Materials

Density, Hooke's law and the spring constant, stress, strain and the Young modulus, and elastic strain energy.

This chapter is about how materials respond to forces — stretching, deforming and storing energy.

Density and Hooke's law

Density

\rho = \dfrac{m}{V}

(kg m⁻³).

Hooke's law: up to the limit of proportionality, extension is proportional to force,

F = kx

, where

k

is the spring constant (N m⁻¹).

Worked example. A spring extends $0.04$ m under a $2$ N load. $k = \dfrac{F}{x} = \dfrac{2}{0.04} = 50$ N m⁻¹.

Create a free account to read this note in full. Every free account gets 2 complete revision notes — no card needed.

Density and Hooke's law

Density

\rho = \dfrac{m}{V}

(kg m⁻³).

Hooke's law: up to the limit of proportionality, extension is proportional to force,

F = kx

, where

k

is the spring constant (N m⁻¹).

Worked example. A spring extends

0.04

m under a

2

N load.

k = \dfrac{F}{x} = \dfrac{2}{0.04} = 50

N m⁻¹.