object
No object in particular
Only non-contact forces
8. A rocket lifts off because:
It has no weight in space
Air pushes it upward
The exhaust gas is lighter than air
Expelled gas exerts an equal, opposite upward force on the rocket, exceeding its weight
9. A 0.1 kg bullet and a 5 kg gun experience equal and opposite forces (2 N) during firing. Why does the bullet have a much higher acceleration than the gun?
The bullet experiences a larger force
The bullet has a much smaller mass, so a = F/m is larger
The gun has friction, the bullet doesn’t
There is no difference in acceleration
10. Why does the Earth not appear to move towards a falling fruit, even though the forces are equal?
The Earth has no gravity
The fruit’s force on Earth is much smaller
Earth’s mass is so large that its acceleration is too small to notice
Earth is not affected by forces
11. While walking, your foot pushes the ground backward. The ground’s friction pushes you:
Forward
Backward
Sideways
Does not affect your motion
12. Two boxes (m₁ and m₂) connected by a string are pulled by an external force F on a frictionless surface. The system’s acceleration is:
F × (m₁ + m₂)
F / m₁ only
F / m₂ only
F / (m₁ + m₂)
13. In the two-box system connected by a string, the tension force is considered:
An external force
An internal force
Not a real force
Equal to the applied force F
14. A canoeist paddles, pushing water backward. The water pushes the paddle forward. Why don’t these two equal-and-opposite forces cancel out?
They do cancel out — the canoe doesn’t move
One force is non-contact
They act on two different objects (water and paddle), not the same object
Water has no mass
15. A 1500 kg car moves at a constant 10 m/s (velocity-time graph is a horizontal line). What is the net force on it during this interval?
0 N
1500 N
3000 N
15000 N
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📋 At a Glance — Part 2 Summary
- Newton’s Second Law: a = F/m (or F = ma). Acceleration is proportional to net force and inversely proportional to mass. Direction of acceleration = direction of net force.
- Newton: 1 N = force that gives 1 kg an acceleration of 1 m s⁻².
- Gravitational force: F = mg, where g ≈ 9.8 m s⁻² (independent of mass).
- Newton’s Third Law: Every action has an equal and opposite reaction, acting on two different objects — applies to both contact and non-contact forces.
- System of objects: Connected objects can be treated as a single system with combined mass; only external forces matter (internal forces like tension cancel out).
← Part 1: Force, Friction & Newton’s First Law
📘 Part 2: Newton’s 2nd Law, 3rd Law & Systems