Materials

Name	Definition	Formulae
LIQUIDS
Upthrust	The upthrust on an object in a fluid =the weight of the fluid displaced by the object	$U=m_{f}^{disp}g$ $U=p_{f}V_{f}^{disp}g$
Terminal velocity	Upthrust + drag = weight No resultant force so velocity is constant
	Falling object: At first, = 0 so drag force increases − − = so resultant force decreases When + = no resultant forces so N1L terminal velocity
Fluid	Substance that can flow
Streamline	A curve whose tangent at any point is along the direction of the velocity of the fluid particle at that point
Path line	The path taken by a fluid particle as it moves
Steady flow	Occurs when no aspect of the fluid motion change with time
Laminar flow	Fluid move with uniform lines in which velocity is constant over time • No mixing of layers • Flows in layers/flowlines/streamlines • No abrupt change in direction or speed of flow
Turbulent flow	Mixing of layers Contains eddies/vortices Abrupt/random changes in speed or direction
Stokes’ Law	For a spherical object of rad r Moving slowly through a fluid with speed v The flow of fluid is laminar	$F_{d}=6Pi eta rv$
Viscosity	The thickness of a fluid. Viscosity increase, rate of flow decrease (spread quicker)Liquids, ⇓ with temperature Gasses, ⇑
Drag for turbulent flow	$C_{d}$ :drag coef, no unit A: area of object facing fluid flow	$F_{d}=frac{1}{2}C_{d}Apv^{2}$
Hysteresis	The extension under a certain load will be different depending on its history of past load and extension
HOOKE’S LAW
Hooke’s Law	The extension, e, is directly proportional to the applied force, if the limit of proportionality is not exceeded k: the stiffness of the spring/ the spring constantOutside the region that obeys Hooke’s law: Extension not proportional to force (greater extension for same force) Deform plastically, not return to original shape
Elastic’s Potential Energy	The ability of a deformed material to do work as it regains its original length Area under a force-extension graph	$W=frac{1}{2}Fe$ $W=frac{1}{2}Ke^{2}$
YOUNG MODULUS
Stress	The force per unit cross-sectional area perpendicular to the surface	$sigma = frac{F}{A}$
Strain	Fractional change in length of the material	$varepsilon =frac{e}{L}$
Young’s Modulus	The stress per unit strain
Young’s Modulus	Using thin long wire to measure Young modulus: Small extension is hard to measure and has high uncertainty $P=frac{F}{A}$ Thin wire has smaller A hence larger P for a given F Long wire: greater extension for a given stress

Name	Definition	Note
GRAPH
P/ Limit of proportionality	The maximum extension or compression that a material can undergo and still return to its original dimension when the force is removed	PEYU
E/ Elastic limits	The maximum extension or compression that a material can undergo and still return to its original dimension when the force is removed
Y/ Yield point	The point after which a small increase in stress produces an appreciably greater increase in strain.
UTS/ Ultimate Tensile Stress	The maximum tensile stress the material can withstand before breaking
State maximum load	If the mass exceeds maximum mass The elastic limit is exceeded Spring deform permanently Spring constant change
PROPERTIES OF MATERIALS
Strength	The maximum compressive stress applied before breaking
Strong/ Weak	Strong: High breaking stress (steel)	Weak: Low breaking stress
Stiff/ Flexible	Stiff: High Young’s Modulus, large stress for small deformation	Flexible: Low Young’s Modulus
Tough/ Brittle	Tough: large plastic deformation region on graph ⇒ absorb lots of energy	Brittle: little plastic deformation before breaking ⇒ absorb little energy
Elastic/ Plastic	Elastic: Regain their original shape when deforming force/stress is removed	Plastic: Extend extensively and irreversibility for a small increase in stress beyond the yield point (copper, clay)
Hardness	Resistance to scratch on surface
Hard/ Soft	Hard: Not easy to scratch or indent	Soft: Easy to scratch or indent
Ductile/ Malleable	Ductile: Undergo large plastic deformation under tension and hence can be made/ drawn into wires	Malleable: Undergo large plastic deformation under compression and hence can be hammered into thin sheets