Contact and non-contact forces

A hand pushing a trolley, a magnet pulling a pin, the Earth holding the Moon in its orbit — every one of these is a force, but they are not all the same kind of force. Physicists sort every force in nature into exactly two families, and the sorting question is beautifully simple: does the object doing the pushing or pulling have to touch the thing it acts on? Forces that need contact — friction, normal reaction, tension — belong to one family. Forces that reach across empty space — gravitational, electric, magnetic — belong to the other, and all three of those share a striking mathematical property, the inverse-square law. This article builds that classification from scratch, shows how the two SI and CGS units of force connect, and works through the exact numbers you will meet in exam problems on this topic.

The core insight

Every force is either a contact force, requiring the two objects to touch (friction, normal reaction, tension), or a non-contact force acting through a field across a gap (gravitational, electric, magnetic), and the three non-contact forces all weaken with the inverse square of distance.

The core idea

Contact forces. A contact force exists only while the two interacting surfaces are physically touching. The syllabus names three:

Friction — opposes relative sliding between two surfaces pressed together; it disappears the instant the surfaces separate.
Normal reaction — the perpendicular push a surface exerts on anything resting on it, balancing the part of the object's weight pressing into that surface.
Tension — the pulling force carried through a stretched string, rope, or cable, transmitted only because the string's material is in contact with itself along its length.

Non-contact forces. A non-contact force (also called an action-at-a-distance force) acts between two objects even when nothing physical connects them, through an invisible "field" that surrounds each object. The syllabus names three:

Gravitational force — every mass attracts every other mass, however far apart.
Electric force — acts between electric charges, attractive or repulsive.
Magnetic force — acts between magnets or magnetic materials, again without touching.

A shared property ties the three non-contact forces together: each obeys an inverse-square law. The force weakens in proportion to $1/r^2$ , where $r$ is the separation between the two objects:

F \propto \frac{1}{r^{2}}

where: $F$ is the force between the two objects and $r$ is the distance separating them. Double the distance and the force falls to one-quarter; triple it and the force falls to one-ninth — it does not simply halve or third.

Figure

Two labelled columns showing friction normal reaction and tension under contact forces on the left and gravitational electric and magnetic force under non contact forces on the right with a field symbol between the objects on the right column

Units of force. In the SI system, force is measured in newton (N). In the CGS system, it is the dyne, and the two are related by

1\ \text{N} = 10^{5}\ \text{dyne}

Force can also be expressed in gravitational units — the force with which Earth attracts a 1 kg mass (kilogram-force, kgf) or a 1 gram mass (gram-force, gf), linked to the newton through the acceleration due to gravity $g$ :

1\ \text{kgf} = g\ \text{newton} \approx 9.8\ \text{N}

where: $g$ is the acceleration due to gravity, taken as $9.8\ \text{m/s}^2$ near Earth's surface unless a problem states otherwise.

Derivation AThe inverse-square law

The main grounded relation of this topic is the inverse-square law shared by gravitational, electric, and magnetic force, together with what it predicts when the separation between two objects is scaled by a known factor — a calculation that appears repeatedly in exam problems and is worth deriving carefully rather than memorising as a slogan.

Step 1. Start from the proportionality. For any of the three non-contact forces, $F \propto 1/r^2$ , which means we can write $F = k/r^2$ for some constant $k$ that depends on the two objects (their masses, charges, or magnetic strengths) but not on the distance between them.

Step 2. Set up two situations with the same objects, so $k$ is identical in both, but different separations $r_1$ and $r_2$ , giving forces $F_1 = k/r_1^2$ and $F_2 = k/r_2^2$ .

Step 3. Divide the two equations so the unknown constant $k$ cancels:

\frac{F_2}{F_1} = \frac{k/r_2^2}{k/r_1^2} = \left(\frac{r_1}{r_2}\right)^{2}

where: $F_1$ is the force at the first separation $r_1$ , and $F_2$ is the force at the second separation $r_2$ .

