Forces

What is a Force?

A force is a push or a pull. Forces can:

• Start or stop an object's motion
• Speed up, slow down, or change the direction of a moving object
• Change the shape of an object (stretch, compress, or bend it)

Forces are measured in Newtons (N), named after Sir Isaac Newton, using a device called a Newton meter (spring balance).

Types of Forces

Contact forces require physical contact between objects:

• Friction — opposes the motion of surfaces sliding against each other
• Air resistance (drag) — friction between an object and the air
• Normal (reaction) force — surface pushing back on an object resting on it
• Tension — force in a stretched rope or spring
• Applied force — a push or pull directly applied to an object

Non-contact forces act at a distance without touching:

• Gravity — pulls objects with mass towards each other; pulls us towards Earth
• Magnetism — attracts or repels magnetic materials
• Electrostatic force — between electrically charged objects

Weight vs Mass

These two quantities are often confused but are very different:

	Mass	Weight
Definition	Amount of matter in an object	Force of gravity pulling on an object
Unit	Kilogram (kg)	Newton (N)
Changes with gravity?	No	Yes

Formula: Weight = Mass x Gravitational field strength (W = mg)

On Earth, g = 10 N/kg. On the Moon, g = 1.6 N/kg, so the same object weighs about 6 times less on the Moon than on Earth.

Worked Example — Weight Calculation

A student has a mass of 50 kg. Calculate their weight on Earth (g = 10 N/kg) and on the Moon (g = 1.6 N/kg).

• Weight on Earth = 50 x 10 = 500 N
• Weight on Moon = 50 x 1.6 = 80 N

The mass stays at 50 kg on both, but the weight changes.

Balanced and Unbalanced Forces

All the forces on an object combine to give a single resultant force.

Balanced forces — equal forces in opposite directions; resultant = 0 N. The object stays still or moves at constant speed.

Example: A book on a table — weight (down) = normal force (up). The book does not accelerate.

Unbalanced forces — resultant force is not zero. The object accelerates in the direction of the resultant.

Example: A falling object where gravity > air resistance — it accelerates downward until air resistance equals gravity (terminal velocity).

Newton's Three Laws of Motion

First Law (Law of Inertia): An object remains at rest or moves at constant velocity unless acted upon by an unbalanced force. Objects resist changes to their motion — this tendency is called inertia.

Second Law: F = ma (Force = Mass x Acceleration). A larger force produces greater acceleration; a larger mass requires more force to reach the same acceleration.

Third Law (Action-Reaction): For every action there is an equal and opposite reaction force. When you push against a wall, the wall pushes back on you with the same magnitude of force.

Worked Example — Newton's Second Law

A car of mass 1200 kg has a resultant force of 3600 N acting on it. Find the acceleration.

a = F / m = 3600 / 1200 = 3 m/s squared

If the engine force is 4000 N and friction is 400 N, the resultant force is 4000 - 400 = 3600 N.

Friction

Friction is a force that opposes relative motion between surfaces in contact.

Useful friction:

• Brakes on a bicycle grip the wheel to slow it
• Shoes grip the floor so you do not slip
• Matches ignite due to friction generating heat

Unhelpful friction:

• Slows down machinery and wastes energy as heat
• Causes wear on engine parts

Factors that increase friction:

• Rougher surfaces — more surface irregularities interlocking
• Greater force pushing surfaces together

Lubrication (oil, grease) reduces friction by separating surfaces.

Key Terms

• Force — a push or pull, measured in Newtons (N)
• Mass — amount of matter in an object, measured in kg
• Weight — gravitational force on a mass, measured in N
• Friction — force opposing motion between surfaces
• Resultant force — the single force representing the combined effect of all forces
• Inertia — the tendency of an object to resist changes in its motion
• Terminal velocity — constant speed reached when driving force equals resistive force

Common Mistakes

• Confusing mass (kg) with weight (N) — they are different quantities with different units
• Thinking balanced forces mean no forces are acting — balanced means equal and opposite forces are both present
• Forgetting that friction can be useful (brakes, grip) not just a problem to overcome
• Assuming the Third Law pairs act on the same object — they always act on different objects

Tips and Tricks

• Draw a free body diagram with arrows before solving any force problem
• Remember the formula triangle: F = ma — cover the unknown to read off the correct formula
• For weight questions, check which planet or body you are on and use the correct value of g
• If the question states g = 10 N/kg, use 10 even if you know 9.8 is more precise
• Resultant force = 0 does NOT mean the object is stationary — it could be moving at constant velocity