Mechanics and Properties of Matter
Mechanics and Properties of Matter
This domain tests kinematics, Newton's laws, momentum and energy conservation, circular and gravitational motion, and the mechanical properties of solids and fluids: density, pressure, buoyancy, elasticity, and flow.
Core rules
- Kinematics: for constant acceleration, v = v₀ + at, Δx = v₀t + ½at², v² = v₀² + 2aΔx. Choose a positive direction and keep signs consistent.
- Newton's second law: ΣF = ma. Identify each force on a free-body diagram before resolving components.
- Momentum: p = mv; impulse J = FΔt = Δp. Total momentum is conserved when net external force is zero.
- Energy: W = Fd cosθ; KE = ½mv²; gravitational PE = mgh; spring PE = ½kx². Mechanical energy is conserved only when nonconservative work is zero.
- Fluids: ρ = m/V; P = F/A; gauge pressure at depth P = ρgh; buoyant force equals the weight of displaced fluid. Elastic stress is proportional to strain in the linear regime.
Worked example
A 2.0 kg block starts from rest and slides 5.0 m down a frictionless incline whose vertical drop is 3.0 m. Find its speed at the bottom. Only gravity does work, so mgh = ½mv². Mass cancels: v = √(2gh) = √(2 × 9.8 × 3.0) ≈ 7.7 m/s. The path length and incline angle do not enter because the normal force does no work.
Traps
- Using weight mg as mass in F = ma.
- Assuming the normal force does work on an incline; it is perpendicular to motion.
- Mixing gauge and absolute pressure.
- Treating momentum as conserved when an external force acts during the interval.
- Forgetting that kinetic energy is scalar and cannot be resolved into components.