Forces, Mass and Weight
What Is a Force?
A force is a push or a pull that acts on an object. Forces can change the shape of an object, change its speed, or change the direction it is moving. They are measured in newtons (N) and are vector quantities — meaning both their size and direction must be stated.
Forces come in two categories. Contact forces require the objects to be touching — examples include friction, air resistance, tension in a rope, and the normal contact force (the push a surface exerts on an object resting on it). Non-contact forces act at a distance without the objects touching — examples include gravity, magnetic forces and electrostatic forces.
Contact forces (friction, tension, normal contact, air resistance) require physical contact. Non-contact forces (gravity, magnetism, electrostatics) act at a distance without touching. Forces are vectors — they have both size and direction.
Mass and Weight
Mass and weight are different quantities that students frequently confuse. Mass is the amount of matter in an object. It is a scalar quantity (magnitude only, no direction), measured in kilograms (kg), and it does not change wherever you go in the universe.
Weight is the gravitational force acting on an object’s mass. It is a vector quantity, measured in newtons (N), and it depends on where you are. The same astronaut has the same mass on Earth and on the Moon, but a much smaller weight on the Moon because the Moon’s gravitational field strength is much weaker.
The relationship between mass, weight and gravitational field strength is:
$$W = m \times g$$
Where \(W\) is weight (N), \(m\) is mass (kg), and \(g\) is gravitational field strength (N/kg). On Earth’s surface, \(g = 10 \text{ N/kg}\); the more precise value is 9.8 N/kg. Weight is measured using a newton meter (spring balance) and always acts downwards towards the centre of the attracting body.
Question: A student has a mass of 60 kg. Calculate their weight on Earth (\(g = 10 \text{ N/kg}\)) and on the Moon (\(g = 1.6 \text{ N/kg}\)).
On Earth: \(W = m \times g = 60 \times 10 = 600 \text{ N}\).
On the Moon: \(W = 60 \times 1.6 = 96 \text{ N}\).
Notice: mass stays at 60 kg in both cases. Only weight changes because \(g\) changes.
Free-Body Diagrams
A free-body diagram shows all the forces acting on a single object as arrows. The length of each arrow represents the magnitude of the force; the direction of the arrow shows where the force acts. By convention, forces are drawn acting from the centre of the object outwards in the direction they act.
A book resting on a table has two forces acting on it: its weight (downwards, caused by gravity) and the normal contact force from the table (upwards, caused by the table pushing back on the book). When these two forces are equal in size and opposite in direction, the book is in equilibrium — it does not accelerate.
When forces acting on an object are balanced (the resultant force is zero), the object either remains at rest or continues at constant velocity. When forces are unbalanced, the resultant force causes acceleration in the direction of the larger force. This is the foundation of Newton’s First Law.
In a free-body diagram, balanced forces (equal size, opposite direction) mean zero resultant force and no acceleration. Unbalanced forces produce acceleration. Arrows show direction; length shows magnitude.
Resultant Forces
The resultant force is the overall effect of all forces combined. For forces acting along the same line, you simply add or subtract them. For example, if a car engine produces a forward force of 2000 N and friction produces a backward force of 800 N, the resultant force is 1200 N forwards — the car accelerates.
When forces act at an angle to each other, you use a scale drawing (or Pythagoras’s theorem for right angles) to find the resultant. Scale drawings of vector diagrams are a Higher-tier skill, limited to parallel and perpendicular forces, but understanding that the resultant is the “net” force is essential at all levels.
Newton’s Third Law states: when object A exerts a force on object B, object B exerts an equal and opposite force on object A. These are called a Newton’s Third Law pair. They are always equal in size, opposite in direction, the same type of force, and act on different objects.
For example, when a person stands on the ground, the Earth pulls the person downwards (weight) and the person pulls the Earth upwards with an equal gravitational force. Separately, the ground pushes the person upwards (normal contact force) and the person pushes the ground downwards with an equal contact force. These are two distinct force pairs. A common error is treating weight and normal contact force as a Newton’s Third Law pair — they are not, because they act on the same object (the person).