Forces, Newton's laws and free-body diagramsEdexcel A-Level Physics: Revision notes

A free-body diagram shows a single object (a particle or rigid body) drawn separately, with only the forces acting on it shown as labelled arrows from the object, drawn along the line of action and with length roughly proportional to size. Never include forces the object exerts on other things.

Common forces: weight W (downwards, from the gravitational field), normal contact force N (perpendicular to a surface), friction F (along a surface, opposing sliding), tension T (along a string), drag or air resistance (opposing motion) and upthrust. Resolve forces that are at an angle into perpendicular components; the resultant is found by adding components in each direction.

First law: an object remains at rest or moves at constant velocity unless a resultant force acts on it. Second law: the resultant force on an object equals the rate of change of its momentum; for constant mass this is F = ma, with the acceleration in the direction of the resultant force.

For equilibrium the resultant force is zero (a = 0), but the object may still be moving at constant velocity. To use F = ma, find the resultant, then divide by the mass. The newton is the force which gives a mass of 1 kg an acceleration of 1 m s⁻².

Worked example. A 1200 kg car with driving force 3600 N and resistive forces 600 N: F = 3600 − 600 = 3000 N, so a = 3000/1200 = 2.5 m s⁻².

Weight W is the force on a mass due to a gravitational field: W = mg, where g is the gravitational field strength. Using g = F/m, g is the force per unit mass, measured in N kg⁻¹ (the same as m s⁻² for free fall). Near the Earth's surface g ≈ 9.81 N kg⁻¹.

Mass is the amount of matter (kg) and does not change with location; weight is a force (N) and does. In a lift accelerating upwards, a passenger feels a contact force N = m(g + a), which is why apparent weight changes while true weight does not.

When an object falls through a fluid, the drag force increases with speed. At first the weight exceeds the drag, so the object accelerates downwards. As speed increases, drag increases, so the resultant force and acceleration fall. When drag equals weight (plus upthrust if relevant) the resultant force is zero and the object falls at constant terminal velocity.

On a velocity–time graph the curve flattens to a horizontal line. If a parachute opens, drag suddenly exceeds weight, the object decelerates, and a new, smaller terminal velocity is reached. Initially, at the start of the fall, drag is zero and a = g.

Third law: when object A exerts a force on object B, B exerts an equal and opposite force on A. The two forces of an interaction pair are always: the same type of force (both gravitational, both contact, and so on), equal in magnitude, opposite in direction, and acting on different objects.

Example: a book resting on a table. The weight of the book (Earth pulling the book) pairs with the book's gravitational pull on the Earth. The contact force of the table on the book pairs with the contact force of the book on the table. The weight and the table's contact force are equal and opposite but are not an interaction pair, because they act on the same object and are different types.