How Forces Affect Motion
Understand what causes objects to move, stop, and change direction — and discover the three laws that explain all motion in the universe.
A force is a push or a pull that one object exerts on another. Forces are all around us — you apply a force when you kick a ball, a bat strikes a cricket ball, or your fingers squeeze a lemon.
Forces can:
- Make a stationary object start moving
- Change the speed of a moving object
- Change the direction of a moving object
- Change the shape of an object
We measure the magnitude of a force using a spring balance. When you pull the free end of a spring balance, the scale shows the force you are applying. The weight of an object is simply the gravitational force the Earth exerts on it, and a spring balance measures that too.
The SI unit of force is the newton (written in lowercase as "newton", symbol N). The magnitude of a force tells us its strength.
The smallest force you can feel in everyday life is around a millinewton (10⁻³ N) — like a very light touch. Scientists in laboratories can measure forces as tiny as a yoctonewton (10⁻²⁴ N)!
In real life, more than one force usually acts on an object at the same time. What matters is the combined effect — the net force.
When two forces acting on an object are equal in magnitude but opposite in direction, they are called balanced forces. The net force is zero and the object does not change its motion.
When forces on an object are not equal, a non-zero net force acts. The object accelerates in the direction of the larger force.
| Situation | Forces | Net Force Formula | Direction |
|---|---|---|---|
| Same direction | F₁ and F₂ →→ | F_net = F₁ + F₂ | Same as both forces |
| Opposite directions | F₁ → and ← F₂ | F_net = F₁ − F₂ (if F₁ > F₂) | Direction of larger force |
| Equal & opposite | F → and ← F | F_net = 0 | No movement |
Multiple forces may act on an object, but its motion depends only on the net (resultant) force.
When you push a box on the floor, you might need to push quite hard before it starts moving. This is because of the force of friction — a force that opposes motion between two surfaces in contact.
The force of friction is larger on rough surfaces and smaller on smooth surfaces. The smoother the surface, the farther an object slides before stopping.
What would happen if friction suddenly disappeared from the world? You wouldn't be able to walk (your feet would slip), vehicles couldn't brake or steer, and nothing could stay still on a slope. Friction, though often a nuisance, is absolutely essential for everyday life!
For centuries, people believed a force was always needed to keep an object moving. In the 17th century, Galileo Galilei challenged this idea through thought experiments — he reasoned that if all friction were removed, a moving object would never stop on its own.
Isaac Newton built on Galileo's ideas and introduced the concept of inertia — the tendency of objects to resist any change in their state of rest or motion. He then stated his First Law of Motion in 1687.
Inertia is the property of an object by which it resists any change in its state of rest or uniform motion. Greater mass = greater inertia.
If friction were zero, an object once set in motion would continue moving forever at constant velocity — no force needed! A force is only needed to change velocity, not to maintain it.
Newton's First Law tells us what happens when net force is zero. But what happens when a net force does act on an object? It accelerates! Newton's Second Law gives the exact mathematical relationship.
Two key observations from everyday experience lead to this law:
- For the same object, a larger force produces a larger acceleration. (Force ∝ Acceleration)
- For the same force, a heavier (more massive) object has less acceleration. (Acceleration ∝ 1/mass)
One newton (1 N) is the force that gives a mass of 1 kg an acceleration of 1 m/s².
Under gravity, objects fall towards Earth with an acceleration called the acceleration due to gravity, denoted by g.
The acceleration due to gravity (g) is the same for all objects regardless of their mass. A feather and a stone fall at the same rate in the absence of air resistance.
The momentum of an object = mass × velocity. The full form of Newton's Second Law states: the rate of change of momentum of an object equals the net force acting on it. This form works even when mass changes (like in rockets). You will study this in higher grades.
Every force requires at least two objects — one that exerts the force and one that receives it. Newton's Third Law tells us what happens to both objects.
Action and reaction forces are always equal in magnitude and opposite in direction — but they act on two different objects. This is why they do NOT cancel each other out.
| Situation | Action (Force 1) | Reaction (Force 2) |
|---|---|---|
| Walking | Foot pushes ground backward | Ground pushes foot forward (friction) |
| Rowing a canoe | Paddle pushes water backward | Water pushes paddle & canoe forward |
| Rocket launch | Engine expels hot gas downward | Gas pushes rocket upward |
| Kicking a ball | Foot pushes ball forward | Ball pushes foot backward |
| Climbing a tree | Legs push trunk downward | Friction from trunk pushes person upward |
| Firing a gun | Gun pushes bullet forward | Bullet pushes gun backward (recoil) |
Yes! Newton's Third Law applies to all types of forces — contact forces (like friction, normal force) AND non-contact forces (like gravity, magnetic force, electrostatic force). For example, the Earth pulls a fruit downward with gravity, and the fruit pulls the Earth upward with an equal and opposite gravitational force.
The Vikram lander of Chandrayaan-3 used its rocket engine to fire in the direction of its motion to slow down. By Newton's Third Law, the expelled gas exerted a backward force on the lander, decelerating it for a safe soft landing near the Moon's south pole!
Newton's laws don't just apply to single objects — they apply to a system of connected objects too. When multiple objects are connected, we can treat them as one combined object and apply the laws to the whole system.
