Chapter 7: Matter and materials Chapter outline ■ ■ ■ ■ ■ ■ ■ ■
define density and pressure derive and use the equation Δp = ρgΔh understand how upthrust arises on a body in a fluid understand the effects of tensile and compressive forces, including Hooke’s law define and use stress, strain and the Young modulus describe an experiment to determine the Young modulus distinguish between elastic and plastic deformation of a material understand and use force–extension graphs, including calculating work done and strain energy from the area under the graph
KEY TERMS
density: the mass per unit volume of a material pressure: the force acting normally in a fluid per unit area of a surface strain: the extension per unit length produced by tensile or compressive forces stress: the force per unit cross-sectional area Young modulus: the ratio of stress to strain for a given material, provided Hooke’s law is obeyed Equations: density =
mass M ; ρ= V volume
pressure =
force F ; P= area A
pressure in a fluid = density × acceleration due to gravity × depth; p = ρ gh stress =
force F ; σ = cross sectional area A
strain =
extension x ; ε= original length L
Young modulus =
stress σ ; E= strain ε
elastic potential energy, E = 12 Fx = 1 kx2 2
Exercise 7.1 Density and pressure A fluid exerts pressure on any surface with which it comes into contact. Pressure is the cause of the upthrust on any object immersed in a fluid. This exercise provides practice in calculations involving density and pressure. Density calculations are not complicated but, in these examples, you will have to calculate the volume of a sphere and work with numbers in standard form (scientific notation).
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