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"A 200 N block on a 30° incline with μ = 0.3. Find friction force."
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Great question. Statics applies when acceleration = 0 (the system is in equilibrium). Dynamics applies when there's net acceleration — you need ΣF = ma.
Free-Body Diagram — Static Block
If the block were accelerating upward at 2 m/s², you'd write: N − W = ma. That's the dynamics version.
Yes — completely identical notation. î, i-hat, and ê₁ all mean the unit vector in the x-direction.
Common Notation Equivalents
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Use KCL (Kirchhoff's Current Law) at nodes when you have parallel branches. Use KVL (Kirchhoff's Voltage Law) around loops when elements are in series.
Quick Decision Rule
KCL
Currents entering a node = currents leaving
Use at: junctions
KVL
Sum of voltages around any closed loop = 0
Use at: loops
For a reversible isothermal process, temperature T is constant, so it comes out of the integral:
Entropy Integral Walkthrough
General definition
ΔS = ∫ δQ_rev / T
T is constant (isothermal)
ΔS = (1/T) ∫ δQ_rev
Integrate
ΔS = Q_rev / T
Units check: Q is in Joules, T in Kelvin → ΔS in J/K ✓
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Statics
Find the reactions at pin A and roller B for a simply supported beam with distributed load 4 kN/m.
Dynamics
A 5 kg mass on a spring (k = 200 N/m) is released from 0.1 m. Find max velocity.
Circuits
Using mesh analysis, find I₁ and I₂ in a two-loop circuit with V₁ = 12V, R₁ = 4Ω, R₂ = 6Ω.
Thermodynamics
Steam enters a turbine at 3 MPa, 400°C and exits at 50 kPa. Find the specific work output.
Fluid Mechanics
Water flows through a pipe that narrows from 10 cm to 5 cm. Find exit velocity using Bernoulli.
Materials Science
A steel rod (E = 200 GPa) is loaded to 150 MPa. Is this in the elastic region? Find strain.
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