Treating connected objects as a single system simplifies calculations enormously. This approach works for any number of connected objects and reveals the power of Newton's laws in analysing complex real-world situations.
| Law | Statement | Key Concept | Formula |
|---|---|---|---|
| First Law (Law of Inertia) | An object stays at rest or in uniform motion unless a net force acts on it. | Inertia — resistance to change in motion | Net F = 0 → a = 0 |
| Second Law | Net force = mass × acceleration. Direction of acceleration = direction of net force. | Bigger force → bigger acceleration; bigger mass → smaller acceleration | F = ma |
| Third Law (Action-Reaction) | Every action has an equal and opposite reaction, acting on different objects. | Forces always come in pairs on two different objects | F₁₂ = −F₂₁ |
When the table moves at constant velocity, its acceleration is zero. By Newton's First Law, the net force must be zero.
This means: Applied force F = Frictional force (in the opposite direction).
∴ The frictional force = F (equal to the applied force, but opposite in direction).
(i) P has net force, Q does not
(ii) P has no net force, Q has net force
(iii) Both have net force
(iv) Neither has net force
Block P: Forces of 5 N and 4 N are opposite → Net force = 5 − 4 = 1 N. So P does have a net force.
Block Q: Moving at constant velocity → acceleration = 0 → net force = 0. So Q does not have a net force.
Force by 95 oarsmen (forward) = 95 × 200 = 19,000 N
Force by 5 oarsmen (backward) = 5 × 200 = 1,000 N
Net force = 19,000 − 1,000 = 18,000 N in the forward direction
(i) Opposite to force, proportional to force
(ii) Opposite to force, proportional to mass
(iii) In direction of force, inversely proportional to force
(iv) In direction of force, proportional to force
Newton's Second Law: a = F/m. Acceleration is in the direction of the net force, and is directly proportional to force (for constant mass).
Object A: straight inclined line | Object B: horizontal flat line | Object C: curved line | Object D: straight inclined line (decreasing)
A curved position-time graph means the object's position is changing at a non-uniform rate — it is accelerating. Acceleration implies a net force is acting on it. All other objects have straight (or flat) position-time graphs, meaning constant velocity (or rest), so net force = 0.
Yes, the boat will move — backward (away from the shore).
When the sailor jumps forward, by Newton's Third Law, they push backward on the boat. The boat receives this backward push and moves in the direction opposite to the sailor's jump — away from the shore.
This is action-reaction: Sailor's feet push the boat backward → Boat pushes the sailor forward.
When the athlete lands, their velocity decreases from a high value to zero. The mat or sand is soft and compressible, so it increases the time over which this deceleration happens.
By Newton's Second Law: F = ma = m × (Δv/Δt). For the same change in velocity (Δv), a larger time (Δt) means a smaller acceleration, which means a smaller force on the athlete's body. This reduces the risk of injury.
If the athlete landed on a hard surface, stopping would be almost instantaneous → enormous force → severe injury.
(i) Loaded exerts more force | (ii) Empty exerts more force | (iii) Neither exerts force | (iv) Both exert equal force
By Newton's Third Law, during any collision, both objects exert equal and opposite forces on each other — regardless of how heavy or light they are. The heavier cart does not push harder; the forces are always equal in magnitude.
From the graph, a × m = constant = 10 N (approximately). So the force F = ma = constant.
The force-mass graph is a horizontal straight line at F = 10 N (constant), because the same force was applied to all objects of different masses to get the readings on the acceleration-mass graph.
From the graph: Initial velocity u = 0 m/s, Final velocity v = 30 m/s, Time t = 8 s
Acceleration: a = (v − u) / t = (30 − 0) / 8 = 3.75 m/s²
Using F = ma: F = 10 kg × 3.75 m/s² = 37.5 N
Given: m = 50 g = 0.05 kg, u = 100 m/s, v = 0 m/s, s = 50 cm = 0.5 m
Using v² = u² + 2as:
0 = (100)² + 2 × a × 0.5
0 = 10000 + a
a = −10000 m/s²
Using F = ma:
F = 0.05 × 10000 = 500 N (opposing direction — deceleration force)
Speed = 108 km/h = 108 × (1000/3600) = 30 m/s
Using Impulse = Force × Time = Change in momentum:
F × t = m × (v − u) = 0.4 × (30 − 0) = 12 N·s
t = 12 / 800 = 0.015 seconds
Total opposing force = 7 + 3 = 10 N
Acceleration (deceleration): a = F/m = 10/2 = 5 m/s² (negative, opposing motion)
Using v² = u² + 2as:
0 = (10)² + 2 × (−5) × s
0 = 100 − 10s
s = 100/10 = 10 metres
From the given information:
F = m₁ × a₁ → m₁ = F/a₁
F = m₂ × a₂ → m₂ = F/a₂
When both are pulled together:
a = F / (m₁ + m₂) = F / (F/a₁ + F/a₂)
Simplifying:
a = F / F(1/a₁ + 1/a₂) = 1 / (1/a₁ + 1/a₂)
Multiplying numerator and denominator by a₁ × a₂:
Yes, by Newton's Third Law, both the bar magnet and the compass needle exert equal and opposite magnetic forces on each other.
However, using Newton's Second Law: a = F/m
The compass needle is very light, so the same force produces a large acceleration on the needle — it moves visibly.
The bar magnet, on the other hand, is much heavier (and is likely being held by a person). Even if it receives the same force, its large mass means its acceleration is negligibly small. The person's grip also provides an additional balancing force. So the bar magnet doesn't appear to move.