# Common force types

> CIE A-Level Physics · Unit 4: Forces, density and pressure
> Source: https://www.owlsprep.com/study/cie-9702-u4-common-force-types/

This sub-topic covers all common contact and non-contact force types tested in CIE A-Level 9702 Physics, including how to identify each type, calculate their magnitudes, and use them in force problems.

**Prerequisites:** [Introduction to forces and Newton's laws](https://www.owlsprep.com/study/cie-9702-u4-introduction-to-forces/)

## Learning objectives

- Identify and describe common contact and non-contact forces for A-Level problems
- Calculate magnitudes of weight, normal reaction, tension, friction, drag and upthrust
- Correctly assign direction to each common force type for free-body diagrams
- Avoid common exam mistakes when working with different force types

## Non-Contact Force Types

**Non-contact force** — A force that acts on an object without physical contact, arising from interactions between force fields

*Example:* Gravitational force acts between the Earth and a satellite without contact

The most common non-contact force at A-Level is weight, the gravitational force on an object's mass. Other non-contact forces you will encounter are electric force (between charged objects) and magnetic force (between magnetic materials/moving charges).

Weight is always calculated with the formula $W = mg$, where $m$ is mass and $g$ is acceleration due to gravity.

**Worked example:** Calculate the weight of a 12 kg uniform block on Earth's surface, where $g = 9.81 \text{ m s}^{-2}$

1. Recall the formula for weight:
2. $$W = m g$$
3. Substitute the given values to get the final answer:
4. $$W = 12 \times 9.81 = 117.72 \approx 118 \text{ N (3 s.f.)}$$

> **Exam tip:** Always use the value for g given in the question paper, do not assume 9.81 without checking

## Contact Forces: Normal Reaction and Tension

**Contact force** — A force that arises from physical contact between two objects

*Example:* A table exerts a contact normal force on a book resting on it

Normal reaction is the force a surface exerts on an object in contact with it. It always acts **perpendicular (normal) to the contact surface**, pointing outward from the surface.

Tension is the pulling force exerted by a stretched string, rope or rod on an object attached to it. It always acts along the line of the string, pulling away from the object.

**Worked example:** A 5 kg mass is hung stationary from an inextensible vertical string. Calculate the tension in the string.

1. The mass is stationary, so net vertical force is zero. Upward tension balances downward weight:
2. $$T - W = 0 \implies T = W$$
3. Calculate weight, then substitute to find tension:
4. $$W = mg = 5 \times 9.81 = 49.05 \\ T = 49.1 \text{ N (3 s.f.)}$$

## Contact Forces: Friction and Drag

**Friction** — A contact force that opposes relative motion between two solid surfaces in contact

*Example:* Static friction prevents a box from sliding down a sloped ramp

Static friction acts to prevent motion, and has a maximum value given by $f_{\text{max}} = \mu_s N$, where $\mu_s$ is the coefficient of static friction and $N$ is normal reaction. Kinetic friction acts when the object is moving, given by $f_k = \mu_k N$.

Drag (air resistance for objects moving through air) is a fluid friction that opposes motion of an object through a fluid. Its magnitude increases with the speed of the object, and it always acts opposite to the direction of motion relative to the fluid.

**Worked example:** A 3 kg block rests on a horizontal surface. The coefficient of static friction is 0.4. Calculate the maximum static friction force before the block slides.

1. For a horizontal surface with no additional vertical forces, normal reaction equals weight:
2. $$N = mg = 3 \times 9.81 = 29.43 \text{ N}$$
3. Use the formula for maximum static friction:
4. $$f_{\text{max}} = \mu_s N = 0.4 \times 29.43 = 11.772 \approx 11.8 \text{ N (3 s.f.)}$$

> **Exam tip:** Friction always acts parallel to the contact surface, never perpendicular to it

## Upthrust (Buoyancy Force)

**Upthrust** — A buoyant contact force exerted by a fluid on an immersed or floating object, acting vertically upward

*Notation:* U

*Example:* Upthrust allows boats to float on water

By Archimedes' principle, the magnitude of upthrust is equal to the weight of the fluid displaced by the object. This gives the formula $U = \rho_{\text{fluid}} V_{\text{displaced}} g$, where $\rho$ is fluid density and $V$ is the volume of displaced fluid.

**Worked example:** A solid cube of volume $0.002 \text{ m}^3$ is fully immersed in water of density $1000 \text{ kg m}^{-3}$. Calculate the upthrust on the cube.

1. For a fully immersed object, the volume of displaced fluid equals the object's total volume. Use the upthrust formula:
2. $$U = \rho V g$$
3. Substitute values to calculate the result:
4. $$U = 1000 \times 0.002 \times 9.81 = 19.62 \approx 19.6 \text{ N (3 s.f.)}$$

## Common pitfalls

- **Wrong:** Assuming normal reaction is always equal to an object's weight
  - Why it fails: This is only true for horizontal surfaces with no other vertical forces acting
  - Correct: Always calculate normal reaction by summing vertical forces for your specific scenario
- **Wrong:** Drawing tension as pushing an object rather than pulling it
  - Why it fails: Tension is always a pulling force along a string; ideal strings cannot push
  - Correct: Draw all tension vectors pointing away from the object along the string's line
- **Wrong:** Always drawing drag as acting downward
  - Why it fails: Drag direction depends on motion direction, not vertical position
  - Correct: Always point drag opposite to the object's velocity relative to the fluid
- **Wrong:** Forgetting to add weight to free-body diagrams of objects in air
  - Why it fails: Weight is a non-contact force that acts on all objects near Earth's surface, regardless of contact
  - Correct: Include weight as the first force on every free-body diagram
- **Wrong:** For floating objects, using the whole object volume to calculate upthrust
  - Why it fails: Only the submerged part of the object displaces fluid
  - Correct: Use only the volume of the submerged part of the object for $V_{\text{displaced}}$

## Cheatsheet

| Force Type | Category | Key Formula | Direction |
| --- | --- | --- | --- |
| Weight | Non-contact | $W = mg$ | Vertically downward |
| Normal Reaction | Contact | From force equilibrium | Perpendicular outward from surface |
| Tension | Contact | From force equilibrium | Away from object along string |
| Max Static Friction | Contact | $f_{\text{max}} = \mu_s N$ | Opposes motion parallel to surface |
| Kinetic Friction | Contact | $f_k = \mu_k N$ | Opposes motion parallel to surface |
| Drag | Contact | Increases with speed | Opposes motion relative to fluid |
| Upthrust | Contact | $U = \rho V_{\text{displaced}} g$ | Vertically upward |

## What's next

Mastery of common force types is the foundational skill for all mechanics topics in CIE A-Level Physics. Once you can correctly identify, calculate and assign direction to each common force, you can build accurate free-body diagrams to solve any force problem. This topic connects directly to equilibrium, projectile motion, circular motion and density-pressure problems in this and later units. Solid understanding here will prevent many common exam errors in more complex topics.

- [Force Equilibrium](https://www.owlsprep.com/study/cie-9702-u4-force-equilibrium/)
- [Moment and torque](https://www.owlsprep.com/study/cie-9702-u4-moment-and-torque/)
- [Density](https://www.owlsprep.com/study/cie-9702-u4-density/)

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