Step 4. Read off the pattern. If $r_2 = n\,r_1$ (the distance is scaled by a factor $n$ ), then $F_2 = F_1/n^2$ . Doubling the distance ( $n = 2$ ) leaves one-quarter of the force; tripling it ( $n = 3$ ) leaves one-ninth. This ratio method — never plugging into a full force formula, just comparing two states — is exactly what ICSE Class 9 problems on this topic expect.

Worked example

A block of mass 3 kg rests on a horizontal table. Find (a) the normal reaction on the block and its weight in gravitational units, and (b) the new electric force between two point charges originally 2 cm apart and exerting a force $F$ , if their separation is increased to 6 cm.

Step 1 — forces on the block. Two forces act on the resting block: its weight $W = mg$ (gravitational, non-contact) acting downward, and the normal reaction $N$ (contact) from the table acting upward. Since the block is in equilibrium, $N = W$ .

Step 2 — compute the weight in SI units.

W = mg = 3 \times 9.8 = 29.4\ \text{N}

So the normal reaction is $N = 29.4\ \text{N}$ , directed upward.

Step 3 — express the same weight in gravitational units. By definition, a mass of 1 kg has a weight of 1 kgf, so the 3 kg block weighs $W = 3\ \text{kgf}$ . Both numbers describe the same physical weight: $29.4\ \text{N} = 3\ \text{kgf}$ .

Step 4 — apply the inverse-square law to the charges. The separation is scaled by $n = 6/2 = 3$ , so by the derivation above, $F_{\text{new}} = F/n^2 = F/9$ .

Final answers: $N = 29.4\ \text{N}$ ( $= 3\ \text{kgf}$ ), and tripling the separation between the charges reduces the electric force to $\dfrac{F}{9}$ .

Competitive stretch

If instead the charges were moved closer, from 6 cm to 2 cm (a factor $n = 1/3$ of the original 6 cm), the force would rise to $F_{\text{new}} = F \times 3^2 = 9F$ — the same inverse-square rule works for approach as well as retreat, just invert the ratio.

Common traps

Treating friction or tension as forces that can act without actual touching — both are strictly contact forces, defined by the surfaces or string being in contact.
Assuming a magnet must touch an iron nail to attract it — this is precisely why magnetic force is classified as non-contact.
Confusing "inverse-square" with "inversely proportional" — inverse-square means $F \propto 1/r^2$ ; doubling the distance quarters the force, it does not halve it.
Mixing up gravitational units with mass units — kgf and gf are units of force (weight), not of mass, even though the numerical value matches the mass in kg or g.

Ask the tutor: Want to see how these same contact and non-contact forces set up Newton's three laws of motion in the next topic?

Why is tension called a contact force when the string can pull an object from far away, like a crane lifting a load high above the ground

The string itself must be continuously in contact with both the load and whatever is pulling it — the pulling effect travels along the material of the string through countless points of contact between its own particles. The load is far from the crane's motor, but it is never far from the string holding it; the string is what actually touches the load. That end-to-end contact is why tension is a contact force even over a long rope.

Does the inverse-square law mean gravitational, electric, and magnetic forces have the exact same formula

No — they share the same pattern of weakening with distance, $F \propto 1/r^2$ , but the constant of proportionality and what it depends on differs for each. Gravitational force depends on the two masses, electric force on the two charges, and magnetic force on the magnetic properties of the objects involved. At the ICSE Class 9 level you are only expected to know that all three follow this shared inverse-square pattern, not their full formulas.

If I forget whether to convert kgf to N by multiplying or dividing by g, how do I check quickly

Remember that a newton is the smaller-feeling unit here for everyday masses, since $g \approx 9.8$ makes a kgf worth almost ten newtons. So converting kgf to N should give a bigger number: multiply by $g$ . Converting N to kgf should give a smaller number: divide by $g$ . A quick sanity check — a 1 kg mass weighs "1" in kgf but "about 9.8" in N — tells you instantly which direction you are moving.

Contact and non-contact forces

The core idea

Worked example

Competitive stretch

Common traps

Before this

Where this leads