Title: InkPhysics / Materials
On every note of this deck, unless a note says otherwise:
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Front: DEFINITION
Define: Tensile stress.
Back: The force applied per unit cross-sectional area: stress = F/A, in pascals.

Front: DEFINITION
Define: Young modulus.
Back: The ratio of tensile stress to tensile strain for a material within the limit of proportionality.

Front: DEFINITION
Define: Elastic limit.
Back: The point beyond which a stretched object no longer returns to its original length when the force is removed.

Front: DEFINITION
Define: Hooke's law.
Back: The force needed to stretch a spring is proportional to the extension, F = kΔL, up to the limit of proportionality.

Front: DEFINITION
Define: Breaking stress.
Back: The maximum stress a material can withstand before it fractures.

Front: DEFINITION
Define: Density.
Back: Mass per unit volume: ρ = m/V, in kg m^−3.

Front: CHECK YOURSELF
A spring with spring constant 25 N m^−1 is stretched by 0.20 m, within its limit of proportionality. Find (a) the force applied and (b) the energy stored. (c) If the extension were doubled, still within the limit, what would the stored energy become?
Show a hint
Energy depends on the square of the extension.
Back: (a) F = kΔL = 25 × 0.20 = 5.0 N.
(b) E = 12k(ΔL)^2 = ½ × 25 × 0.20^2 = 0.50 J.
(c) Doubling ΔL quadruples the energy, because of the square: 2.0 J. Picture the triangle under the force-extension line: doubling the extension doubles both its base and its height.

Front: DEFINITION
Define: Limit of proportionality.
Back: The point beyond which force is no longer proportional to extension, so Hooke's law ceases to apply.

Front: CHECK YOURSELF
A wire of length 1.8 m and diameter 0.40 mm extends by 1.8 mm under a load of 25 N. Calculate the Young modulus of the material.
Show a hint
Find the area from the diameter first, working in metres.
Back: Area: A = πd^2/4 = π × (0.40 × 10^−3)^2 / 4 = 1.26 × 10^−7 m^2.
Stress: F/A = 25 / 1.26 × 10^−7 = 1.99 × 10^8 Pa. Strain: ΔL / L = 0.0018 / 1.8 = 1.0 × 10^−3.
Young modulus: E = 1.99 × 10^8 / 1.0 × 10^−3 = 2.0 × 10^11 Pa, the textbook value for steel. A strain of one part in a thousand from a 25 N pull is the Young modulus of a metal doing its job.

Front: DEFINITION
Define: Tensile strain.
Back: The extension per unit original length: strain = ΔL/L, a ratio with no unit.