Force, gravity and apparent weight

A book rests motionless on a soft cushion but leaves a dent. Being at rest does not mean that no forces act. Let us identify what acts on the book, what the book acts on, and why these actions need different names.

To open a door, it matters how hard you push, in which direction, and where. So we describe force F by its magnitude, direction and point of application. Force is a vector quantity that measures mechanical interaction between objects; it can change motion or deform an object. Its SI unit is the newton, N. A force arrow belongs to the object the force acts on. Always also identify the other object exerting that force.

Remove the table beneath the book and the book starts falling. Earth's attraction was already acting before the table was removed; the support was holding the book up. Gravitational force is the force with which Earth attracts a nearby object. It acts on the book, approximately vertically downwards towards Earth's centre. Motion is not a test for the presence of force: gravity acts on a resting book as well as a falling ball.

At the same place, how much more strongly does Earth attract two kilograms than one? About twice as strongly. Near Earth's surface, each kilogram experiences about 9.8 N. The ratio of gravitational force to mass is g: here g ≈ 9,8 Н/кг. The same coefficient equals the free-fall acceleration, about 9.8 m/s². These two units express the link between attraction and falling. Use the value of g given in the problem.

To find the force on the whole mass, multiply force per kilogram by the number of kilograms: Fтяж = mg. At fixed g, doubling mass doubles force. The units confirm this: кг·Н/кг = Н. Move the same object to another planet: its mass, a measure of inertia, stays the same, but g and gravitational force may change. Kilograms therefore cannot replace newtons, even when household scales are marked in kilograms.

Now consider the table. Because Earth attracts the book, the book presses on the table. Here we call the object's force on a support or suspension its apparent weight P, measured in newtons. Gravitational force acts on the book; apparent weight acts on the table. To keep them separate, mentally draw a boundary first around the book, then around the support, and ask whose motion or deformation we are discussing. Equal numerical values do not make two forces the same force.

The book rests on a horizontal table: the upward support force balances the downward gravitational force. With no other vertical actions, the book exerts P = mg on the table. Now imagine scales in a lift accelerating upwards. To accelerate the object with the lift, the support must exert a greater force, and the load on it increases. P = mg describes the stated conditions of rest, not every situation involving a support.

Imagine releasing the lift, scales and load so that they fall freely together. The load and support have the same acceleration; the support no longer needs to prevent the load from falling. The load exerts no force on it: P = 0. This is weightlessness. Earth still attracts the load, and its mass has not vanished. This conclusion requires joint free fall and negligible other actions, such as air resistance.

A load of mass 2 kg rests on a horizontal table. Only gravity and the table's support force act on it; g = 10 Н/кг. Find its gravitational force and apparent weight.

First consider the load. Earth exerts a downward force on it: Fтяж = mg = 2·10 = 20 Н.

The load is at rest, so the table's upward force balances gravity and is also 20 N.

Now consider the table. The load exerts a downward force of 20 N on it: this is the load's apparent weight. The equal magnitudes belong to forces acting on different objects.

Fтяж = 20 Н on the load; P = 20 Н on the table.

Every force has a source and an object it acts on. Rest does not mean an absence of forces.

Mass is measured in kilograms; gravitational force Fтяж = mg and apparent weight are measured in newtons.

Apparent weight describes force on a support: in ordinary rest P = mg, while in joint free fall P = 0 even though gravity remains.

A spring can measure force. The next lesson explains deformation and adding forces.