How do the following properties change as length scale shrinks down? Provide som
ID: 2307787 • Letter: H
Question
How do the following properties change as length scale shrinks down? Provide some justification for your answers.
Example:
Beam length Beam surface area Beam volume
L L2
L3
Mass (m)
Cantilever spring constant as all dimensions scale – bending
Cantilever spring constant as all dimensions scale – tension
Pressure exerted by a body on the ground due to gravity
Friction force (assume ? is constant – a simple, but poor assumption!)
Energy stored in a capacitor
RC time constant
Thermal time constant
Example:
Beam length Beam surface area Beam volume
L L2
L3
Mass (m)
Cantilever spring constant as all dimensions scale – bending
Cantilever spring constant as all dimensions scale – tension
Pressure exerted by a body on the ground due to gravity
Friction force (assume ? is constant – a simple, but poor assumption!)
Energy stored in a capacitor
RC time constant
Thermal time constant
How do the following properties change as length scale shrinks down? Provide some justification for your answers. Property L scaling Example: Beam length Beam surface area Beam volume Mass (m) Cantilever spring constant as all dimensions scale- bendin Cantilever spring constant as all dimensions scale tension Pressure exerted by a body on the ground due to gravity Friction force (assume u is constant a simple, but poor assumption! Energy stored in a capacitor RC time constant Thermal time constantExplanation / Answer
Answer:
1) Pressure exerted by gravity on ground changes by L2 (it's gravitational force per unit area)
2) Friction force independent of lengh shrinkage L0 (As it is dimensions independent)
3) Energy stored in capacitor changes by L, ( since stored energy = 1/2 CV2 where stored energy depends on capacitance i.e two parallel plates C = epsilon A/d)
4) Time costant is indepedent of length shrinkage in RC R changes by L, and C changes by 1/L
5) cantilever spring constant k = ( E * w * t3) / (4 * L3)
it changes by L since it is amount of force per unit length
6) Cantilever spring constant as all dimensions scale – tension as L3
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