Forces, density and pressure

Linear Momentum and Its Conservation

Linear momentum is a vector that tells us how much motion an object has. It is simply the mass of the object multiplied by its velocity.

\$p = mv\$

⚽️ Imagine a soccer ball rolling across a field – the heavier the ball or the faster it rolls, the more momentum it carries.

Forces and Momentum Change

When a force acts on an object, it changes the object's momentum. This is described by Newton’s second law:

\$F = \frac{dp}{dt}\$

  • ⚡️ A stronger force changes momentum faster.

  • 🕒 The longer the force acts, the greater the change.

Density and Pressure

Density (\$\rho\$) is mass per unit volume:

\$\rho = \frac{m}{V}\$

Pressure (\$P\$) is the force applied per unit area:

\$P = \frac{F}{A}\$

In a fluid, the pressure at a depth \$h\$ below the surface is:

\$P = \rho g h\$

🐠 Think of a deep aquarium – the deeper you go, the higher the pressure on the fish.

Conservation of Momentum

In an isolated system where no external forces act, the total momentum before an event equals the total momentum after:

\$\Delta p_{\text{total}} = 0\$

  • 💥 Elastic collision: both kinetic energy and momentum are conserved.

  • 🛠️ Inelastic collision: momentum is conserved, but kinetic energy is not.

Exam Tips

  • 📌 Always check units – momentum is kg·m/s.

  • 📌 For collisions, set up equations for conservation of momentum in each direction.

  • 📌 Remember that external forces (like friction) can change the total momentum.

  • 📌 Use diagrams to visualise forces and directions.

Key Formulae

QuantityFormula
Momentum\$p = mv\$
Force (Newton’s 2nd)\$F = \frac{dp}{dt}\$
Pressure in fluid\$P = \rho g h\$

Common Mistakes

  • ❌ Mixing up mass and density.

  • ❌ Forgetting that momentum is a vector – direction matters.

  • ❌ Ignoring external forces in real‑world problems.

Quick Recap

  1. Momentum is \$p = mv\$.

  2. Force changes momentum: \$F = \frac{dp}{dt}\$.

  3. Pressure in a fluid: \$P = \rho g h\$.

  4. In isolated systems, total momentum is conserved.

Further Reading (Optional)

Explore online simulations of collisions and fluid dynamics to visualise these concepts. Good resources include PhET and BBC Bitesize. 🚀