Forces

A force changes the shape, speed or direction of an object. It is a vector: it has a size in newtons and a direction.

Contact forces — the two objects must touch:

• Friction — opposes relative motion between two surfaces.
• Drag (air resistance, water resistance) — friction from a fluid.
• Tension — pull along a rope, string or wire.
• Normal contact force (reaction) — push perpendicular to the surface from the ground or a wall.
• Upthrust (buoyancy) — upward push from a fluid.
• Applied force — anything you push or pull on an object directly.

Non-contact forces — they act through space, even in vacuum:

• Gravitational force (weight) — between any two masses.
• Magnetic force — between magnets, magnetic materials, and currents.
• Electrostatic force — between charged objects.

Forces are best drawn as arrows from the centre of the object, in the direction of the force, with length proportional to size (this is a "free-body diagram").

The resultant force is the single force that would replace all the individual forces and have the same effect.

For forces along one line (1-D), simply add the same-direction forces and subtract the opposite-direction forces.

If the resultant is zero, the object is in equilibrium — at rest or moving with constant velocity. If the resultant is non-zero, the object accelerates in the direction of the resultant.

Newton's first law. An object stays at rest, or carries on moving in a straight line at constant velocity, unless a resultant force acts on it. So if you see a constant velocity, the resultant force is zero (not that there are no forces — they just cancel).

Newton's second law. The resultant force on an object equals its mass times its acceleration:

$F = m \, a$

Units: F in newtons, m in kg, a in m/s². A 2 kg trolley with a 6 N resultant force accelerates at 3 m/s². If you double the force, acceleration doubles. If you double the mass for the same force, acceleration halves.

Newton's third law. Every action has an equal and opposite reaction. If you push the ground backwards with your foot, the ground pushes you forwards. A rocket pushes hot exhaust gas downwards; the gas pushes the rocket upwards. Important: the two forces act on different objects, which is why they don't simply cancel.

$F = k \, e$

where F is the force on the spring (N), e is the extension (m), and k is the spring constant (N/m).

A stiff spring has a large k; a slinky has a small k.

The straight-line region obeys Hooke's law. Beyond the elastic limit the spring stretches more for the same extra force — and once you go too far, it won't return to its original shape (plastic deformation).

A standard Hooke's law lab investigation:

• Variables. Independent: force (controlled by adding 100 g masses → 0.98 N each). Dependent: extension (m). Controlled: same spring, same room temperature.
• Method. Hang the spring vertically. Record unstretched length. Add masses one at a time, recording the new length each time. Repeat readings to find means.
• Processing. Plot force on y-axis, extension on x-axis. Gradient = k.