Forces and Motion — The Basics
What Is a Force?
A force is a push or a pull. Forces are measured in newtons (N) and they always arise from an interaction between two objects. Every time one object exerts a force on another, the second object exerts an equal force back — forces never exist alone.
Forces can be contact forces (friction, tension, normal contact force, air resistance) or non-contact forces (gravity, magnetism, electrostatic attraction). Both types are vector quantities — they have size and direction.
Newton's third law states that when two objects interact, they exert forces on each other that are equal in size, opposite in direction, and the same type of force. These forces act on different objects — they never cancel each other out on the same object.
Weight and the Gravitational Field
Weight is a force — the gravitational pull on an object. It is proportional to mass and is calculated using:
$$W = mg$$
where \(W\) is weight in newtons (N), \(m\) is mass in kilograms (kg), and \(g\) is the gravitational field strength in N/kg. Near Earth's surface, \(g \approx 10\) N/kg.
Mass is a measure of how much matter an object contains. It does not change with location. A student with a mass of 60 kg has that same mass whether on Earth, the Moon or in deep space. Their weight, however, changes with location: on Earth \(W = 60 \times 10 = 600\) N; on the Moon, where \(g \approx 1.6\) N/kg, \(W = 60 \times 1.6 = 96\) N.
Weight is measured using a Newton meter (spring balance). Mass is measured using a balance that compares against known masses — this works even in reduced gravity because both sides are equally affected.
Resultant Force
When several forces act on an object, their combined effect can be described by a single resultant force. If forces act in the same direction, they add together. If they act in opposite directions, the smaller is subtracted from the larger — the resultant acts in the direction of the larger force.
If the resultant force is zero, the object is in equilibrium: it stays still or moves at constant velocity. If the resultant force is non-zero, the object accelerates in the direction of the resultant force.
A free body diagram represents all the forces acting on one object. Each force is drawn as an arrow starting from the object, pointing in the direction the force acts. The length of each arrow is proportional to the force's size.
Example: a book resting on a table has two forces — its weight acting downwards and the normal contact force from the table acting upwards. If these are equal in size, the resultant is zero and the book stays still. Newton's insight is that this is no coincidence: the book pushes the table down; the table pushes the book up — a Newton's third law pair.
Newton's Laws in Action
Newton's first law: if the resultant force on an object is zero, its velocity does not change. A moving object at zero resultant force keeps moving at the same speed in the same direction — it does not slow down without a force acting on it. This was a profound insight: before Newton (and Galileo before him), many believed a force was needed simply to keep an object moving.
Newton's second law: the acceleration of an object is proportional to the resultant force and inversely proportional to its mass:
$$F = ma$$
where \(F\) is the resultant force in newtons (N), \(m\) is mass in kilograms (kg), and \(a\) is acceleration in m/s\(^2\). A larger force produces a greater acceleration; a larger mass requires a greater force to produce the same acceleration.
A 900 kg car has a driving force of 3600 N and experiences 900 N of friction. Calculate the acceleration.
Step 1: Resultant force = 3600 − 900 = 2700 N (in the direction of motion)
Step 2: \(a = \frac{F}{m} = \frac{2700}{900} = 3\) m/s\(^2\)
Always find the resultant force first before substituting into \(F = ma\).
Inertial mass is formally defined as the ratio \(m = F/a\) — how difficult it is to accelerate an object. A heavy truck has far greater inertia than a bicycle: the same resultant force produces much less acceleration. Newton's discovery that this same quantity governs both resistance to acceleration and gravitational attraction (weight) is one of the great connections in physics — a striking example of creative scientific thinking (IaS3).