Forces and their Interactions

Scalar quantities have magnitude only:

• Mass (kg), time (s), temperature (°C/K), distance (m), speed (m/s), energy (J), power (W), pressure (Pa), volume (m³), density (kg/m³).

Vector quantities have magnitude AND direction:

• Displacement (m), velocity (m/s), acceleration (m/s²), force (N), weight (N), momentum (kg·m/s), gravitational field strength (N/kg).

Common scalar/vector pairs:

• Distance (scalar) vs displacement (vector — straight-line from start to finish).
• Speed (scalar) vs velocity (vector — with direction).

Worked example. A jogger runs 400 m around a track and returns to the start.

• Distance: 400 m (scalar — total path).
• Displacement: 0 m (vector — start and end are the same point).

Contact forces require physical touching between two objects:

• Friction — opposes relative motion of two surfaces in contact.
• Air resistance (drag) — opposes motion through air.
• Water resistance — opposes motion through water.
• Normal reaction — surface pushes back perpendicular to its plane.
• Tension — pulling force along a rope, string or cable.
• Push/pull (applied force) — direct contact between hand/tool and object.

Non-contact forces act between objects that are NOT touching:

• Gravitational — between any two objects with mass (Earth pulls you down even though Earth's centre is 6371 km below).
• Magnetic — between magnets / magnetised materials.
• Electrostatic — between charges (e.g. charged balloon attracting paper).

Mass is a measure of how much matter an object contains. SI unit: kilogram (kg). Same everywhere — your mass on the Moon is the same as on Earth.

Weight is the FORCE of gravity acting on a mass. SI unit: newton (N). Varies with location because gravitational field strength varies.

$W = m \, g$

• $W$ in N.
• $m$ in kg.
• $g$ in N/kg (gravitational field strength).

On Earth: $g = 9.8\,\text{N/kg}$ (printed on the AQA data sheet from 2024).

Worked example. A student of mass 65 kg.

• Weight on Earth: $W = 65 \times 9.8 = 637\,\text{N}$.
• Weight on Moon (g ≈ 1.6 N/kg): $W = 65 \times 1.6 = 104\,\text{N}$.

Same mass; different weights because g differs.

Gravitational field strength g varies because:

• Stronger gravity for more massive bodies.
• Weaker gravity at greater distance.

So Earth's surface has higher g than the Moon's because Earth is more massive, even though the Moon's surface is closer to its centre.

A Newtonmeter (or spring balance) measures weight by Hooke's law: the spring stretches in proportion to the force applied.

To find weight:

1. Hang the object from the Newtonmeter.
2. Read the force in newtons directly from the scale.

To find mass:

1. Measure weight on a Newtonmeter.
2. Divide by g (e.g. 9.8 N/kg on Earth).
3. Or use a balance, which compares masses directly.

In daily life UK shoppers buy fruit and vegetables in 'weighs' that are actually masses (kg) — this is colloquial. A balance scale measures mass; bathroom scales actually measure weight and convert to kg assuming g = 9.8.

When forces act along the same line:

• Same direction: add magnitudes; result points in that direction.
• Opposite directions: subtract; result points in the direction of the larger force.
• Equal and opposite: cancel; resultant = 0.

Worked example 1. A box has two people pushing it with 80 N and 60 N in the same direction. Resultant? $F_{\text{net}} = 80 + 60 = 140\,\text{N (in pushing direction)}$

Worked example 2. A 600 N car engine forward, 250 N friction + air resistance backward. $F_{\text{net}} = 600 - 250 = 350\,\text{N forward}$

Worked example 3 (balanced). A book rests on a table. Gravity 5 N down; normal reaction 5 N up. Resultant = 0 → book stays at rest.

A zero resultant force does NOT mean motionless — it means no acceleration (constant velocity or rest, by Newton's first law).

A free-body diagram isolates one object and shows ALL forces acting on it as arrows. Conventions:

• Arrow starts at the object (or its centre).
• Length proportional to magnitude.
• Direction = direction of force.
• Label each arrow with the force type and value.

Example: car driving at constant speed on a flat road.

• Weight (W) — down.
• Normal reaction (R) — up (equal in magnitude to W).
• Engine driving force (F) — forward.
• Air resistance + friction (D) — backward (equal to F at constant speed).

(HT only) When forces act at angles, simple add/subtract doesn't work. Use a scale drawing:

1. Choose a scale (e.g. 1 cm = 1 N).
2. Draw the first force as an arrow.
3. From the END of the first arrow, draw the next.
4. Repeat for any further forces.
5. The resultant is the arrow from START of first to END of last.
6. Measure its length (and divide by scale) to find magnitude; measure its angle with a protractor.

Example: 4 N north and 3 N east → resultant 5 N at 37° east of north (by Pythagoras / scale drawing).