Introduction
A force is a push or pull on an object. Forces can change an object's speed, direction, or shape. Isaac Newton formalised the relationship between force and motion in three fundamental laws that form the cornerstone of classical mechanics.
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Key Concepts
- 1. Force
- Force is a vector quantity. SI unit: Newton (N).
- 1 N is the force needed to accelerate a 1 kg mass at 1 m/s2. So 1 N = 1 kg m/s2.
- Forces can be contact forces (friction, normal reaction, tension) or non-contact forces (gravity, magnetic, electrostatic).
- A net (resultant) force is the vector sum of all forces acting on an object.
- 2. Newton's First Law of Motion (Law of Inertia)
- · "An object at rest remains at rest, and an object in motion continues in a straight line at constant velocity, unless acted upon by a net external force." ·
- Inertia: the tendency of an object to resist changes in its state of motion. More mass = more inertia.
- Examples: passengers jerk forward when a bus brakes; a tablecloth can be pulled out leaving dishes behind.
- 3. Momentum
- Momentum (p) = mass (m) x velocity (v).
- p = mv. SI unit: kg m/s (or N s).
- Momentum is a vector quantity.
- 4. Newton's Second Law of Motion
- · "The rate of change of momentum of an object is directly proportional to the net force applied on it, in the direction of the force." ·
- F = ma (when mass is constant).
- More precisely: F = (mv - mu) / t = m(v - u)/t = ma.
- Larger force = larger acceleration; larger mass = smaller acceleration for the same force.
- 5. Newton's Third Law of Motion
- · "For every action, there is an equal and opposite reaction." ·
- Forces always occur in pairs. The action and reaction forces act on different objects.
- Examples: rocket propulsion (gases pushed back = rocket pushed forward); swimming (push water backward = move forward); a book rests on a table (book pushes down on table = table pushes up on book with equal force — normal reaction).
6. Law of Conservation of Momentum
When no external force acts on a system of objects, the total momentum before a collision equals the total momentum after the collision.
- m1u1 + m2u2 = m1v1 + m2v2
- 7. Friction
- Friction is a contact force that opposes relative motion between surfaces.
- Static friction: prevents motion from starting. Maximum static friction = just before sliding.
- Kinetic (sliding) friction: acts once object is moving; usually less than maximum static friction.
- Friction depends on: nature of surfaces (coefficient of friction, mu) and normal force (N). f = mu x N.
- Friction is useful (braking, walking) but also causes energy loss (heat).
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Worked Examples
A force of 20 N acts on a 4 kg object. Calculate the acceleration.
F = ma: 20 = 4 x a: a = 5 m/s2
A 1500 kg car accelerates from 0 to 25 m/s in 10 s. Find the net force.
a = (25 - 0) / 10 = 2.5 m/s2. F = ma = 1500 x 2.5 = 3750 N
Calculate the momentum of a 0.5 kg ball moving at 12 m/s.
p = mv = 0.5 x 12 = 6 kg m/s
A 2 kg trolley moving at 3 m/s collides with a stationary 3 kg trolley and they stick together. Find their common velocity after collision.
Conservation of momentum: m1u1 + m2u2 = (m1 + m2)v
(2 x 3) + (3 x 0) = (2 + 3) x v
6 = 5v: v = 1.2 m/s
Why do passengers lurch forward when a bus brakes suddenly?
Due to inertia (Newton's First Law). When the bus decelerates, the passengers' bodies tend to continue moving forward at the original speed because no force is immediately applied to them.
A rocket expels gas downward at great speed. Explain its upward motion.
By Newton's Third Law, the rocket pushes gases backward (action); the gases push the rocket forward/upward with an equal and opposite force (reaction). This reaction force propels the rocket.
A 5 N force acts on a 2 kg object for 3 seconds, starting from rest. Find the impulse and final velocity.
Impulse = F x t = 5 x 3 = 15 N s (= 15 kg m/s).
Final momentum = 0 + 15 = 15 kg m/s.
v = p / m = 15 / 2 = 7.5 m/s
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Common mistakes
- Thinking action and reaction forces cancel out — they cannot cancel because they act on different objects.
- Confusing mass (amount of matter, scalar) with weight (force of gravity on mass, vector = mg).
- Assuming an object moving at constant velocity has no forces on it — it could have balanced (equal and opposite) forces, giving a net force of zero.
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Summary
Forces are vectors described by Newton's three laws of motion. Inertia (First Law) resists changes in motion. F = ma (Second Law) links force to acceleration. Action-reaction pairs (Third Law) always act on different objects. Momentum (p = mv) is conserved in closed systems. Friction opposes motion and depends on the nature of surfaces and normal force. These laws explain nearly all everyday mechanical phenomena.